JPRS ID: 9911 TRANSLATION TROOP CONTROL THROUGH PERT METHODS P.V. SKACHIKO, VI. M. KULIKOV AND G.K. VOLKOV

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JPRS L/9911
13 August 1981
= Translation
TROOP CONTROL THROUGH PERT METHODS
By
P.V. Skachko, VI. M. Kulikov and G.K. Volkov
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JPRS L/9911
13 August 1981
TROOP CONTROL THROUG~I PERT METHODS
Moscow UPRAVLENIYE VOYSKAMI S POMOSHCH'YU SETEVYKH METODOV in Russian
1974 (signed to press 7.7an 74) pp 3-143
[Book by Pavel Grigor'yevich Skachko, V1adiTnir Maksi~novich Kulikov,
and Georgiy Kitovic.h Volkov entitled "Troop Control With the Aid of
Program Evaluation and Review Technique Methods," Voyenizdat, 13,000
copies, 143 pages; annotation, foreword, conclusion, and table of
cor~tents translated and published in JPRS 63371, 5 Nov 74; UDC: 398;
15.9: 355. 5 (07) ]
CONTENTS
Foreword to the Second Eclition 1
Chapter I. General Concepts and Elements of a Program Evaluation and Review
Technique System. Procedure of Constructing Network Schedules..... 5
1. General Method Concepts 5
1. Description of Program Evaluation and Review Technique Method.......... 5
2. Division of a Program Evaluation and Review Technique System........... 7
2. Fundamentals of Construction of Network Models 11
3. Elements o~ Netw~rk Schedules.. . 11
4. Procedure of Constructing Network.Schedules 18
General Principles 18
Numbering of Events 20
Representation of Parallel Operations 21
Representation of Differentiated-Dependent Operations 21
External Insertions in Schedules 22
Procedure of Representation of Organizational Links 23
'Iwo-Way Linkages 24
Simplification of Linkages 25
Verification of Correctness of Construction of a Network 26
Joining Networks 26
Sequence of Operations in Constructing Network Schedules 29
.
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Chapter II. Methods of Calculating Network Schedules 35
1. Detercaining Duration of Operations 35
2. Calculating Network Schedule Parameters 43
5. Analytic Method of Calculation 44
Determination of Early and Late Event Occurrence Times 45
Determination of Early Start and Finish Time of Work Operations........ 54
Determination of Critical Path 55
Determination of Latest Allowable Operation Start and Completion Times. 60
Computing Time Reserves of Events, Work Operations, and Paths.......... 62
Determination of Path Full Time Reserve 63
Dete~mination of Time Reserves of Events 65
Determination of Time Reserves of Work Operations 65
Determination of Coefficient of Intensity of Work Operations........... 70
Determination of Coefficient of Availability 72
Determination of Probability of Occurrence of a Concluding or Any
Reference Event on Schedule 72
6. Tabular Method of Calculation.. 74
Determination of Early Start and Early Completion of�Work�Operations... 74
Determination of Late Start and Late Completion of Work Operations..... 78
Determination of Full and Partial Time ReservES of Work Operations...., 80
7. Graphic Method of Calculation 81
Calculation of Earliest Possible Commencement Time of Work Operations., 84
Calculation of Latest Allowable Couuaencement Time of Work Operations... 85
Calculation of Time Reserves 85
Chapter III. Optimization of Network Schedules and Their Utilization in
the Course of Plan (Project) Execution 88
1. Methods of Optimizing Networks 88
8. Network Optimization by Time........�...��....��������������������~ 89
9. Network Optimization by Resources��.�..�������������~������~������� 95
10. Optimization of Network Schedules by Flow..........�..�.��..������� 101
2. Tying in Network Schedules to Calendar Timetables and Constructing
Scale Network Schedules. . 114
. . .
3. Utilization of PERT Methods in Process Management/Control,,,,,,,,,,,,,, 120
4. Some Recommendations on Adoption of PERT Methods in Line Units,
Military Edueational Institutions and Establishments 125
Conclusion 129
Appendix. Example of Solving the Problem "Planning A Tank Battalion
March" B~ PERT 131
Bibliography 143
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FOREWORD TO TEiE SECOND EDITION*
In the comparatively short period of time which has passed sincE practical incor-~
poration of initial experience with the program evaluation and review technique
(PERT) method, its effectiveness has been graphically revealed in the most
diversified areas of military activity, both in planning small processes pertaining
to servicing and readying combat equipment for utilization, and in planning overall
combat operations of subunits and units.
Experience has shown that two conditions must be observed for effective application
of the PERT method in any program:
1) the basic elements of the PERT method (including preliminary project
analysis, construction of a network schedule, deterndnation of time and other in-
- dices) should be thoroughly studied;
2) the PERT method can be pLactically adopted only following thorough train-
ing of personnel, with a full comprehension of control objectives and complexity of
the processes being planned; at ttie same time it is essential to have a precise idea of
means and available time when drawing up network schedule plans.
Experience has confirmed that a superficial attitude towa~d PERT method invariably
leads to discredit and project failure. Systematized and sequential study and dis-
semination of the PERT method, as well as thoroughly thought-through organization
of work with network schedules is a guarantee of succe~s in working with applica-
tion of program evaluation and review technique.
Amassed experience in application of a PERT system indicates that strict observance
I of the following conditions is essential from an organi~ational-practical stand-
point for successful mastery of this system:
thorough study, by commanders of all echelons, of the fundamentals of planning
with the employment of critical-path methods;
* The First Edition was published in 1968, under the title "Planirovaniye boyevykh
deystviy i upravleniye voyskami s pomoshch'yu setevykh grafikov" [Planning Combat
Operations and Troop Control With the Aid of I~etwork Schedules].
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ability of staff officers to construct network schedules applicable to
the specific conditions of military life and ac~ivities;
precise execution of all measures specified by network schedules.
Organization and implementation of a program evaluation and review technique system.
As experience shows, the entire PERT work cycle breaks down into two stages:
construction of a network schedule plan and its analysis for the purpose of
determining available reserves of time and resources (as a rule this job con-
tains several sequential stages, at each of which a better plan is formu~ated than
the plan produced at the previous stage); ~
regular comparison of the plan with the actual course.of progress of the
process, since following final adoption it becomes a concrete project calendar
network schedule and is utilized for improving activities pertaining to direction
_ and monitoring of process execution; bottlenecks in the project process are revealed
in the course of such an analysis, resources are redistributed, and the schedule is
revised up to the end of the process; execution of these nycles is of fundamental
importance.
The first e3ition of this volume was useful for initial adoption of grogram
evaluation and review technique methods into the practical activities of troops,
staffs, and military establishments.
In this present edition the fundamentals of program evaluation and review technique
are presented in a simple ai~d easily understandable form, and recommendations are
given on its application with a number of practical examples.
As follows from the very essence of the PERT system, the authors emphasize that it
is an aggregate of computation methods, organizational measures and monitoring
techniques, taking into account tlie complex processes of combat activities of
- troops and staffs. Following are the end objectives of employment of a PERT sys-
tem:
elucidation and m~bilization of reserves of time and resources hidden in
efficient organization of combat operations;
exercise of control of combat operation processes according to the principle
of "leading ~lement," with prediction and prevention of potential malfunctions in
the course of e:ecution of comb at operations, and improvement of the combat in-
dices of planned proce~ses connected with the conduct of combat operations;
improvement in,the effectiveness and efficiency of control as a whole, with
clear-cut distribution of responsibility among commanders of different levels and
their staffs.
One of the specific features of a PERT system is utilization of a new, highly
sophisti~ated form of plan representation. It is proposed that the entire process
of conduct of combat operations be depicted in a single network flowchart,
which not only substantially facilitates perception of substance of the process
but also greatly facilitates the entire subsequent process of direction of combat
operations durinb their execution. A network model of combat operations provides
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much more information than the presently employed combat operations planning
documents.
A high degree of planning and control objectivity, considerable flexibility and
efficiency, and creation of conditions for rapid and efficient management are the
principal characteristic features of a program evaluation and review tect~nique
system. A high degree of objectivity is achieved due to precise plan revision and
ad~ustment in the course of combat operations, which makes it possible to examine
adopted decisicns taking account of the actual state of affairs, to obtain fore-
casts of the f.uture, to provide for the subsequent development of e~ents, and to fore-
- see possible departures from the schedule and influence of these deviations from
execution of subsequent operations and for a finite period of time.
A program evaluation and review technique system makes it possible quantitatively
to measure the degree of uncertainty inherent in any process connected with the
conduct of combat operatians. In controlling combat operations,the commander as
a rule encounters a large number of surprises which are difficult to foresee in
advance. PERT methods make it possible to determine the potential nature of uc-
tions by the enemy and enable one to be prep~ed to localize these unexpected oc-
currences.
A program evaluation and review technique system compels the commander to concen-
trate his attention and efforts in those areas which are a bottleneck at a given
moment and threaten failure to iaeet the timetable of execution of the combat mis-
sion and demand immediate correctian. At the same time other operatlons, although
not diverting the commander's attention, do not get out from under his observation
- and control.
A PERT system helps the commander separate the main from secondary matters and
precisely to specify those tasks which are performed at each level of leadership.
Control in a PERT system i.s based on a specially created flow of current infc~rma-
tion, which continuously or periodically is received by the commander.
A network model forms the basis oi a PERT system a graphic representation of a
combat operations plan, which in the literature is called a network schedule or
network chart. It is precisely the type of employed model which determined the
very name of the system. Theory of linear complexes constitutes the mathematical
, foundation of program evaluation and review technique [literally: network planning
and management (control~J method. The network method of planning and management, in
contrast to other methods of investigation, does not require a special mathematical
structure, and the terms and concepts which one encounters in employ~ng this method
are perceived almost intuitively. Because of this, the PERT method is easily
mastered.
In this, second edition the authors have expanded the basic terms and concepts of
critical-path, program evaluation and review technique method, have made the
material more easily understandable, have added additional terms and definit~ons,
have simplified a number of inethods, and have employed a number of new examples for
demonstrating the range of application of PERT methods in military affairs, partic-
ularly in the area of direct planning and control of combat operations.
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In this volume the authors present examples applying to the battalion level. It
did not make sense from a methodological standpoint to c ite examples of a larger
scalc, since this would sharply increase the amount of labor required and would
~ make it somewhat difficu~t to understand the substance of the matter. The prin-
ciples of application of the PERT method are the same for any echelon, and there-
fore the reader, after gaining an understanding of the method, will be able to
apply it in planning any complex process and scientific management and control of
that process.
In this second edition the authors have succeeded in stressing the fundamental idea
of program evaluation and review technique the constructed network model should
be ad~quate to the system being simulated. They have drawn the reader's attention
to the fact that construction of a network model is one of the most difficult and
critical tasks of simulation and modeling. .
The authors have elaborated and presented in a very comprehensible form methods of
manual calculation of network schedules, which is extremely important when work~ng
in field condizions.
One should bear in mind that the more complex the planned process, in which large
numbers of personnel take part, the greater the results produced by the PERT
ruethod. Tiie method of constructing scale network schedules proposed by the
authors furnishes commanders and staffs precisely with that tool which enables
them to construct a flawless system of interaction and coordination of the personnel
and resources taking part in combat operations.
Further serious and thorough study of this scientific method, which enables one to
reach optimal solutions in many areas of troop combat activities, and extensiv~
adoption of this method in combat activities and daily troop routine will un-
questionably produce considerable results.
Lt Gen Tank Trps Prof G. T. Zavizion,
Doctor of Military Sciences
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Chapter I. GENERAL CONCEPTS AND ELEMENTS OF A PROGRAM EVALtTATION AND
REVIEW TECHNIQUE SYSTEM. PROCEDURE OF CONSTRUCTING NETWORK SCHEDULES
1. General Method Concepts
l. Description of Program Evaluation and Review Technique Method
At the present time, in light of the resolutions of the historic 24th CPSU Congress,
there is taking place in the nation's economy rapid development of a new direction
in organization of the complex processes connected with expenditure of manpower,
material, energy and other resources. Critical-path method or program evaluation
and review technique method is experienc3.ng the greatest dissemination among the
most important new forms and methods of improving management. The successful and
rapid spread of this method literally in almost all areas of human activity is
due first and foremost to its great advantages over planning methods based on strip
or linear charts.
These advantages consist in the following.
1. ~mployment of the program evaiuation and review technique on the basis
of better, logically and mathE~:a*.ically substantiated work organization, as practi.cal
experience has shown, generates :~ignificant economy of manpower, time and resources,
ensures planning and monitoring of complex projects* simultaneously in several
directions, makes it possible to eliminate from the area of intensified monitoring
tY~se ac~ivities which do not influence prompt and timely accomplishment of the task
as a whole, and promotes findin$ bottlenecks and overce.aing them in a prompt and
timely manner.
In military affairs employment of program evaluation and review technique, on the
basis of precise calculations and analysis of logical and process relations, also
makes it possible to gain time and to economize in manpower and resources in solving
problems pertaining to many matters of logistic support and troop comb at training.
* The term project in program and evaluation review technique method (PERT) is
defined as a specific, prior established aggregate of all operations which must be
performed in order to achieve the stated goal. We shall also encompass with this term
the planning of any combat operati,ons at all echelons.
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2. Network schedules furnish a graphic and easy-to-percei~e representation
of a plan, elaborated both as a whole and part by part. They make it po~sible to
revise decisions taking into account the actual state of affairs, to obtain fore-
caSts, and to predict possible departures from the plan and their consequences
which may affect the plan execution timetable. Network schedules will make it pos-
sible quantitatively to measure the uncertainty characteristic of any plan. A
_ program evaluation and review technique system (PERT*) makes it possible extensive-
ly and efficiently to employ electronic computer hardware.
3. Program evaluation and review technique, utilizing network schedules as
project models, makes it possible precisely to represent the volume and extent of
the prob lem; to elucidate with any degree of detail the operations involved in
a project; to establish the interrelationship betweer~ these operations; to deter-
mine the events occurrence of which is essential in order to achieve the stated
partial and end objectives; precisely to distribute responsibilities among project
participants; to exclude the possibility of omitting operations which are objective-
ly necessary in order to achieve project goals.
4. Program evaluation and review technique makes it possible more extensive-
ly to utilize in planning activities the experience of the most competent and highly
trained project personnel,as well as practically verified statistical data in order
to achieve the most realistic estimate of requirements in manpower and resources
required for performance of operations; in advance, in the course of project model
analysis, to locate hidden reserve potential and to specify ways to utilize this
- potential and, in particular, ways to utilize noncritical project resources,
a channeling them toward acceleration of critical operations, achieviiig accomplish-
ment of the entire project in a shorter period of time and with less expenditure of
manpower and material resources.
5. Program evaluation and review technique makes it possible to employ a
simple method of introducing changes, refinements and additions to pro3ect plans,
which leads to flexibility and continuity of planning and ensures simplification
of information and the system of record keeping, as well as rapid project enlistment
of new management personnel and unin*_errupted control when replacing project
managers. When employing electronic computers, program evaluation and review
technique ensures rapid computation of a large number of project plan variants,
~rom which the optimal vari3nt is selected.
Thus program evaluation and review technique makes it possible to obtain scientif-
ically substanriated answers to the most important questions which arise during
plannir.g and coordination of many interrelated projects.
Concluding this general description of program evaluation and review technique, we
must note that it can be employed regardless of the scale and complexity of the
project. Program evaluation and review technique produces the greatest effect in
complex projects, in complex dynamic controlled systems, where extensive employment
of electronic computers is possible. But in addition, program evaluation and
review technique also produces substantial positive effect in executing extremely
* Henceforth the term program evaluation and review Cechnique will sometimes be
abbreviated to PERT for the sake of brevity.
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small-scale projects which include only several dozen events. For example, program
evaluation and review technique can be successfully applied ~n elaborating not only
an entire system of troop combat training or combat readiness measures but also in-
dividual system elements.
2. Division of a Program Evaluation and Review Technique System
Program evaluation and review technique is directly related to cybernetics as the
- science of optimal control of complex dynamic systems.
We know that any control, botti in the national economy and military affairs, presup-
poses the existence of:
a controlled object (controlled system);
environment (situation c4nditions);
a system or device acting upon the controlled object (controlling system).
The object of control can be machines, persons, and military subunits (establish-
ments).
The most characteristic objects of control under present-day conditions are objects
with a substantial number of collective bodies participating in an operation (project)
and with a large number of operations, that is, complex dynamic controlled systems.
The complexity of a controlled system is characterized by the number of elements,
nature and number of relations between them, as well as number of various possible
- states of the system. The dynamic nature of a system is manifested in constant
change of states, environment, as well as change in parameters.
En-~ironment (situation conditions) is defined as external influences on the object
of control, the conditions in which a controlled system is operating and will be
operating in the process of achieving the designated goal. The environment for
military troops is the concrete situation in which they are operating, tliat is, the
degree of hostile activity, conditions of terrain and season, weather, logistic
support, etc. System parameters change together with a change in external in-
fluences, as a consequence of which attainment of the ultimate goal is made more
difficult or facilitated..
Control sy~tem is defined as a control agency (headquarters staff, establishment,
factory management, etc) which possesses an appropriately developed network of sub-
ordinate control agencies (headquarters staffs, establishments, shops, sections)
or individual executors (commanders). In other words, it is a ramified management
(administrative) edifice which possesses the requisite resources and equipment for
executing development management functions (troop actions, design activities, or
production process). A control system, in conformity with the principles of modern
cybernetics, should possess the same degree of ramification as the controlled sys-
tem in order to provide for the control process. The operating effectiveness of a
control system depends first and foremost on the quality of operation of the in-
formation service.
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Contr~l process research investigations conducted both here and abroad indicate
that approximately 40 percent of the time e~ended by the manager and his support
- edifice goes for acquisition, study and analysis of information, 12 percent on
decision-making, 30 percent on giving instructions and orders and communicating
assignments to executing personnel, and 18 percent on verifying execution.
Thus collecting and processing information take up the greatest amount of time in
control and management. This fact has influenced the classification and division
of control systems.
As practical expexl.ence has indicated, control systems can be classified by pur-
pose, contf'~1 parameters, technical level, and by types of models. Such a division
also occurs in a program evaluation and review technique sy~tem.
Prograui evaluation and review technique systems are subdivided by purpose into
single-function and multipurpose.
A single-function system is characterized by an aggregate of actions aimed at
achieving one specific goal, although many individual executants or subunits may
take part in this aggregate of actions; but they have a single goal, such as to
ensure a high degree of subunit combat readiness, to plan and execute a battalion
exercise in a prompt and timely manner, etc.
A multipurpose system is employed when it is necessary to control the activities
of a number of subunits (units) of different arms, which are pursuing different
goals within a unified aggregate of missions.
Program evaluation anc? review technique systems are subdivided by control parameters
into systems based only on time parameters or various parameters in combination:
time, cost, resources, and technical-economic indicators.
The time parameter is considered in all cases.
The following eight versions of control system can be listed, in relation to the
combination of various parameters:
1) PERT time;
2) PERT time-cost;
3) PERT time-resources;
4) PERT time-technical and economic indicators;
5) PERT time-cost-reso~ir~es;
6) PERT time-cost-technical and economic indicators;
7) PERT time-resources-technical and economic indicators;
8) PERT time-cost-resources-technical and economic indicators.
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In practice PERT systems with the time parameter are most common.
All PERT systems can be characterized, on the basis of technical level, as
machine ~ystems, b ased on extensive employment of various means of inechanization,
computer hardware, communications, and television.
Five levels of a PERT control system are distinguished.
1. Zero level, which is characterized by employment of only the simplest
_ means of inechanization of management labor and the simplest computer hardware.
At this level there is no control system in the broad meaning of the term.
- 2. First level this represents a qualitative leap forward in development
of a planning and management system, although externally this level differs little
from the zero level in scal.e of application of ineans of inechanization and com-
puter hardware.
The first level is characterized by regular arrival of input data and their
processing according to a specified program, by regular utilization of output
information by management, and by uniformity of input and output info~rmatio~ as a
rule only in one parameter.
3. The second level is characterized by employment of high-powered
electronic computers with highly developed machine memory systems. Information
based on diversified parameters is utilized in second-level control systems.
- 4. The third level is characterized by the creation of special integrated
systems with simulation, as well as with managerial training. Control systems of
this level are distinguished by exceptionally high information service performance
quality.
5. The fourth level coastitutes development of third-level systems. Fourth-
level control systems provide for modeling/simulation, playing through a process,
managerial training, and ~utomation of part of the decision-making process.
Control systems are broken down on the basis of types of models into systems em-
ploying linear models and systems employing network models. Model in this context
~ is defined as a plan of development prepared in such a manner that it most fully
reflects the entire course of events pertaining to achieving the stated goal under
given conditions.
Graphic methods of modeling are the most common in practice. They are more
versatile and visually graspable. Graphic methods of modeling (planning) can also
be extensively employed in practical troop activities.
~;xamples of such modeling include various calendar schedules of events, combat
training schedules, plans for conduct of field exercises and other documents drawn
up on maps or in the form of diagrams and charts with the necessary explanatory
notes. One version of graphic modeling of combat operations employed for organiza-
tion of coordination, training of officers and for other purposes is sandbox
simulation of a possible combat situation.
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- In the past, before the appearance of network schedules, various versions of
linear charts (Figure 1) were in widespread use and continue to be employed today.
UMB- ~4 C!1 1 2 3 4 i 6 7
~2~ HO0aM4 a6
1-u npoyecc
8-u npoyecc~3
3-u apoidecc
' 4- u npoyecc
u m8.
a ~
, .
too ~npoyeccb? (4)
� 90
~e~ tu
. ~ 70~ 2 u
0 4u
. tl 60 ~ 3 G
(6) � so 5-u
~ 40 �
~
0 30
ZO
10
ep 6 s~ (5)
Figure l. a-- linear; b-- cyclogram
Key:
1. Dates (hours) 4. Processes
- 2. Designation of process (operations) 5. Time
3. lst process, 2nd process, etc 6. Volume of work, as percentage
Alongside the positive aspects of linear charts and cyclograms (graphic expression
of assigned tasks, sequence and timetable of execution), however, they contain
serious drawbacks. Following are the principal deficiencies: ,
inadequate reflection of the links between processes and operations and
their interdependence;
a particularly static approach to their preparation, since the solutions
embodied in them take on a congealed form; the schedule is disrupted and becomes
unrealistic;
limited possibilities of predicting and monitoring the course of project
execution;
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the composition of operations and the timetable for their execution are
designated unambiguously, which inevitably leads subsequently to revision of the
plan model, which is very difficult to do on linear charts;
linear models do not reflect that uncertainty which is inherent in the
processes and projer_t as a whole.
Therefore it became necessary to construct a model which would make it possible
to carry out with great effectiveness planning, monitoring, plan correction and
revision, control, and extensively to employ electronic computers.
Network schedules and a program evaluation and review technique system, the
virtues and advantages of which were discussed above, are fully in conformity with
these requirements. We should emphasize here, however, that network schedules,
while providing a high degree of objectivity in planning and forecasting the
course of project development, as well as a high degree of flexibility and ef-
ficiency of management, do not exclude in control and management employment of
linear charts, cyclograms, and particularly graphic schedules of troop combat
operations worked out on maps or diagrams.
2. Fundamentals of Construction. of Network Models
A program evaluation and review technique system is based on graphic representation
of the project plan in the form of an arrow logic diagram (network schedule), in
which the entire aggregate of operations is broken down into separate, clearly
defined operations. The network schedule presents the logical interrelationship
and interconditionality of all operations and the sequence of their execution,
from the beginning to the final goal of the project.
' 3. Elements of Network Schedules ~
Let us examine the basic concepts, definitions and terms required to master
program evaluation and review technique.
In constructing network schedules, one proceeds from three basic concepts: work,
event, and path.
Work is any labor prqcess or action accompanied by expenditures of time and re-
- sources. For example, loading ammuiition at a military supply facility, march by
a subunit (unit) into a concentration area, etc.
The term "work" also bncludes waiting (a passive process), which requires neither
expenditure of labor nor resources. For example, day or night halt for personnel
during execution of a march, waiting one's turn to cross a water obstacle on a
ferry or bridge in conformity with the crossing schedule, etc.
The term "work" is also defined as a simple relationship between two or more
measures (processes). This will be fictitious, or empty work, which requires
neither the expenditure of time, labor, nor resources.
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'Che duration of work, just as any process, can be measured quantitatively in units
of time: minutes, hours, days, etc. Work can also have other quantitative evalua-
tions, such as laboriousness/labor intensiveness, cost, expenditure of material
resoLrces, etc. In addition, each job should have aclesignation, which reveals its
content, such as "Piission Briefing," "Situation Estimate," "Alert-Warning Subunits,~'
"Loading Ammunition on Alert," "Unit March From Point A to Point B," "Unit (Subunit)
Halt During March," etc.
An event is the result of a given process, the intermediate or end result of per-
formance of one or several preceding work operations, which makes it possible to
proceed to subsequent operations. For example, assembly and formation of colunazs
~ of subunits on a combat alert at permanent basing locations are completed, which
- makes it possible to commence their movement to the designated concentration area.
Thus an event, in contrast to a work operation, is not a process, has no duration,
and is not accompanied by any expenditures (time, resources).
An event on network schedules is usually represented by circles, work by solid
arrows, and empty work (dependence) by dashed arrows (Figure 2).
(1) Co~b~mue (4l Pa6omct (2)
OyenKd J6amanoeKU u
~ (OpuRav na n uHAm~ ew n rr
~ ~ NGCmyRllantl~ ~ 3
rtbnyven) '~o'qy BO
' Q?pede(5)
~ 3~ OpoBo xcumenenocme.- ~0 A Cy4, Xoaocma~
~Q~OR161 ~ d M{IM~ Z ~~p~
~NOCq16~ 6~ �
Figure 2. Representation of Events and Work Operations in a Network Chart
Key:
1. Event 5. Issuing of warning orders
2. Work 6. Empty work (dependence)
3. Duration of work (in minutes) 7. Attack order received
4. Situation estimate and decision-
making
The arrows are not vectors. They can be of any length and direction.
Any work operation (arrow) on a network chart joins only two events and represents
the process of transition of one event to another. The event from which arrows
originate is called initial (or preceding); an event at which arrows end is
called terminal (or succeeding) for the given work operations. One and the same
event may alternately be preceding and succeeding. The initial event for an entire
network is called the starting event, while the terminal event of an entire network
is called the concluding event.
Work operations in a network are usually coded by the numbers of the events between
which they run. For example, the work operation "Mission Briefing" (Figure 3) will
be coded (1, 2), while operation "Time Calculation" may be assigned code (2, 3).
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~ YstcHenue oaaa~~ Z Pac~em~ e eMenu 3
Figure 3. Coding Work Operations by Events
Key:
1. Mission Briefing 2. Time Calculation
In Figure 3 event (2) is the succeeding event for operation (1, 2) and the preced-
ing event for operation (2, 3).
One and the same event may terminate several work operations or only one operatinn,
while one or several operations may also originate from it. Therefore occurrence
of an event may depend~on completion of one or several work operations respective-
ly.
It is evident from Figure 4 that operations (d and e) can begin only if operations
(a, b and c) are completed.
, 4 4
6
A e.
c
Figure 4. Dependence of Operations
All work operations in a network chart differ in character and are of differing
duration.
Thus an event is considered accomplished only when the most protracted of all
operations terminating at that event is completed.
The internal relationship between operations in a network schedule is determined
by observance of a fundamental rule: in a network schedule all operations are
interlinked the commencement of a succeeding operation is dependert upon com-
pletion of a preceding operation. It follows from this rule that in a network
schedule there cannot be a single operation which is not connected at its initia-
, tion and termination to other operations through events. In other words, there
can be no events in a network schedule the commencement of which would not signify
the termination of at least one operation and simultaneously the commencement of
another.
Starting and concluding events are an exception. A starting event does not have
a preceding operation and is initial for the entire program (for example, "March
Order Received," "Signal to Sound Unit Combat Alert Received"), while a conclud-
ing event signifies a conclusion to the entire aggregate of project measures (for
example, "Regiment Ready to Carry Out Combat Mission").
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Each operation contained in the schedule should possess quite specific content.
One should not, for example, designate an operation as "Commencement of Ammuni-
tion Loading" or "Conclusion of Allocation of Missions to Subunits," for sub-
jective notions about the terms "Commencement" and "Conclusion" are possible here.
In some cases accomplishment of part of some work operation is a condition for com-
mencement of one or several other operations. In this instance the operation can
- be broken down into two or severaZ independent segments, concretely specified by
time (resources). Each segment of the divided operation should be viewed as an
independent operation.
It is just as important precisely to formulate the designation of events. It is
incorrect, for example, to designate an event "Conclude Situation Estimate." Such
an event should be designated "Situation Estimate Concluded." A precise formula-
- tion of events concentrates the attention of schedule preparers and persons super-
vising and managing the pro~ect not only on what operations should be performed to
- attain the project final objective but also on what should be the result of each
operation or group of operations preceding a given event and in what concrete form
an operation (operations) should be concluded so that the following operation can
commence.
In a network schedule there should be no closed loops, that is, circular couplings,
since such a coupling can be logically absurd. The linkage of operations shown in
Figure 5, for example, cannot occur in practice, since situation estimate per-
formed following time calculation cannot precede mission briefing.
~ OyeHKalo6cmaHOeKU 3
yQyQ~~cE~) (3, e C~C~O
~l~yQ/~Qy QaC~eif~
2
Figure 5. Closed Loop
Key:
1. Situation estimate 3. Time calculation
2. Attack mission briefing
A path is any uninterrupted logical (technological) sequence of work operations
(chain of operations) from the starting (first) to the concluding event, that is,
from commencement of plan elaboration to the final goal. Here one should bear in
mind that no path can pass twice through the same event; any path may run along an
empty operation; several paths can pass through one and the same event.
Path length is determined by the sum total duration of operations lying on that
path. There may be many paths from the starting to the concluding event. As a
result of preparation and analysis of a network schedule, one reveals that path
the total duration of operations on which will be maximum. This path is called
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critical. It determines the requisite time of execution of all operations contained
in the network schedule.
A11 operations lying on the critical path are also critical operations. The dura-
tion of these operations determines duration of the critical path. Shortening
criticaZ operations or extending the timetable of operations will correspondingly
lead to a shortening or lengthening of the path. Thus all critical operations are
potentially a plan bottleneck.
A network may contain several critical paths. Paths close in time to critical are
called subcritical. All other paths, and these are the ma~ority, differ downward
significantly in duration from critical and subcritical paths. Such paths are
called unstressed (or noncritical) paths.
Operations lying on a critical path are designated by heavy lines or a double
(colored) line, as is shown in Figure 6. Designation on the chart of operations
which are on a critical path makes it possible to present in graphic form that
se~uence of operations which determines the total task accomplishment time. This
is especially important when analyzing complex plans, execution of which involves
the participation of a large number of executants.
~ 2 yacarS Z 3
vaca S 4
~yaco rs ho ,~4e�'
3
Figure 6. Representation of a Critical Path (path 1, 3, 4 is critical)
Six complete paths can be found on the chart (Figure 7), depicting an aggregate
~f principal measures pertaining to readying a subunit for an attack. In order to
determine which of these paths is critical, their duration must be compared:
L~ = (0, 1, 3, 7, ! (L~) _ (5 5 60 `l0) _ ~0 min;
Lz =(0, 1, 3, 5, 7, .9); l(Lz1= (5 5-}- 0-{- 60 20) = 90 min;
L~ _(0, 1, 2, 5, 7, J); [(L,) _(5 15 GO GO 20) = 160 min;
L~ 1, 2, C, 8, y)~ 1~)�( 5-}- 15 15 31~ 15 80 min;
LL 1, 4, b'. 8, 9)~ l(LS) =(5 5-}- 0-{- 30 15) - 55 min;
min.
Lu =(D, 1, 4, 8, 9); l(/.n) _(5 5-}- 30 15) = 5:~
The third of these paths is the longest, and it will be the critical path. The
first and second paths are subcritical. The remaining paths in this network
schedule will be unstressed (noncritical).
In addition to complete paths, the following are also distinguished in a network
schedule:
path preceding or following a given event; the path from an initial event
to a given event is called preceding, and a path linking this event with the con-
cluding event path following the given event;
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: (5) '
AoBznn?oeRa 6oee~rz no8paaaeneMUu
3 ?c nacm nneMUro ~ p
, Oi~~O~ s~~~ N
A
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~ ,~2) lr~'~Q~ b ~nu 60 ~~~11~
, .Qo o - oAo ~~s~~
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oq~'~� ( 6 ) ~o e� . '~o G~
a~''~' .t.~~~~ ~O ~ . �~s
1 a~QQ. ~q) cFQti~ ~ ts~
lpeireane saaaYn a pecaem Of~EMKQ, o6c)t?drrOeltu C~ ~
epe~?+e~u u nprrMtrmpe pttueKaR ~ � ' y
0 S 1 4 0 ~ Z~s~~ . ~`~,~a~J
P'~p ~~ey - eQ4 J
~ ~ 9 sQ ~.r '�o~ o ( 8) (12) e o�~
; QQ(4) '�oQd 4 ~~y
- o`OO' ~Qy '~y~+~e~ h
, ~ ' mP O,o~ (10) o'~t~Q ~
~ , o~ , fi `AOy` ~o~~
p~ � ' ~ "v ~ ~ ~4 GCp~
~ob
uo+ ~ ~ ( 9 ) `p0 p'e`c
~y Oo.'~,'
~ ~f?a7~or~oerca. r~b,~oebrs no8pa~ ''a e
- 4 K OE6~IM eucmeus+M 8
. - 3p .
Figure 7. Paths in a Network Schedule
Key:
1. Mission briefing and time cal- 7. Organization for attack in
culation the subunits
2. Issuing of warning order to com- 8. Allocation of tasks to rear
bat subunits services subunits
3. Situation estimate and decision- 9. Readying of rear services sub-
making units �or combat operations
4. Issuing of warning order to rear 10. Organization of support of
services subunits combat operations
5. Readying of combat subunits for 11. Take up position in assembly
attack area
_ 6. Allocation of tasks and organiza- 12. Movement by rear services sub-
tion of cooperation and coordina- units to assembly area
tion
a path between any two events in the chart, neither of which is a starting or
concluding event.
. In the chart (Figure 7), for example, path (0, 1, 2) will be preceding for event
(2); paths (2, 5, 7, 9) and (2, 6, 8, 9) will be succeeding for this event. Paths
(1, 3, 5) and (1, 2, 5) are paths between two events, such as events (1 and 5).
Any noncritical path has a time reserve which is equal to the difference between
the duration of the critical path and the duration of the noncritical path.
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Operations lying on a noncritical path also possess a time reserve, that is, they
allow for changes in their execution timetables.
The existence of time reserves in noncritical operations makes it possible freely
to maneuver internal resources by increasing the execution time of certain non-
critical operations (within the limits of time reserve) and thus to speed up
execution of critic~l and subc:itical operations. It is precisely this which is
the main element in program evaluation and review technique.
In Figure 7 we took a simple network in which it is not difficult to find the
critical and subcritical paths. For more complex networlcs with a large number of
events, calculation must be performed according to a method specially developed
for this purpose. Small networks (schedules), containing up to 150-200 events,
are usually calculated manually. Networks with from 200 to 1000 events or more are
as a rule calculated on electronic computers. One should bear in mind, however,
that large networks (more than 1000 events) are visually poorly graspable. In con-
nection with this, in Iarge pro~ects it is advisable to construct several network
schedules.
In constructing network schedules, it is recommended that increasing empty linkages
(operations) be avoided. They should be employed in a network only if they are
essential.
Detailing of a network schedule is determined by the extent and complexity of the
project, computer capabilities, as well as the structure (level) of control. The
higher the control level, the fewer details in the network.
For a program with up to 200 events, usually a single general network schedule is
constructed. Several networks are constructed in planning large-scale operations,
in the accomplishment of which many executing entities participate. Tn such cases
there usually can be three degrees of network detailing.
Networks of the first degree of detailing are constructed in consoli.dated form,
for elaboration of the overall structure and course of operations these are net-
works for the top level of leadership (summary networks). In such networks opera-
tions (arrows) represent entire aggregates of ineasures on a large scale.
Networks of the second degree of detailing are constructed for the middle leader-
ship echelon. Such networks are particular or local networks, which are worked
out in greater detail, although each arrow in these networks can also represent
several operations (aggregate of operations).
Primary network schedules are designated for the lower leadersh~p echelon. These
schedules can be detailed to the level defined by the boundaries of responsibility
of executing personnel and agencies (for example, operations under the authority
of a single executant). Primary networks contain a larger number of events.
Detailed networks, in connection with the necessity of reflecting a large number of
_ interrelationships and dependences, contain a substantially larger number of empty
operations.
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Since there are several versions of networks based on degree of detailing, net-
works are constructed both in a descending and ascending direction, most frequently
ascending. In this case there arises the task of unifying primary networks into
particular (local) ones, and subsequently into summary or consolidated networks.
So-called ~oining of networks is perfoYmed.
The list of general concepts should also include the question of modification of
graphic representation. This also can include the following three variants:
first networks with orientation on operations; above the arrows operations
- are designated, while only a number is assigned to events;
second networks with orientation on events; in these networks not opera-
tions but events are designated on the charts, while arrows indicate only the
linkage between events;
third combined orientation (both operations and events are designated).
Networks of the second and third variants are employed in large-scale plans in ~
preparing synthesized (consolidated) schedules.
Networks of the first variant are more advisable for small and medium networks.
These are most frequently a technological plan (project) model. It more graphical-
ly shaws the sequence of operations and their interlinkage. Networks of the first
variant are recommended for beginning study and assimilation of program evaluation
and review technique.
Finally, we should mention division of network schedules into two variants con-
nected with the elements of uncertainty in given programs. nao types of network
models are distinguished on the basis of this attribute: determined and stochastic
(probability).
Determined models are defined as models in which there are no uncertainties; evrry-
thing in them is known.
Stochastic models are models in which there are elements of uncertainty. For
example, in scientific research and experimental design pro~ects it is impossible
precisely to establish expenditures of time and resources, and the number o~ per-
sonnel required for performance of given particular operations. In these cases
one employs the probability method of estimating pos~ible expenditures of time,
resources, etc. '
4. Procedure of Constructing Network Schedules
General Principles
There exist several general procedures of constructing network schedules:
from beginning ~o end (from starting to concluding event);
from middle to end and beginning;
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from end to beginning.
_ We shall follow the most widespread method from beginning to end, from left to
right. Each event with a larger serial number is positioned somewhat to the right
of the preceding number. Arrows may be of any length and direction, but mandatori-
ly running from left to right. It is essential to avoid if possible mutual inter-
secting of arrows (Figure 8).
2 1 4
1 2 4
1 4 2
3 3 3
Unde~irable Better
Figure 8. Construction of a Network
To achieve this, it is better to shift various events on the di.agram ox to xepresent
- the arrow in the form of a broken line.
In proceeding to construct a network, it is essential:
to establish what operations should be completed before a g~ven operation
begins (what operations should precede a given operation);
to determine what operations can be commenced after completion of a gi.ven
operation;
to determine what operations can be performed simultaneously with a given
operation.
In constructing a network, a rough version is always first prepared (Figure 9).
As a rule the external appearance of the network is ignored. The rough network
usually appears very complex. Principal attention is devoted to a logically cor-
, rect determination and mutual sequence of events. After the network has been con-
structed and the logical linkages checked and verified, 3.t can be placed into
better order (Figure 10).
- 8
7. 12
5 9
t ~
~ 6 10 ~3
~ I I
Figure 9. Preliminary, Rough Network Schedule
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7 - 10 ~
2 1Z
~ 8 8 14
~3 4 8
13
5 11 '
Figure 10. Ordered Version of Network Schedule
Even after a network has been put into order, however, intersecting operations
(arrows) may remain. This is undesirable from the standpoint of a chart's visual .
appearance and ease of working with it, but it is entirely allowable and sometimes
unavoidable by virtue of the logical linkages and interdependence of events in the
program.
Frequently it is necessary to add so-called "forgotten" operations in the process
of putting a network in order.
Numbering of Events
As stated above, events are numbered in such a manner that a larger serial number
is positioned somewhat to the right of the preceding number, according to the
following rule: the number of a preceding event of an operation cannot be larger
than the number of a succeeding event of. this same operation.
In constructing complex networks, however, one encounters certain difficulties in
numbering events, as a result of which errors occur, which subsequently can lead
to errors in computations. In order to eliminate errors and facilitate the number-
ing of events in networks, the so-called arrow deletion technique is employed.
This technique consists essentially in the following.
~ � If
Z 5
o ~
~ 4
- r
~ 3 6 m
Figure 11. Numbering Events by the Arrow Deletion Method
First one finds an event on the chart (Figure 11) which does not have incoming
operations (the first, that is, starting event of a schedule is always such an event),
and a zero rank is assigned to this event; we mark the zero rank number above event
(1) .
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We then mark through (with one line) all arrowa proceeding from this event and
among succeeding events we look for those which do not have incoming arrows (other
than deleted), and assigi: them first rank (I).
We then mark (with two lines or a different-colored pencil) all arrows proceeding
from events of first rank (I), and au~ong succeeding events look fo~- those which
do not have incoming arrows, and assign them second rank (II).
We continue in this sequence up to the end of the chart, assigning subsequent events
which do not have incoming arrows, third (III), fourth (IV) ranks, etc. Events are
numbered by rank in ascending order, beginning with the starting event.
Representation of Parallel Operations
In constructing t:etwork schedules one very frequently encounters complex linkages
where two or more operations have common initial and terminal events. These opera-
tions are carried out in parallel (jointly), but they are of differing duration.
Parallel performance of operations should be depicted in such a manner that any
operation can be joined only with two events. In this case it is necessary to
depict the interlinkage of operations, introducing an additional event and an empty
link (Figure 12).
3'
. ~1'
ye~a 2aa
3 4
S yacos 3 f yO~O� 4
- ~2~ HenpaennbHO npaoue6MO ~3~
Figure 12. Graphic Representation of Parallel Operations
Key:
1. Hours 2. Incorrect
3. Correct
Representation of Differentlated-Dependent Operations
In constructing network schedules one can encounter conditions where in order to
perform an operation, such as operation (5, 6) in Figure 13a, it is necessary
first to perform several operations: in Figure 13a operations (2, 5), (3, 5)
and (4, 5), while for another operation (5, 7), proceeding from common event (5),
performance only of one of the preceding operations (4, 5) is a preliminary con-
dition. In this case the interlinkage and interdependence of operations cannot be
portrayed as is indicated in Figure 13a, for with such a representation the com-
mencement of operation (5, 7) depends on accomplishment of all three preceding
operations (2, 5), (3, 5), (4, S), and this is not in conformity with the program
conditions.
Here, just as in representation of parallel operations, one should introduce an
additional event (4') and an empty link into the network (Figure 13b).
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Z 6 2
5 6
3 5 3
� ~ 4 7 �
4 4
Incorrect Correct
a b
Figure 13. Construction of a Network Taking Into Account the Relationship of
Operations
As already stated, in some cases accomplishment of a portion of any operation is
a condition for commencement of one or several operations (see operation (5, 6) in
- Figure 14a), operation (4, 5) in Figure 14a). Therefore it would be incorrect to
represent on the chart (Figure 14a) the preceding operation entirely, and then to
delete from the terminal event (5) of this operation the succeeding operation (5,
~ 6), the commencement of which depends on completion of only part of the preceding
~ operation. In this case, for a correct representation of the interlinkage and
sequence of performance of operations, we must divide operation (4, 5) in the
chart into component parts which are concretely time-determined, and introduce an
additional event (4') F:Lgure 14b.
~ 6 6
4 5 ~7 4 4 5 7
Incorrpct Correct
a b
Figure 14. Construction of a~ietwork Allowing for the Fact That Subsequent Opera-
tions Can Begin Following Completion of a Portion of the Preceding Operation
External Insertions in Schedules
In order to reflect in a draft plan the time and place of arrival in the unit (sub-
unit) of additional supplies, personnel replacements, technical documentation (for
example, for performance of design activities) and other information, so-called in-
sertions ar~ placed on network schedules. External insertions, in contrast to
operations and events, are customarily depicted separately: by a double circle with
a zero (Figure 15) .
0, T Fuel
- Vehicle Servicing
5 6 7
Figure 15. Representation of External Insertions on a Chart
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If there are two or more operaCions proceeding from an event with which it is
necessary to link an insertion, the latter is depicted in a linkage with an event
additionally introduced via a fictitious operation (Figure 16).
~ ~~T Fuel
Vehicle Servicing
~ g 6' 7
8
Figure 16. Representation of External Insertions on a Chart With Two or More Opera-
tions Proceeding From an Event
Procedure of Representation of Organizational Linkages
In constructing schedules one must represent not only technological links and rela-
tions but also organizational linkages, such as the sequential movement of teams of
repair personnel and the requisite equipment for organizing repair or servicing of
motor transpc,rt and armored vehicles in field conditions. Let us assume that there
are three work operations: A, B, and C(A repair of tracks and suspension; B--
repair of engine; C-- repair and zeroing of weapons), which must be performed on
two tanks. For performance of repairs there are three teams of maintenance
- specialists for each type of work operation, furnished the required equipment and
tools, whereby only one team for tracks and suspension maintenance is avail-
able at the commencement of repairs.
These operations can be performed at once on two tanks in parallel, sequentially
shifting maintenance specialist teams and their equipment from one (I) damaged tank
to the other (II). The sequence of perfozmance of these operations can be rep-
resented in a twofold manner in a network schedule (figires 17 and 18).
e ~n ~
t;J~
' ~ Bl 1
� � 8 en e .
. c?,
Incorrect ~p Cu
Figure 17. Incorrect Representation of Sequence of Performance of Technological
and Organizational Linkages
/1 pl s BI 9
( 5 1--- ~
Organizational Links
90 I
Correct 8 BIt 10 Cn n
Figure 18. Correct Representation of Sequence of Technological and Organizational
Linkages
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Upon examining the chart in Figure 17, we can establish that organizational and
technological links in this chart are shown incorrectly. This is due to the fact
that in this segment of a schedule of tank repair in field conditions, the dashed
arrows indicate not organizational links but the technological dependence of com-
mencement of work on repairing the engine of tank (II) on completion of repair of
the tracks and suspension of this same tank or commencement of repair of weapons
on completion of engine repair. In addition, job commencement (CI) has entirely
unwarrantedly been placed in a dependence on completion of work operation (AII).
In this case all organizational and technological links must be represented as
shown in Figure 18.
Two-Way Linkages
In addition to organizational linkages, charts can also reflect two-way linkages
- (relations) which, just as in other cases, are represented by introduction of
fictitious operations (dashed arrows). For example, there are three processes:
A, B, C. Completion of process C depends on the results of processes A and B. In
this instance there arise two-way relations which can be depicted as shown in
Figure 19. .
R~ Ry
Process A O- A �
~
Process ~ ~ C C
B~ B= / 8~
Process a ~ .
Figure 19. Representation of Dependent Processes
When introducing fictitious operations into a network, however, one should bear
in mind that their quantity and the direction of dashed-line arrows (linkages) may
reflect on the critical path (Figure 20).
Z 5 4 3 5__-4 ~
ti ~ ~
' i - 5 ~ ii 5.
~0 3 5 '0 4
2
tKP- 10+b-15 tKp-t0+Of5+4 -19
Q 6
Figure 20. Influence of Direction of Fictitious Operations on Length of Critical
Path
As is evident from Figure 20a, fictitious operation (2, 3) does not affect the
critical path. In the other case (Figure 2Ob), with a change in the direction of
dependence in the same program, the fictitious operation led to an increased dura-
tion of the critical path. Therefore when introducing fictitious (empty) operations
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Ln~o a network, in each instance it is essential rigorously to analyze the necessity
of a given linkage (dependence) in the program.
Simplification of Linkages

_a
When constructing network schedules it is sometimes advisable to consolidate opera-
tions by replacing a number of operations with one "aggregate" operation if some
group of operations has a single initial and a single terminal event (Figure 21).
This figure contains the simplest example of consolidation of operations.
In practice, however, there more frequently occur cases where a group of operations
- possessing a single initial and terminal event cannot be replaced by a single
~ "aggregate" operation due to the linkages of individual operations within the
group via intermediate events with other parts of the network schedule. In this
case one usually does not go beyond simplification of the network of the group
of operations in question (Figure 22).
b 6 9 .
. s I e ~ 5 ~s 8
~ ~ .
Figure 21. Replacement of a Group of Operations by a Single "Aggregate" Operation
~ s a s . ..s
. ~ a~ s~
5 ~ 10 io e ~2 s ZS ~2
~ ~ ~ 9
8 4 11 B .
lKo�ES tKp~2S
a d
Figure 22. Replacement of a Group of Operations in Networks With Events Possessing
Intermediate Linkages
It is evident in Figure 22a that one cannot replace the original network with a
single "aggregate" operation as is done in the first instance, since it is linked
through events (8 and 9) with other parts of the network schedule of the entire
program. We have simplified the network, but we have left in it events (8 and 9),
without disrupting the linkages of the process in question with other parts of the
network schedule (Figure 22b).
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Such a simplification of networks ~ignificantly improves the visual appearance of
the overall network schedule and simplif3.es its calculation and optimization.
Verification of Correctness of Construction of a Network
A network schedule constructed according to the procedures described above is
usually checked. During this verification one determines whether the chart con-
tains operations bearing identical codes (especially for parallel operations). If
such operations are discovered, additional events and fictitious operations should
be added.
One then checks to determine whether there are dead-end events in the chart, that is,
events from which no operation begins, other than the concluding event of the
schedule. If such events are discovered, the operations which enter such events
and the events themselves must be eliminated from the schedule. It is also neces-
sary to eliminate events which are not preceded by an event, other than the start-
ing event.
Finally, one checks the order of presentation of differentiated-dependent operations,
organizational linkages, and checks to make sure there are no closed loops in the
chart (Figure 5).
In complex programs, following verification of primary and local network schedules,
they are joined into a consolidated network schedule of the overall program.
Joining Networks
It was stated above that network schedules in complex programs are subdivided, by
de~ree of detailing and function, into consolidated networks, particular (local), and
primary networks. Such a division makes it possible to determine the level of
detailing of network schedu.les and creates more favorable conditions for monitoring
the course of their development and control, and also makes it possible, when con-
structing the initial program schedule as a whole, to enlist the efforts of special-
ists or commanders (executants) of subordinate units (subunits) or sections who are
well acquainted with the sequence, extent and qualitative evaluations of operations
at their echelon. ~
In connection with such a division of network schedules by degree of detailing,
- when constructing consolidated overall program schedules there arises the necessity
of unifying (joining) particular (local) schedules into a general (consolidated)
network. The process of connecting networks is accompanied by discovering and cor-
recting mismatches, various discrepancies, and by simplification of 1oca1
schedules.
For ease of joining networks and in order to eliminate the repetition of operation
codes, in a consolidated schedule a specific quantity of numbers is given to each
executant (subunit, section) for numbering events, and input or output boundary
events of the networks they are constructing are determined (matched). For the
sake of clarity of representation, each subunit (section) can be assigned its own
event symbol (Figure 23). More than enough numbers are assigned to the sections
(subunits). For example, from No 121 to 140 to the first subunit, from No 140 to
No 160 to the second, etc.
26
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1-u' , 2
,u ,uaea ~0 ( ~ i2i,uilpu;~ a (3)
' 2-0 7~
(1~' / 20 a~ 40 ' eM nu~paa8e
_ ~Ma~- I enu
1 H~ 1O ~ 16
1
40 3~ r 60 �
e~e
i~ie~ ,
-e
61 4 ~ 80
e~enue
Figure 23. Schetaati.c Diagram of Networ~. Joining
_ Key: ~
1. Command 2. Section
3. Subunit
Joining of networks can be performed in detail, when part~.cular networks are being
connected for the most part in the form in which trey are submitted to higher head-
quarters, or in less detail when a consolidated network is constructed chiefly of
~ "aggregate" operations which include an entire aggregate of ineasures (operations)
performed by a given section (subunit).
Networks are more frequently connected in an ascending direction, from lower to
' higher echelons, by boundary events, Boundary event is the term employed for
events which are linked by operations to other responsible executants of subunits
(sections) and are thus common to two and more networks. Boundary events may be
input (in Figure 23 10, 20, and 40 respectively for the first, second, and third
, sections) and output (in Figure 23 10, 20, and 40 respectively for the command,
the first and second section).
Input events indicate what group of operation results must be�received by a given
execut~.ng agency from other executing agencies. The output event fox each executing
agency ~n turn will be those operation results which 3.t is to transmit to another
' executant. For example, event (5) "Tank Engine Repair Completed" (Figure 24) will
' be the output boundary event of a particular network schedule of one maintenance
subunit and the input boundary event for the schedule of another subunit, which
installs tank equipment.
Figure 24 shows a method of joining networks. As we see, networks are connected
by a transition event, after which all other elements of the particular schedule
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Particular Consolidated (Connected)
Networks Network
r~`
6 6 ''r~' ~
1 4 ~ q ~ '
5 5 LI 2
J~
21 ~ o.~ 22
~ ` T . 20
20 Z .
Figure 24. Method of Joining Networks
are eliminated (if they are not simplified or consolidated), and conditional
starting and concluding events are additionally introduced (indicated by dashed-
line circles).
. ~ ~ :81
~ r
~
�
~ ~
Figure 25. Possible Numbering of Events in a Ma.tched and Joined Network
Introduction of conditional starting and concluding events is of importance for
subsequent calculations on a consolidated network schedule. A numbaring oi e;~ent~
which is continuous for the entire schedule is then performed on the matched and
joined network, while also leaving the old number in the circle indicating each
event (Figure 25), so that in the consolidated network it is easy to determine what
subunit (section) bears responsibility for performance of a given operation.
In complex programs, when matching and ~oining primary schedules and particular
schedules, a certain number of operations and events, responsibility for which is
assigned to individual subunits, can be omitted and replaced by "aggregate" opera-
tions, since the details of individual particular tasks are of no great sig-
nificance for a higher level of control. For example, in designing and building
new models of equipment, or at a repair plant, the designing (assembZy) of
specific machine components.(assemblies), consisting of a number of individual
operations, is included in the consolidated network as one independent operation
(Figure 26).
28
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Design of assembly
?,1 24
` 20 208i~cu 26
20 ZT 25 26 ~g '
23
tKpa2U
days
Figure 26. Replacement of a Bundle of Operations by a Single Operation in Con-
structing a Consolidated Schedule
We have presented the basic rules and procedures for constructing network schedules,
which should be observed when proceeding with.program evaluation and review or
analysis of any processes (programs) in military affairs.
Sequence of Operations in Constructing IVetwork Schedules
' Construction of network schedules should be based first and foremost on a com-
prehensive analysis of the basic and intermediate program objectives.
The first stage of construction of a network model of a given process in military
affairs is formulation of the task which determines the ultimate objective of the
program. In addition to the principal (ultimate) objective, however, the program
should also specify intermediate goals, which should be interlinked both in sequence
and in attainment resuits.
Intermediate goals determine the level of program execution and constitute partic-
ular tasks, which must be accomplished in order to achieve the main goal. For
_ example, the end objective for a program modeling a unit march to an exercise area
will be concentration of t:ne unit by the designated time, in area A, B, C, let us
say, in a state of readiness to carry out the combat mission, while the following
will correspondingly be the intermediate goals of this program:
organization of the unit's march;
execution of the march and concentration of subunits in area A, B, C;
making the subunits combat ready .following the march in the new concentration
area.
The second stage of the operation, preceding construction of a network schedule,
consists in preparing a block diagram of the program, or a so-called "program tree,"
which should graphically show the extent and stages of operations.
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F o r construction of a block diagram ("program tree"), the entire program (system)
is divided into subsystems, the subsystems in turn are divided into groups, and the
groups into individual elements.
It is recomnended that a block diagram be developed primarily in complex plans,
when there are several intermediate goals, while they in turn can have their own
subgoals. One feature of such a complex structure is the presence at each level
of a number of independent terminal or intermediate units (subunits) which perform
their Casks independently of one another. The number of levels in the structure
depends chiefly on the complexity of the program and can differ for individual
branches of the structure. One branch develops in a fair amount of detail and
possesses many levels, while another ends at the second or third level and does not
divide further.
Preliminary development of a block diagram improves the visual clarity of the
program, establishes a more clear-cut interrelationship between its individual
parts, and simplifies management within the boundaries of each 1eve1.
The higher commander (higher headquarters) should be responsible for preparing
the block diagram; the higher commander determines the degree of breakdown of
the program development (lower J.evel), designates persons and agencies responsible
for operations in the componen*_ parts of the program (other than staff), and
furnishes executing persons and agencies input data for program evaluation and
review.
Figure 27 contains a sample version of a program block diagram ("development tree"),
the goal of which is design and construction of a new machine (we shall conditional-
ly designate it "Ob3ect T-100").
In those cases where preparation of a block diagram is acknowledged to be inad-
visable, the overall volume of operations can be broken up by another method
by constructing a consolidated network schedule (Figure 28).
. ~ ,
OpueeBeMUe
va mu e no� ~acm~ 4
somoea
- OpuKa~ coc e~o- Pp~Ma uia ~
- na Ma~w mopu~ace e~~~~~p
no~y an ~ s ~ oa a
xp~ I
P ~ ~Qd
. ~4 4~b ~
4acmb _
K MOpW~
, tOrno a 2
Figure 28. Consolidated Network Schedule
Key:
1. March order received 4. Unit ready to execute combat
2. Unit ready to march mission
3. Unit concentrated in area A, B, 5. Organization of march
~ 6. Execution of march
7. Making unit ready after march
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oMCmpu,rccKUr D� 11 ~
41 meon u KQ.7ENNOK u aawum.e~u nt
4 3 amuaoum a mnoe cmpo cme ~ K ~nnr~iue 6nwn 12 ~ a
tlmoMamu�a nepe~upAxronu
44 noeopoma~~6nruNU 1
45 roKir Kps?w~unrcno ~
ooaoa nyne~nem ucm~,:~a;eptia.mua 14
~ neti+ern nwMu
47 3eHUrnn~,i~.nyiieeiem l ~ty~~~K~ 15 ~
L_ ~ri nr~ieu~~i ~ ~ a 3
48 uecwunn~ inan~ynu??~3~+emr~~i~?i Y . 16 ~
49 ~zQflU;1M YIl9u~lOCppC(~rAENUN
U~�~ hpuqerii,ireia n,i
n ueiroi~o6nemu~ 1~ ~
ip 6on
ue uaAicu~enucZcenu~U
50 onn. r?ucuc u Rpu6opa ~""~mP~~ Ko~!nnen?na 18
51 euzamen~ ~9
acA. nator ~
nNt?Qopsr~~ "?ml?~uaj . CucmeMU numanun 20 p e 4
l- cucmeMa e~,aaKU o a
Oo~na PnBuamop D nnpoe utmeMa orn4~t
zs52 ~npu6ope~ 22 w ~O
~ ucme,~a oanycKa 23
~3 Ka me
4 l?nanemnpneie pA bi rnaexeili ~puKyuox 24 ~ h 5
y~js puR uoNNeie ~neMCnm~~ Kopo6rca nepeJa~~ ~ Q
< 56 czaNUan+ nepeRSrowenuA nrpe ay n+a
T ezaKUSM noenpama ~ 26 i p o
~a 54 nna?iemap~iere pa ai r�~`e8a�v'u 27 P~ n
1
~ 55 vuKyuoynb~e 9aeMe~rme~ ~
~57 AKK M!?A~nopM~1C 6ama eu r ~nrovnuRU~iumanaA 28 y
9 58 rer~rpamop Crnaprnep 2.~ 6 ~ ,
m 3neKin on ueoaei o
O 59 BM f11pCNHAfl Q N m,
,0 60 HCpy7KMpy1 UCr?ICMQ OCECtl~CMUp 3 ~
Beapu nap ucmeMa
_ .0 61 cuznase~a urr 32
0 62 3e Koeos+
~ 6 feemooaA Pa uocmnnyuA 3 ~ ~
hb
~ 6 . n ueMnuK 4�'
ll[pc amyuK �~pcnnet nepez
6 n~e cin oGcmeo 4 p
6 snoK numanur+ ~
, CCMWMIIU ~IIf,1(URI! 5 k
Be ue Koneca r o
~
( g r cenuvneie yenu ~ v
69 no nen ano e arueoro ue Komxu ~aBeeerca 36 b
~p an aenAro ue Konectl c~t,[ xamA
� o y eahur ea no
71 Ynp eue ~neMenm?i eo~MUZO eoxr enuA 37 a~z
72 R~o mu~nmo ~i CprBcmea neaurp~en q�; .
pr~lcme~ NacKUpoe ; a~u .
CdA
o~ ~ p 4 10
o ~
� P c~ 4 W ~ N
' ~ ao ~ q R~
o- a r
Figure 27. Structural "Development Tree"
Key:
1. Object T-100 6. Electrical equipment
2. Hull and turret 7. Communications gear
- 3. Armament 8. Tracks and suspension
4. Powerplant 9. Special equipment
5. Transmission 10. Level
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(Key to Figure 27 on preceding page, cont'd)
11. Geometric shapes and protec- 45. Hull machinegun
tive properties 46. Turret mounted machinegun
12. Turrent ring and securement 47. Antiaircraft machinegun
13. Turrent traverse mechanism 48. Crankshaft and connecting
14. Hatches, hatch covers, seal- rod assembly
ing system 49. Valve gear, etc
15. Gun 50. Fuel pump, feed lines and
16. Machineguns instruments, filters
17. Aiming devices 51. Oil pump, feed lines and
18. Ammo stowage instruments, filters, etc
19. Engine 52. Pump, radiator, feed lines
- 20. Fuel system and instruments
21. Lubrication system 53. Gearbox
22. Cooling system 54. Epicyclic gears
23. Starter system 55. Clutch elements
24. Master clutch 56. Gear shifting mechanism
25. Gearbox 57. Storage batteries ~
26. Steering mechanism 58. Generator
27. Final drive 59. Interior
28. Power supply 60. Exterior
29. Starter 61. Emergency
30. Electric drives 62. Horn
31. Lights 63. Light
32. Signaling system 64. Receiver
33. Radio 65. Transmitter
34. Intercom 66. Power supply
35. Track drive 67. Driving sprockets
- 36. Suspension 68. Tracka
37. Equipment for operation sub- 69. Road wheels and top rollers
merged 70. Idler wheels with track
38. Heaters tensioning mechanism
39. Means of camouflage and con- 71. Elastic elements
cealment 72. Shock absorbers
40. Etc
41. Barrel and breech ring
42. Breech mechanis~n
43. Recoil system
44. Automatic loading system
The third stage of operations in constructing network schedules is the listing
of operations at each echelon of program development and determination of time
~stimates.
The list of operations can be reduced to a table, an example of which is con-
tained in Tab le l.
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Table 1.
Ai I(UA 76UT ~~P~~~A*Ht07bNOCTb
no nop. 4 tl~n?itiiaNxxe p~6or 5 P 6 p~6ur. .~ax
1 Yecueune ~aAayu . . . . . . . . . U~ ~ iG
q ilpeueap~iTeabiiae pacnop~~ce~iye ~2. 3~ 30 ,
noapaaAeaeNHau . . . � � � � � (2~ 60
3 OIleI1K8 06CT8NODNN 11 T. A~
Key :
1. Mission br:~efing 3. Situation est~.mate, etc
2. Warning orders to subunits 4. Operations
5. Code of operations
6. Duration of operations, minutes
The "Code of Operations" column in the table can also be filled in after preparation
of the initial chart. As regards making operation time estimates, for frequently
repeating operations, for which specific standard times are available, duration of
operations shall be specified in conformity with these standards and taking con-
crete situation conditions into account.
In those cases where there are no objectively substantiated time standards for dura-
tion of operations (in scientific research, experimental design and other activi-
ties), one employs the probability method of determining their duration. A method
of formulating time estimates with this technique is presented in Chapter II.
Then an initial network schedule is constructed at each echelon proceeding from
the list of operations, it is calculated and analyzed, and on the basis of this
one determines the degree to which the initial schedule corresponds to the mission
assigned the unit. If the initial network schedule of performance of an aggregate
of operations d~ta not provide for prompt task execution, schedule optimization
(improvement) is effected, in the interests of prompt and timely achievement of the
program goal at the given echelon. Optimized schedules of subunits (sections) are
submitted to higher headquarters, where a consolidated network schedule is drawn
up.
Sometimes, however, desirable or necessary calendar timetables for execution of
assigned operations will not be indicated in research programs for subunit com-
manders (executing agencies) at the stage of drafting the initial plan when assign-
ing the task of analysis of a model of an aggregate of various measures, for the
purpose of achieving greater objectivity of estimating a pro~ect timetable. In
this case executants wi11 determine only the duration of individual operations, the
sequence of their execution and logical linkages of operations, independent of
the calendar timetable of their execution, which can be determined in a substan-
tiated manner only as a result of network calculations.
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A consolidated network schedule of the program as a whole, following verification
and elimination of all disagreements and discrepancies, is calculated, analyzed
and, when necessary, reoptimized.
Such a schedule, depending on the quantity of operations and events encompassed
by it, may be fully represented or constitute a consolidated network with fragments
of more important details.
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Chapter II. METHODS OF CALCULATING NETWORK SCHEDULES
1. Determ3ni.ng Duration of Operations
Network schedules which reflect troop combat operations are as a rule constructed
on a time line. They can, however, also be constructed not on the basis of time
but other parameters, such as based on consumption or supply of resources or on the
basis of monetary expenditures. In these cases network calculation should also be
performed according to the corresponding parameter on the basis of which the network
is constructed. In this study we shall examine construction and optimizat~on of
network schedules, that is, their improvement on a time parameter.
The duration of each operation in time is usually written down in the process of
constructing the network. In cons~ructing a network, as soon as two events and
the operation linking these events have been specified, the operation name or
designation is written above it, and below it its time of duration in seconds,
minutes, hours, days, or weeks (depending on the nature of the process and con-
venience of working wifih the network schedule).
One should bear in mind the fact that correctness of statement of time charactez-
ist~.cs is of paramount i.mportance. The quality of a chart and the efficiency of
process management on the basis of a given chart wi11 depend on the correctness of
the designated time estimates. If, for example, operat3on executioa times are
understated, that is, are less than actually required, this wi11 lead to haste in
preparation for doing a given job and the entire operation as a whole. Such haste,
as 3ndicafied by the experience of the last war, can lead to failure of combat opera-
tions and consequently to unwarranted and useless casualties. Obviously the c?b-
jective of the combat engagement wi11 not be achieved under such conditions.
On the other hand, overstating the time for carrying out individual operat~ons can
lead to delay in the timetable for commencement of combat operations, that i~, to
purposeless and unwarranted loss of time, of which the enemy can take advanfiage and
strengthen his defense or prepare for and mount a counterstroke.
Where should one obtain time estimates of operations which are closest to rea~~ty?
There exist two possibilities fox this.
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For work actions or operations on which a fair amount of experience has been
amassed both in peacetime and in time of war, estimates can be adopted on the
basis of this experience, that is, such estimates can be taken from standard
figures derived in the course of combat training or in the course of combat opera-
tions.
- The correctness of unambiguous.selection of such time indices is grounded in
_ probability theory.
In military affairs one is usually dealing with random variables. We know from
probability theory that with a large number of tests, the arithmetic mean value
of a random variable remains practically constant ;stops changing). In other words,
with a large number of independent tests, the arithmetic mean of obtained values of
random variable Ni* [X] converges in probability with its mathematical expectation
M[X]. This relationship betwaen the arithmetic mean and the mathematical expecta-
tion of a random variable comprises the content of one of the forms of the law of
large numbers. This is exceptionally important for practical activities in the
respect that with a large number of experiments one takes the statistical (ex-
perimental) value of a given variable, considering it as differing little from the
actual value. Therefore utilization of statistical, that is, experimental data is
a scientifically substantiated approach to solving all types of problems connected
with random processes.
An important conclusion proceeds from this: it is essential to amass experimental
data on all operations connected with troop combat activities and to summarize
' them into standard reference tables and catalogues. This also applies to expendi-
tures of resources (manpower, material, monetary, energy). If one has such
standard catalogues available, it will be easy to place time and other parameters in
network schedules.
Thus employment of experimentally obtained statistical data is one of the possibili-
ties for determination of time and oCher characteristics necessary for estimating
the duration of work operations or expenditure of resources and their placement in
network schedules.
There is also another possibility of obtaining the characteristics indicated above.
It is based on probability methods of determining random variables. The ~act is
that in random or stochastic processes on which there is insufficient experience,
or in totally new processes, for which there is no experience whatsoever, there is
also a possibility of determi?iing a quantitative estimate of random phenomena. This
quantitative estimate can be determined on the basis of the probability of occur-
rence of a given event. For all practical purposes in this ~ase ic i~ ad~?isable
to proceed in this manner. Three time estimates: optimiutic, pessimistic, and most
probable are given by experienced commanders or military engineers (schedule
executants) for operations for which there are no time estimates.
- Optimistic estimate the shortest operation duration of those possible, that i~,
time during.which an operation can be performed with the most favorable confluence
of circumstances. We shall denote this estimate by t~n. As we know from experience,
in most cases the probability of accomplishing ~he ~ob in this time is approximately
0.01.
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Pessimistic estimate the greatest possible work operation duration from the ex-
perience of the executant, that is, time to do the ~ob with an extremely in-
felicitous confluence of circumstances. We shall designate this esti~ate with
tmgX. The probability of accomplishing the job in this time is also approximately
0.01.
Most probable estimate the possible time of accomplishment of a given 3ob under
the condition that no unexpected difficulties arise. We shall designate this es-
timate with tN.g. Probability of accomplishing the job in this time will be
maximum.
If we require of operation executants only one estimate in place of three, the pos-
sible result is that the estimate may prove to be overstated or understated, that
is, unrealistic. An unrealistic operation time or unrealistic material expendi-
tures indicated in the schedule can lead to the same miscalculations which are
frequently encountered in planning processes with the aid of linear charts, that
is, with the aid of presently existing traditional methods.
The probability of completing a work operation in a time less than the optimistic
estimate will be very small. The probability of completing a work operation in
a time exce~ding the pessimistic estimate will similarly be small. The probabili-
ty of completing a work operation in the realistic estimate time, that is, in the
time of the most probable time estimate, wi11 be the greatest. Proceeding from
this, at first glance it may seem that one must employ the most probable time es-
timate. However, if everything is weighed well, this should not be the procedure.
Let us examine this with a specific example.
We know that the number of target points scored at the firing range is a random
variable which is characterizAd by a certain distribution of probabilities for
each person on the firing line. In carrying out his firing assignment, each in-
dividual may score a certain minimum, maximum and most probable number of points.
The presumable estimate of number of points scored for each individual on each
round fired is quite similar to the tentative estimate of the time required to
accomplish each work operation in our case. We shall now assume that the number
of points scored by the rifleman is characterized by the statistical series
presented in Table 2.
Table 2.
(1) HtQOMt110CT? (p) O,s o,s o,~ ~~,o~ o,a~ I u,va aW
/2` CAY'1~11111~N BCA11411118 (BlAall- . .
Twc npi~ c'rpea~6e oyKU) 10~ 9 8 7 6 5 1
Key:
1. Probability 2. Random variable (target points
scored)
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We see from this series that a hit in the nine ring is most probable (p=0.6).
If we take the most probable score as our criterion, we can assume that a given
soldier will score 900 points with 100 rounds fired. But this will be incorrect.
We know from theory of probability that in order correctly to determine the
presumab le number of points which will be scored by an individual, it is necessaYy
to find some average quantity. For this we must multiply the value of the random
variable by its corresponding probabilities and add the obtained results. For our
example the arithmetic mean value differs from the most probable, which is equal
to 9. Thus the number of points scored by an individual with 100 rounds will be
close to 883.
Consequently, if in determining time estimates we take only one realistic or most
probable estimate, we shall be making the same mistake as with the soldier on the
firing line. There will be no such error if three time estimates are employed to
calculate the expected time for accomplishing each work operation.
In a theoretical respect, solving such a problem involves certain mathematical dif-
ficulties, since this would require knowing the distribution function of the
probabilities which characterize the duration of work operations.
When a commander gives three time estimates on the duration of performance of some
operation, that is, gives an optimistic, most probable, and pessimistic estimates,
he is defining a certain probability distribution analogous to the distributions
presented in Figure 29.
m m m m
i i ~ ;
~ A, te ~ a te 6 a te b a te 6
A 8 C D
Figure 29. Possible Probability Distributions
A-- optimistic estimate of duration of work operation; m-- most probable estimate
of duration of work operation; B-- pessimistic estimate of duration of work opera-
tion; te average duration of work operation if the given operation were ~
multiply repeated
Quantity te for each of the distributions contained in Figure 29 constitutes the
mathematical expectation or statistical average value of three work operation
_ duration estimates. In other words,_quantity te is the average duration of a given
_ work operation in case of multiple repetition.
The relative positions of quantities a, m, and b(Figure 29) depend on the numerical
values of these quantities, specified by the commander. Their relative positions in
turn determine the value or position of quantity te.
The value of quantity te based on three estimates is determined with the formula
~ _ n+d~n+b . ~1)
P- 6
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We shall examine below the derivation of this formula. A special analysis and ex-
perience in employing PERT methods indicate that this formula is an intelligent
c~mpromise between potential result accuracy and awkwardness of the computation
process.
However, in order to be certain of the value of the anticipated work operation per-
formance time, which nevertheless remains a random variable, it is necessary to
know what error we make in our estimate, that is, by what amount the actual work
operation performance time may deviate from the expected values. To estimate the
degree of possible deviations from the expected value, one customarily employs the
sums of the products of the squares of the differences of the random variab les and
their mathematical expectations by the value of the probabilities of these random
variables. The quantity obtained in this manner, characterizing possible variance
of the random variable relative to its expected value,is called standard deviation.
Random variables are continuous and discontinuous, and therefore standard deviations
- for these variables are also respectively determined with the following formulas:
for discontinuous variables: n
)
D [x1= (x~ - m.~~)'Pi~ (2
for continuous variab les: a
D ~X] _ ~ (x~ - nr..~.)~ f.e rlx, (3)
.
- where D[X] is standard deviation; xi value of random variable; mX mathematical
expectation of random variable; Pi probability of obtaining the value of a random
variable.
Of importance for program evaluation and review is that the overall distribution
variance of the sum of a set of mutually independent random variables is equal to
the sum of the values of the distribution variances for each random variable
separately.
We recommend that a reader who is unfamiliar with probability theory, for practical
determination of standard deviation, employ the following formula:
o~ _ ( 6 8 a '~4)
- where Q Z is standard deviation; b-- pessimistic estimate; a-- optimistic es-
timate.
This formula and the curves in Figure 29 show that the further apart the optimistic
- and pessimistic estimates, that is, the greater the span of distribution, the
greater will be the uncertainty connected with the operation in question and, on
the other hand, the less the variance, the more accurate the operation duration
estimate will be, and consequ~ntly the optimistic and pessimistic estimates lie
closer to one another. ~
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For example, let us say that two commanders have determined the duration of some
one operation, the estimate of which is contained in Table 3.
Table 3.
~2~ OueNK~ '
`1~ ~CTO O~QlAlAtlT ~ ~p11TN?INCTN~ilCK~e I H~M60~A,~ ;P~pT� ~
~lcCll4 i~'H4lCKi�
~J ~~J ~
(6) Ilepnwii KoMaunnp 4 6 8
(7) BTOpoii KuMaunup 10 12 13
Key:
1. Who determines 4. Most probable
2. Estimate 5. Pessimistic
3. Optimistic 6. First commander
7. Second commander
In order to determine which commander more correctly determined duration of the
operation, we must compute the variance for each of them:
oz = ( 8 ~ 4 _ ( 6 ~ (~,67)~ = 0,45;
~ \
~q _ (13 G 1Q l~ _ ~ ~ _ ~~~5~~ = 0,2~5.
~ 1
Our calculation indicates that variance is less with the second commander, and
consequently his estimates are more correct: It follows from this that these
estimates should be used for our calculations.
Thus in order to determine who is less confident of his estimates, we must cal-
culate the standard deviation of each set of estimates and compare the obtained ~
standard deviations.
Let us examine the derivation of formulas (1) and (4). These formulas are con-
nected with ~ -distribution.
p-distribution is a distribution of random variable t, which changes in the in-
terval [A, B], where A> 0, B> 0, the density of probability of which is determined
by the formula u - oo ~ t C A ~
(t - .4)" ~IJ - (~r
f fwP ~L~ ~s. ~ = ~co,,~ + ~c?, ~ -F~ t~z, ~ + ~c~, s~ ~ 5 + 5 + 5 +
15 = 30; `
2~ t~P ~c~ uo, - � 85 - l 5= 70~
Pn s) S~n. x~~~ s~ - tn, u~~, 1 S--- 15 = 0~ .
~a, e~ � ~n. H (J, A) ~n. u (3, s? = 1 UO - 15 = 85;
pii ~n. i~ 7) - tn. u(3, s? - l 20 --15 =105.
~n fact, the determined figures are entered in column 10 opposite these opexat~.qns
in Table 8.
To determine partial reserve of the second type Pn of a given operation, w= examine
operations possessing identical terminal events. We select from column 5 of these
operations the maximum operation completion time, from which we subtract tP,o of the
operation in question.
~ If only one operation terminates at an event, the partial reserve af the second
type Pn of this operation is equal to zero. With Table 8 we determine the part~.al
reserve of the second type of operation (5, 9). In column 2 we find operations
possessing identical events. There are two such operations: (5, 9) and (6, 9).
We turn to colunm 5, where the tP.o of these operations has been calculated. For
operation. (5, 9) tP,o(5, 9)=45, while for operation (6, 9) tp,o(b.9)=55. We take
the larger figure, 55. From this quantity we subtract tp,o of each operation.
Consequently P,;~s,Q~ =55-45=10; P,~~~ =55-55=0.
Indeed, in column 11 of Table 8 we shall see the number 10 opposite operation (5, 9),
and the figure 0 opposite operation (6, 9).
For operation (3, 6), only one operation enters the terminal event, and consequently
Pn~3, 6)=0.
7. Graphic Method of Calculation
The graphic method is employed as a rule in calculating small networks. One feature
of this method is the facr_ that all calculated parameters are determined directl; on
the chart.
There are two variants of the graphic method of calculation: calculation with
recording of calculated parameters and with change in the graphic configuration of
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the network, and calculation with recording of calculated parameters without recon-
figuring the network.
The latter method of calculation is subdivided in turn into multisector and four-
~
sector.
In military affairs the four-sector graphic method of calculation is most acceptable,
since it is more compact and convenient for rapid computation of small networks. �
This is valuable when employing critical-path method in conditions of a rapidly
changing situation during combat. With this method the network circle which desig-
nates an event is divided into four parts (sectors). The symbols adopted for the
four-sector method of network calculation are shown in Figure 53.
Hnu6onee panaee 1lnuAneee no~anee
en~MO~rcnae epeMw (1) 8~nycmuMOO ~peM~ (4)
Mayana o �ombi. Mqya~a p 6om~i,
4bixo8au~e~1 u3 e?~soBAWe~ u3
daMM080 C066frt1Uft 3 3 6 S dOMMOQO C06bIf11UA
4
_ 3 ~5~ it
0
~e~epe epaMenu ~ d
aMHazu co6~cmun
(2) MoMep
CD6Nmu71 ry
0 ~ 0 Kp~mGyecKUu
0 4 nyme
~ 3~ vnr,~
H~ pe~epe
ApoBon~cu men~nocme p p , nepnoao eu8a Go
paQame~ Ronne~u peaepe d
4 2 4 ~8~ Pn6oinei 6~ S
. p S ~ 19 19 ,
(9) vacmnei~i pe~r,pe ~
emoposo auda
Figure 53. Four-Sector Method of Network Calculation
Key:
l. Earliest possible start time 5. Time reserve of given event
for work operation proceeding 6. Critical path
from a given event 7. Partial reserve of first type
2. Event number 8. Full reserve of work operation
3. Duration of operation 9. Partial reserve of second type
4. Latest allowable starting time
for an operation proceeding from
a given event
Proceeding from Figure 53, one can include the following: the event number is placed
in the upper sector; we place in the left-hand sector the earliest possible starting
time of an operation proceeding from the event in question; we place in the
82
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right-hand sector the latest allowable starting time of an operation proceeding
from the event in question; we place in the lower sector the time reserve of the
event in question.
The numbers above the arrows indicate the following: the number at the beginning
of the arrow duration of the work operation; the mixed number at the end of
the arrow operation time reserves, with the integer indicating full reserve of
the work operation, the numerator of the fraction partial reserve of the first
type, and the denominator of the fraction partial reserve of the ~econd type
of the operation in question.
Let us examine the procedure of network computation by the graphic method. For
this we shall take our initial network readying a tank battalion for attack from
a position of close contact with the enemy (Figure 33). Figure 54 contains our
initial network schedule calculated by the graphic method.
We stiall describe below the network computation procedure.
. gp ~ 70
PQC4CRi F1aHHE20 U ~03aNC20(1~ .
MQYQ/!Q JJQO.^/T � ~
tp�(~,~}-mas[tpn(h,~i't;h.i)J~ 4 ~---~0 890 s~ ~a 151t

s:~ tn.n(i,j)=men [tnn(j,K:-t;i,1J) 0 0
" N
O ~ .
P � '
Pacvem pe3epeoe : ~
.epcMenu co6a~muu ~2~ ~ 85~ 5~ , 30 85� *
P~Z) - tn(i)-tp(t) ' ~ . o
o I . ot~
b ~q
o� 0 5�~ s.' s 5_�a ~o Z~o S�II. ~5 315 ~ o s o;s ss, s s~s ~oo,~ ~
a o 0 0 0 ~ o
pacyem pesepao6 pa6on? (3) ' ~ o
Pn=tn '^tPl~l-t1~,1) noaMeiu SO' 85,Q ~ r~ ~ .
~1) P~~epe ( 4 ~ . $S
, 5 4ccmNeiu pe~epe ~
P�~tn(j)-tr.(i)-t ~,1~ nePe02o eu8�
h
� 4acmNeiu peoepe ~ ' �p ~
Pn=tp(1)'tp(t)'t(i,!) emopo2o euaa 7 p f05 10 30 8pa ..i~
(6)~ 0 81Z5 75;Sa
6u
� 3U . 705 �
Figure 54. Four-Sector Graphic Calculation of Initial Network Schedule
Key:
1. Calculation of early and late 4. Full reserve
start of operations 5. Partial reserve of first type
2. Calculation of time reserves 6. Partial reserve of second
of events type
3. Calculation of reserves of work
, operations
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Calc~ilatioii of Earliest Possible Commencement Time of Work Operations
The earliest possible time of commencement of work operations is calculated from
left to right, beginning with the starting event and ending with the concluding
event. We take as the earliest work operation commencement the greatest accumulated
time figure for all paths which lead to the event in question. Calculation is per-
formed in the following sequencE using the algorithm, formula (25).
Early beginning is equal to zero for the starting event, and consequently also for
work operations procee3ing from the starting event.
We shall formulate in words the algorithm represented by formula (25): early begin-
ning of the operation in question (i, j) is equal to the maximum value of the sum
of the early start and duration'of the operations preceding the operation in
question.
If the operation in question is preceded by only one operation, its early start is
equal to the sum of the early start and duration proper of the preceding operation.
For example, we shall determine the early start of operations (1, 2) and (2, 3):
~n. � tP. ~a, i? -1' r~a, = 0 5 = 5;
,ri = tP. u, ~ -i- :n = 5 5 = ~ 0�
We proceed as follows in determining the early start of operation (1, 2) with the
chart: we find event (G1), take in its left-hand sector the starting time of opera-
tion (0, 1), which is equal to zero, and add ta it the time of operation (0, 1)
proper, which is equal to 5 minutes. We enter the resulting sum in the left-hand
sector of event (1). The number 5, entered in the left-hand sector of event (1),
indicates the early starting time of operation (1, 2).
To determine tp H~2 3~ we find event (2), take the starting time of operation
(2, 3) in its left-~iand sector, which is 10, and add to it the time of the operation
proper, which is equal to 5 minutes. We enter the resulting sum in the left-hand
sector of event (3). This time will be the early starting time for all operations
proceeding from event (3), that is, operations (3, 4), (3, 5), (3, 6), (3, 7).
If the operation in question is preceded by several operations, the early commence-
ment of this operation is determined from the maximum sum of starting time and
duration of all preceding operations. In aur illustration, for example, in deter-
mining the early start of operation (8, 11) we examine all preceding operations,
namely operations (4, 8) and (5, 8). We determine tp,H(8, 11~ for these incoming
operations:
u~a. ii~ 1P. n~~, e? !1/, B? = 20 0= 20;
l P. ~e, n? ~~s, e~ � 30 60 = 90.
We take the maximum sum, that is, tp,H(8, 11)=90, and enter it in the left-hand
sector of event (8). This is the Parly start of operation (8, 11).
We employ these procedures to determine the early start of all operations and reach
the concluding event in the network.
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Calculation of Latest Allowable Commencement Time of Work Operations
The latest starting time of an operation is figured in reverse order, that is,
proceeding from right to left, beginning with the concluding event and ending with
the starting event.
For the concluding event in the network the early start of subsequent operations,
of which this event has none, as we know, denotes at the same time the late com-
pletion of all preceding operations. Therefore the early beginning of an opera-
tion is transferred from the left-hand sector of the concluding event to the right-
hand sector of the event in question, and we begin calculating in reverse order
(from right to left) back to the starting event. We enter in the right-hand sector
the minimum values of the difference between the late start of a subsequent opera-
tion and the duration of the operation in question.
We perform our calculation with the algorithm, formula (27).
We shall calculate for our schedule the late start of operations (11, 14), (8, 111
and (5, 8):
~n, x ~rr, � ~n. x p~, - ~'u ~a, rs~ ~3 ~ ~~5 > 0)i
Pa ~re, ~9> > Ro w. >>~�n~~e, ra~ ~2~5 71 ~ 0)~
f'p~~o,a~~Ro~,rv>Pn~ao,aa~~l~6=1,5>0).
In order to achieve continuous, uninterrupted work in the 4th process, we shall
refine the schedule, beginning with the end.
The third gap is equal to 1.5 hours.
Since operation (20, 22) has a total reserve of Pn~2p~ 22~=1.S,we can shift its
commencement and completion time by the amount of the gap, without risking extend-
ing the onset time of the concluding event.
110
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- Reasoning in similar fashion, we shift the execution times of operations (16, 19)
and (9, 15), achieving continuity in the work of the filter flushing team.
We organiae flow in the Sth process as well with this same method, by shifting
from early to late commencement and completion times for operations (24, 25),
(21, 24), and (15, 21).
Thus we flow-optimize the network schedule and achieve efficient organization of
utilization of maintenance shop personnel as well as PTO gear and equipment for
servicing vehicles.
With the first schedule (before optimization), the maintenance shop filter flushing
team coffienced work 1.8 hours after vehicle servicing began, while with the new
schedule this team can commence work in 4.8 hours. And this will have no effect on
the time specified for completion of the aggregate of work operations pertaining to
servicing all vehicles.
In addition, according to the original plan the maintenance team was compelled to
].ose 3 hours on idle time in the course of performing filter flushing operations
for all tank subunits. Now the maintenance shop personnel can utilize this time
for other work operations.
The above example of flow optimization of a network schedule clearly shows that the
dscribed method is an effective tool for achieving efficient organization of a com-
plex aggregate of work operations, during execution of which idle time for skilled
personnel, vehicles and equipment is eliminated.
The above-discussed techniques of network flow optimization can also be utilized
in solving other operational-tactical and technical problems. ~
Let us examine one more example, in order to gain a better understanding of the
question of network schedule optimization.
A subunit headquarters staff was assigned the task of organizing an exerc3.se to
- demonstrate weapons and combat equipment for four groups of trainees of various
occupational specialties. Each group can inspect equipment simultaneously only at
one training station. The sequence of arrival of groups at the first training
station, specified by the higher commanderr is known. The groups should not waste
time waiting their turn to inspect equipment.
Equipment inspection time at each training station differs for each group and is
indicated in Table 16.
Table I6. (l, (2~O~1CMA OCMOTPi TCXIIHNII~ II~IOAYIylACN H3 )''1t6NWX MOCt~I~ v
\ I
1'pynn~
~u 1 I 4 I 7a 3
1-a 2 1 1
2-a 0,5 ! 2
3-e 0,5 2 0,5
9-a 0,5 1 0,5
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Key t~ Table 16 on preceding page:
1. Group 2. Time for ~.nspecting equipment
at training statlons, hours
~1~ Pam~ee rravano
o ~2 z,s ~ s,s
(z~ 9yc6noe ~ocmu l11~1 1 ~Z Z 0,5 3 0,5 4 0,5 5
~ 0~
iU
Yye6noe ~ ~ izp f 2z Z 3zp 4 4e 0 16
Mecmu Nr'L ~ 0 6 ~ 7 ~ 8 Z 9 ~ ~
~0 0/
~ 1 3 9 4 ~
SNe6MOe ~ueemo lihs 11 ~ZP iZ ~Z 13 3z 14 4Yp IS
~ ~ z o,s as
Figure 62. Initial Network Schedule of Demonstration of Weapons and Combat Equipment
Key:
1. Early start 2. Training station...
~ Z p . Group
The task is to determine an optimal variant of combat equipment and weapons inspec-
tion by all groups, whereby the least amount of time would be expended. Analyzing
the process of equipment inspection at three training stations, we shall obtain
the schedule shown in Figure 62. Optimizing this schedule for the purpose of im-
- proving the inspection flow, we shall obtain a new network schedule (Figure 63).
AL 14
.(1) yY~QMOQ Mecmo M H ~`p ~ 7 11 ~ 13 ~P
' 11 . ( '
_ 11 ~
4tp
Yye6noo Mecmo Ma ~'P 3 5 Z v 6 9 ab 12 0,5
I (
. ~ I
1 ~
�!?yeQnoe Nec; o M1 Z Etp 4 ~`P B 4ZP
' ~ $ as as o,s
Figure 63. Optimized Network Schedule of Demonstration of Weapons and Combat
Equipment by Process Flow
Key: .
1. Training station... ~,p. Group
Table 17 contains network schedule parameter calculation figures.
Proceeding fromthe ascending order of early completion of work operations, the
equipment inspection sequence will be as follows: training station 1, training
station 3, and training station 2.
i1z
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_ Tab le 17 .
Koeuve� ~ZRot
cr~o npeA� p
(1) wecrsyai po6or ~U~ A~Y. x(1, p~p. o(1~ A 1n. u(!~ A~a. o(1. JI pn (l~ p u(1~
uaqt p~6oT
. 0 1--2 2 0 2 0 I 2 0 0
1 2-3 1 2 3 2 3 0 0
` ~ 2-4 0,5 2 2,5 2,5 3 0,5 0
~ ~ 3-5 0�� 3 3 ~ a U U
1 3-7 1 3 �1 5 1 1
1 4-b 0 2,5 2,5 1 ~ O,~i 0,5
1 4-8 0,5 2,5 3 5,b 2,5 .0
2' 5-6 2 ' 3 5 3 5 0 0
' 1 G-7 0 b b u ~ 0 0
' 1 6--~J 0 b 5 ~+,5 t~,5 O,;t I)
2 7-11 1 5 G ~ U
] 8-9 0 3 3 5.~~ 5,5 2,5 'l
. � 1' 8-12 0,5 3 3,5 7 7,5 4 2
2 J-l0 0,5 5 5,5 5.5 r, 0,5 u
1 10-11 0 5,5 5,5 6 G 0,5 0,5
� 1 10-12 0 b.5 5,5 7,5 7~5 2 0
3 It-13 2. 6 8~' G 8 0 0
2 12-13 0,5 5,b 6 7,b 8 2 2
2 13-14 1 8 9 8 ~J U U
Key:
1. Number of preceding operations 2. Code of work operations
The process of network model flow optimizaLion is shown in a linear chart (Table 18).
~ epeti~r oc~:ompa, y
~1~ Ppynna Table 18.
1 2 J~ 4 5 6 7 8 8
1 ~ II
1-A tpynna ~ _ , ~
~ m II
2-A epynna II~4 s n~
~ ~ " x-x
/ ID II
M A g 10 1~
3-s epynna ~ IIt II
x ~r-x
. t ~ n
a ~z ~Z ~s ~a (Legend and key
4-~ apynna ~ to table on
~ x
X� following page)
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,
Y C /1 O 8 M 6l C O 6 O J H Q 4 6 M Ct A ~ 3~
~4) F-- ~-=-1 yve6~~oe nrecmo Ns1 - a
w F-~-----I l+ye6~ioe n~ecmo Nr2(6)
(5) y~+e6:~oc w-tcr.mo Ne3 ~iC~XciOnmuMU~upoaar?netu(7)
' nomarc
~ Key:
1. Group 4. Training station 1
2. Inspection time, hours 5. Training station 3
3. Legend 6. Training station 2
7. Optimized flow
Thus we have studied methods of ~ptimizing network schedules, with the aid of which
we have changed the duration of operations, distributed resources or determined
flows, which in complex processes can provide a r.eliable guarantee of observance
of specified timetables.
2. Tying in Network Schedules to Calendar Timetables and Constructing Scale
Network Schedules
Since netw~rk schedules ar.e a control and management tool, following calculation
and optimization, schedules are usually tied in to calendar timetables.
- Schedules are tied in to calendar timetables proceeding from the concrete condi-
tions of planning and consideration of the conditions in which the process will be
carried out. Two methods of tying in network schedules to calendar timetables can
be employed: time-linking with the a3.d of time scales, and tying in with the aid
of constructing scale network schedules. Both these methods can be successfully
employed in military affairs. Let us examine them.
Tying in schedules to calendar timetables with the aid of time scales is usually em-
play~ed when planning prolonged processes (combat operations), such as when planning
construction of large military installations and structures, the training process,
the process of manufacture, repair and renovation of combat equipment, large-scale
projects, etc.
In these cases network schedules are tied in to calendar timetables in the follow-
ing sequence. First of all two time scales are plotted one above the other~�
One places on the upper time scale a natural series of numbers from 1 to the nu~
ber signifying the end of the scheduled process. This upper series is nothing other
than the number of units of time required for completion of the entire process.
One places in the lower series calendar times (calendar days of months, minus days
off and holiday), if the process is taking place in peacetime.
Let us take, for example, the process of major overhaul of a group of combat
~ vehicles, scheduled by network method, figured for 21 days. The process of over-
hauling this group begins on 1 November 1972.
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Table 19 contains a tie-in of the calculated schedule to calendar dates.
Tab le 19 .
� (1) a~~~~ ~~~~H~~oA~Te~ ~,~~T
Pac~ieTUWe I~ I Z( 3 I~ I 6 I ~ I ~ I 8( 9 lU I I I 12I I:s I I I I 15 I I~i I7 I Itl I 19I I�,I
~2~ CPUNII 0 AlIY1
(3) Kaneunap. I.I I 2 3 4 9I 10 13 14 15 IG 17 20 21 '?1 'l'3 21 27 'l8 2~ 3f1 I.1?
u~ie AaTw
I
Key:
1. Days of performance of work 2. Calendar times in days
operations 3. Calendar dates
Calculated times are placed in the upper scale of Table 19, and in the lower
calendar dates minus days off and holidays.
Tying in to calendar times with the aid of a scale network schedule is accomplished
as a rule in processes connected with planning troop combat activities, as well as
all types of combat, combat service and logistic support. Such tying in essentially
constitutes constructing a scale network schedule and makes it possible to employ a
scale network schedule as an operating document for allocating tasks to troops,
for organization of coordination and all types of support, as well as for directing
the planned process in the course of combat actions.
Let us examine a scale network schedule and the principles of its construction. As
an example we shall take an optimized initial network schedule, as shown in Figure
55, and transpose it to a scale (Figure 64).
A scale network schedule (Figure 64) is a definitively calculated and optimized
network schedule transposed to a time scale. Construction of such a schedule is
_ a very useful stage in the overall process, and in many cases an essential stage,
since a scale network schedule gives a cl~ar picture of the course of a process on
a time axis. With the aid of such a schedule one can see the entire planned opera-
tion (process) on a time axis in that process sequence in which the given operation
(process) should develop. Essentially a scale network schedule reflects the process
of coordination of the personnel and equipment participating in the operation
(process) as regards missions, objectives and time, and therefore constitutes, as
it were, a coordination schedule table.
In addition, a scale network schedule can serve as an operation document, on the
basis of which one can assign fully substantiaCed and consequently objecti~re tasks
to sub units and units participating in an engagement (process). At the same time,
possessing a scale network schedule, one can control a process, utilizing internal
resources and time reserves, since a scale network schedule enables one to see the
entire planned engagement (process), to see available internal resources and
reserves, and thus efficiently to control the course of an engagement (process).
Knowing the entire course of combat actions (process) as a whole and possessing
time and resource reserves, one can maneuver these resources and reserves, achieving
completion of all events in the network on schedule.
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~1~~ AodtomosMn m~~so~?~s
~ - _ nodpC~dt~enuu ~ ( )
~6~ ~7~_________ boee?~~+ dtucnie 1.~
OmBanut ~ocmnnoeKa p,;-65 ~ 7C IlepeMeu~rwue
~O nDedeCp. ~oaa" mrinoe noo0aatle~ Opznnus 4 obetnr� m~inoe?is nodpQ~
eO uoo= eanuMOdeucme ~en a~'oeee~z a anuo~ eu~cuoora .
oc ~ pacn_; ],~~�-a0 me iu 15 n uuu
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nE i~~ !10 . pa~� ~oMmbons :w tler� ~
ee iro pnad nonh nou~cau
e,~ ~ ~p s J~ t0 ~p 14 3nnAr~ue
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a pcno / D
, o a~na ~l 15 ~aaeeeRr _ - eu6erodeMUA
;oc pero~noE- ~ ~S ~uMrmy~-- D~-60 ~5
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( o n ~aM u ~boee.iz ~ada~ u ~ u mp u nocm u a nnuJ quuH y;fu �
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9f~cMenue Pa~em Ortidnnue Kn- p~Wenua eaau.+oaeucme.e t u 2mp mue esi~rcud ~ u 2 mv
aadavo eDaMenu ~cnuD ~W no~uuuu
~ S ~ s Z 5 3 ~s 5 ao 8 zo ~2 4o t8
nocmaMOeKO ~19~ ~nunAmue pemen ~nNamue eer~t
Q~ 6oees~x aadn~ RoM 3 mp. u rtoc noauquu �
,=O Y OPZQNY.~GI(~.~CM KT( 10dOVY na sonP- ~ u 2 mp ~Z L
EJCUMOB2LLCT0 t ONa'C ROJt!� ~
~5~ ~o,�~e e 3 mo ~0 u~u 20 P~-20 ~s/
9
� u~a 20 v ZO 2~ Rocmar?oeKa sa8av u ~
_ . �~"_~Ta oaaaMU,qy. uaau.+oa
~ a ~ v ~odtomoeKO 3 mp R nacmyn~renuro y rtoB a9deneM 3 mu I
~ =q� ~22~ eo '3 (23) ~ ~
~ ~
3~n ,
!
O O
~24~ cnamur earcu8am ~
no~uuuu ~25~
_ 4 Iloa2omoEKn 1 u 2 me R nacmynnextno ~ mp
P~-t0 60 20' p~ -'LO
0~ 2~ 4$ u i o 3 10 11 1Z 17 14 15 20 25 90 55 40 45 50 b5 &0 65 70 75 80 85 90 95 WDi05r~I1D.115 120 125 1;f0 ~ur?
(G6~ (YY./OMYM~
Figure 64. Scale Network Schedule of Preparation of a Tank Battalion for an Offen-
sive Action
Key:
1. Mission briefing 11. Preparation cf reconnaissance
2. Time calculation subunits
3. Issuing instructions to execu- 12. Verification of execution of
tive officer order
4. Issuing warnirg orders to rear 13. Organization of support of
services subunits combat actions
5. Issuing warning orders to com- 14. Reconnaissance subunits occupy
bat subunits observation posts and organize
6. Issuing warnin~ orders to recon- surveillance
naissance subunits 15. Issuing warning orders to re-
7. Commander's reconnaissance, situa- connaissance
tion estimate, and decision-making/ 16. Allocation of combat tasks and
planning organization by tank battalion
8. Allocation of missions to rear ser- commander of coordination in
vices subunits and organization of lst and 2d Tank companies
coordination 17. Decision-making/planning by
9. Preparation of rear services sub- commanders of lst and 2d Tank
units for combat actions companies and allocation of
- 10. Movement of rear services subunits tasks to proceed to and occupy
into assembly area assembly area
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(Key to Figure 64, cont'd)
18. Allocation of tasks and organiza- 22. Preparation of 3d Tank Company
tion of coordination in subunits for the attack
of lst and 2d Tank companies 23. Allocation of tasks and otga-
19. Allocation of combat missions and nization of coordination in
organization by tank battalion subunits of 3d Tank Company
second in command of coordination 24. Preparation of lst and 2d
in 3d Tank Company Tank companies for attack
20. Decision-making/planning by com- 25. 3d Tank Company proceeds to
mander of 3d Tank Company and al- and oc~.upies assembly area
location of tasks for proceeding 26. 2 hours and 10 minutes
to and occupying assembly area
21. Proceeding to and occupying as-~
sembly area by lst and 2d Tank com-
panies
A scale network schedule provides the possibility of forecasting the course of com-
bat actions (process), of predicting possible deviations long before they occur,
and of taking prompt measures to prevent them. A scale network schedule makes it
possible to make optimal decisions in each concrete situation.
Thus a scale network schedule is a reliable instrument of troop control during
execution of diversified tasks.
A scale network schedule should be constructed in the following sequence. A time
scale is plotted on mill~.meter graph paper or on a ruled sheet of paper. Seconds,
minutes, hours, days, weeks, or months can be taken as unit of time. This is
decided specifically on each occasion, depending on conditions, and one takes those
units of ineasurement which are convenient for process control and management.
Minutes are taken as unit of ineasurement in Figure 64.
We shall note that f~r convenience it is more advisable to vary the time scale.
This is necessary in order graphically to portray brief-duration operations and
to accommodate the designation of a work operation aoove the arrow. This has been
done in our example (Figure 64). From 0 to 15, time on the scale is 3ndicated
every minute, while trom this point to the end of the scale time is indicated every
5 minutes.
After the scale is plotted with the aid of an optimi.zed schedule and calculation
table, the scale schedule is plotted. Construction begins with the critical path.
Critical-path work operations in the schedule are extended into a single line, which
also determines the length of the schedule.
The starting event (the zero event in our schedule) is placed on the zero ordinate
at the center of the chart. The entire network is plotted at scale from this event.
Each work operation is laid out in scale, based on the duration of each operation.
Each work operation terminates with the event which follows it.
The centers of events are placed on vertical lines running from their completion
time marks on the scale~ Operation (0, 1), for example, terminates with event
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(1). The duration of this work operation is 5 minutes. tde find on the time scale
the mark with the number 5 and run from this mark a line perpendicular to the time
scale. On this perpendicular line we place opposite the zero event event (1), the
center of which we place on the perpendicular line. We join the zero and first
events with an arrow, above which we write the designatio~ of the work operation,
and below the arrow we indicate its duration in m~nutes.
All other work operations are plotted in scale in like manner. In those cases
where a work operation proceeds at ar. angle to the scale, its duration is measured
as a projection onto the scale. The events between which a work operation lies
should be plotted onto the scale network schedule according to the opt3mized
schedule calculation table, taking into account partial reserves of work operations.
We shall utilize Table ~0, which contains this calculation, to construct our scale
network schedule.
Table 20. Optimized Network Schedule Calculation Table
~ents
0 WTNq
~p. u ~i~ A~U.1) ~p. o N, Il ~n.u ~~./1 ~Ih /l ~a. at. ~1 Pn pn Pn
i I /
0 1 0 5 5 0 b b 0 0 0
1 2 5 b 10 5 b lU 0 0 0
2 3 10 5 15 10 5 15 0 0 U
3 4 15 5 20 25 5 30 10 lU 0
3 5 15 15 30 15 15 30 0 0 Q
3 6 15 10 25 GO 10 70 45 A5 U
3 7 15 5 20 80 5 85 G5 65 0
4 12 20 GO RO 30 GO 90 10 U IU
q 13 20 6U hll 30 60 9U 10 0 O
5 8 JO 4U 7U 30 40 70 0 0 U
5 9 30 20 50 5U 20 70 20 2~) n
5 10 3~1 15 45 85 15 1~(1 55 55 1ll
5 II 70 15 45 70 15 85 ~IU 4U U
G I(1 25 30 55 7U 3U 1W 45 0 0
7 15 20 30 50 85 3U 11b G5 0 25
g 12 70 ?0 90 70 20 ~JO 0 0 U
9 13 5~ 20 70 90 2U ~JO 2Q 0 10
10 14 55 ~0 85 lU0 30 130 45 15 U
10 l5 55 15 70 115 15 13A GO U GO
11 15 45 30 75 85 30 115 40 0 0
12 I fi 91) 20 110 110 20 130 20 2Q 0
12 18 ~JU 40 130 ~JO 40 130 U 0 0
13 17 SO 20 IUO 110 20 130 30 20 0
13 I~ 90 4U 1?0 ~JU 40 130 I~) 0 10
14 !8 d5 0 85 13U 0 130 9i 0 45
15 . 18 15 15 90 115 15 130 dQ 0 40
I6 18 I10 0 110 130 0 130 20 0 20
17 16 100 0 100 13U 0 130 30 0 30
Note: In Tab le 20, 22, and 23, critical work operations are set off by heavy lines
If a work operation possesses a time reserve of the first type, the operation
should be plotted in scale, beginning with the initial event. The end of a work
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operation should be marked with a vertical stroke, from which the first-type
time reserve of this operation is laid out by a dashed line to the terminal event.
The value of this reserve is indicated under the dashed line. For example, let
- us plot operation (5, 11) onto the scale network schedule (Figure 64). We find
this work operation in Table 20 and see that the given oneration has a first-type
partial time reserve of 40 minutes. Tt?is work operation has a duration of 15 ~
minutes. We plot this operation in scale from event (5). Since the work operation
began 30 minutes after work commencement by the battalion commander, it will ter-
minate at 45 minutes. We run an arrow (work operation) to this time and terminate
it with a vertical stroke. We then run a dashed line equal to 40 minutes, indicat-
ing the partial reserve of this work operation, and plot the terminal eve~t (11)
of this operation, the late compl?tion time of which is_85 minutes. Under this
dashed line we indicate the amount of this reserve Pn, equal to 40.minutes.
If a work operation has a second-type partial time reserve, the operation is in-
dicated beginning from the terminal event, plotted according to late completion
time. For example, let us plot operation (10, 18) on the chart. It is evident
from Table 20 that the work operation has a second-type partiaJ~ time reserve uf
60 minutes. We plot the terminal event (18) on the basis of late completion time,
which is equal to (according to Table 19) 130 minutes. From event (18) we lay out
in scale operation (10, 18), equal to 15 minutes, and mark the start of this
operation with a vertical stroke. This operation will begin 15 minutes after the
battalion commander's work commences and will end after 130 minutes, terminating
with event (18). We then run a dashed line in scale, equal to 60 minutes, fro~n
the start of this operation to event (10), indicating under the dashed line the
amount of second-type time reserve Pn.
If a work operation does not possess partial time reserves, it is plotted at the
calculated early start and complet3on time. For example, operation (6, 10) does
not possess partial time reserves, and therefore we plot it at scale on the scale
network schedule by early start and completion time.
Possessing a scale network schedule, one can see the entire process as a whole,
can see work operations and their available reserves, as well as mutual process
and logical linkages on a time axis. For a given concrete time one can see
process progress, what work operations should commence later, and which ones should
begin earlier than the calculated time. One can establish from the schedule from
what work operation one should begin, what resources should be utilized and for
what time in order to speed up the entire process as a whole.
The availability of the scale networ.k schedule will help distribute work operations
among process executants. For example, in our sche3ule (Figure 64) all operations
lying on the critical path up to event (8) will be performed by the battalion
commander. Beginning with event (5), however, principal work operations pertain-
ing to organization of combat ac,tions and coordination are performed in parallel.
Operation (5, 8), for example, is performed by the battalion commander, operation
(5, 9) by his second in command, and operations (5, 10) and (5, 11) by the bat-
talion executive officer. The battalion executive officer will begin performing
work operation (S, 11) upon completion of operation (5, 10), utilizing the reserve
of operation (5, 11), which is equal to 40 minutes (Table 20).
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The network schedule is also a reliable instrument in process control and manage-
ment, which will be examined below.
3. Utilization of PERT Methods in Process Management/Control
In the preceding sections we have examined in detail the methods of constructing and
optimizing network schedules. The reader has been able to see that as a result of
- detailed analysis of a network model one can find a practical and expedient solution
and specify an optimal plan for execution of an aggregate of work operations.
This does not yet signify, however, that input data and an optimized network schedule
are absolutely accurate and that there will be no deviations from the specified plan
in the process of execution of work operations. The probability of occurrence of
such deviations is due to the presence of random factors which affect the performance
of work operations but cannot always be taken precisely into account. Therefore it
is essential to manage and control a planned process in a flexible and efficient
manner. It will be necessa.ry to introduce corrections in the course of execution
of the original plan.
How does process control/management take place with the existing traditional method
of planning?
In the course of accomplishment of work operations a situation may develop where
everything is proceeding according to plan at one place and a delay occurs else-
where. Steps are taken to correct this delay, and the plan is reworked. In these
conditions, however, it is impossible to know what effect the delay will have on
the end result of combat actions (project). Work operations are suitably ad~usted
by adopted measures at one point, but then a delay occurs at a third location, etc.
Network methods are effective in that they enable one to investigate and grasp the
picture in the course of combat operations or a process. After receiving informa-
tion on the status of work operations, the entire network is analyzed: the length
of the new critical path is determined, reserves are calculated, occurring obstacles
are determined, and their effect on other work operations is estab lished. Methods
and means to eliminate them are determined proceeding from the overall situation.
This makes it possible to direct a process~with foresight and to forecast a process
in a prompt and timely manner.
While in projects where program evaluation and review technique is not employed,
observation of the:~Yocess is conducted as if through a narrow slit, enabling one
to see only a small area of work operations, with PERT methods one can scan the
entire complex aggregate of ineasures down to the tiniest details. A network model
enables one scientifical~y to analyze the course of a work operation and to make
the most expedient decisions.
Critical-path method possesses the advantage that it enables one to employ special
means and methods which provide full-valued information on the actual status of
the program and its completion prospects relative to assigned tasks, and also
enables one to elucidate critical areas in the course of process execution on the
i2o
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basis of various parameters (time, resources, etc). Such information enables one
to make prompt and effective decisions on control/management of the process.
. The stage of process control and management begins following final network cor-
rection and adjustment. It begins at the moment the network is activated and enda
simultaneously with completion of the aggregate of work operations. The purpose of
this stage is to achieve a situation whereby the terminal event of the network
schedule will occur at the predetermined time and within the limits of allocated
resources, in spite of possible unforeseen difficulties and deviations in the com-
pletion times of individual schedule work operations.
In connection with this, planning tasks in the course of performance of work opera-
tions include monitoring the actual status of operations, determination and
analysis of occurring changes, plan correction and adjustment, redistribution of
resources, and on each occasion preparation of a new forecast chart.
_ Critical-path method specifies a number of ineasures for successful accomplishment
of these tasks, providing for continuous surveillance of the progress of work
operations, thanks to a well organized information service and periodic reports
received from executants on progress in accomplishment of work operations on the
critical and subcritical paths, and less frequently on other work operations as
well.
Information volume and content should be differentiated in conformity with different
levels of leadership, and the volume of received infor~ation should be maximally
precise and concise. Information periodicity depends on concrete conditions and is
determined by the project supervisor.
~ Information transmitted in an upward direction should contain not unly data on the
status of work operations in progress but also on all likely changes. Reports may
contain information on new work operations and events, on possible changes in the
linkages and topology of networks, on revision of time estimates, on change in times
of allocation of manpower, supplies and other resources, and on fu11 or partial com-
pletion of given work operations.
Information on these questions shoi~ld be presented in encoded form. It is best to
employ a single-digit code to designate the status of work operations. For example:
0-- work operation removed, eliminated;
1-- additional work operation, newly adopted;
2-- work operation proceeding with delay (not be3ng carried out);
3-- work operation proceeding on schedule;
4-- work operation proceeding ahead of schedule;
5 completed work operation.
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A two-digit system of codes can be employed to communicate the reasons for non-
_ accomplishment of work operations. Applied to control and management of combat
training, this system of codes could be as follows:
11 inadequate motor transport availability;
22 personnel diverted to other activities;
33 training facilities not in a state of readiness;
44 weather factor;
88 other reasons.
Three-digit codes can be adopted to communicate an evaluation of the quality of
a completed work operation:
101 work operation performed with mark of excellent;
102 work operation performed with mark of good;
103 work operation performed with mark of satisfactory;
104 work operation unsatisfactory.
Each received report should be submitted by the executing agencies to the higher
agency by the rigorously specified time, in the form of a card, such as that con-
tained in 'Pable 21.
Tab le 21.
[IIN~p a~aeae Wu vacTx, noA� `wWxq~p oTeer� (4) ~,i ~5~
61'OT~KHA� i9AlAlIIiIY~ OTAl11/ f~~cTeeuuoro H~IlU0pN84N11 ~T! 11{11pOp118411H
cnoruxfea�
_ 07 09 023 10 15.6
1 oriio~ Pc~c~d~pc� " ~18~
Koa p=6oTw (9) (~~?~a (11) 12~ P I ue~w ~~~acrwaA) ~
~ ~ ~ ~ COCTOAIIN! P~boTa OK011401~I1!
-t.r-s------ Pa6oTU �
p~6oTU ~ K~x' (n~iiwooe) � ~
nu ocTee�
MtMTlAb' A~ ~~I~ IW_ IACA
N~4~110 K011l4 G".,
~ IIUCTL / 7 7 l
L.Y.R-,L_
1 2 3 ~ 6 I 8 7 ~ 8 fl 10
~ 85 87 5-103 7 14.G - - - -
g9 50 2-22 6 10.6 10 14.G 8 a -
Key:
1. Combat training section code S. Date of report
2. Code of unit, subunit, section 6. Work operation code
3. Code of executing agency 7. Start
4. Report number 8. End
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(Key to Table 21, cont'd)
9. Status of work operation 14. Date
10. Time of work operation in days 15. Time reserve (partial)
11. Completion of work operation 16. According to plan
(scheduled) 17. Remaining
12. Forecast 18. Comments
13. Duration
This card is essentially a standard document which contains a large quantity of in-
formation. At the same time this document can be prepared very quickly and trans-
mitted to the command authority by any communication channels.
In Table 21 the codes signify the following: 07 the report pertains to weapon
- training; 09 3d Tank Battalion; 023 tank battalion commander. Let operation
(85, 87) in our example signify performance of a training exercise with a sub-
caliber tube; the numbers 5-103 in the first row of column 3 denote that the
exercise performed by this subunit received a mark of satisfactory.
Work operation (49, 50) signifies live-fire activities by tank platoons.
The number 2 in the second row of column 3 indicates that the work operation is
proceeding with delay, while the number 22 in that~same column indicates the
reason for the delay (personnel diverted to other activities). The duration.of
this work operation, according to the original schedule, was 6 days (column 4),
while its completion was scheduled for 10 June (column 5). Adjustment had to be
made, however. The executant, performing calculations taking account of the new
conditions, determined that duration of the work operation would increase to 10
days (column 6), while its completion time would have to be extended to 14 June
(column 7).
According to the original schedule, operation (49, 50) had a partial reserve of 8
days (column 8). In the new version of the local network schedule, this reserve
was reduced to 4 days.
On the one hand, strict order in submitting reports creates a precise work rhythm.
Deliberation of the work operations schedule and estimating their duration dis-
- ciplines executants and prevents them from arbitrarily changing the completion times
of work operations or cancelling them. On the other hand the project supervisor
is kep~ continuously informed on the situation and sees those work areas which are
threatened by potential difficulties, which enables him promptly to take the
requisite steps to correct them.
After gathering information on th~ course of work operations, one proceeds to up-
date the network schedule. The initial network schedule is revised by the im-
mediate executing agencies. Local schedules are refined by middle-echelon leaders,
while the consolidated network schedule is refined by the highest control echelon.
Processing of data does not differ from the analogous procedure employed in con-
structing the original network: calculation of critical path, determination of
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work operation completion times and reserves, drafting of recommendations, etc,
that is, the already familiar process of network optimization is repeated.
A new network schedule is constructed as a result of updating a number of initial
plan estimates. Thus it is a collective forecast of the course of work operations
at a given moment in time. anaiys~s of the new schedule makes it possible, just
as in the original plan, to determine the critical path, to reestimate time reserves
for events of unstressed paths, and to estimate the probability of event completion
on schedule.
- One should bear in mind that a new network schedule may differ greatly from the
initial optimized schedule.
Recommendations on decision-making are presented on the basis of data obtained with
the aid of the new network schedule.
Network schedule analysis data at each stage (following each report) should be sent
to the executing agencies in order that they be informed of their status in the
overall course of work operations. This element is new in comparison with existing
methods of control and management of aggregates of work operations.
In the absence of electronic computers for collecting, processing and analyzing in-
formation, it will evidently be necessary to expend a comparatively large amount of
time on decision-making. At the present time this circumstance limits the area of
application of critical-path methods in the course of control and management of
processes which are of short duration. Program evaluation and review technique
provides an opportunity to forecast short-lived processes as well, altering the
network model in conformity with the projected conditions which may occur in the
couise of a short-lived process. And this makes it possible in the planning stage
to provide for requisite measures if delays occur in the course of the process.
We shall clarify this with the following example. Let us assume that the battalion
commander and his staff have the task of determining the optimal variant~of subunit
response to a combat alert. The solution can be found by ~eans of repeated prac-
tical response to a combat alert. But this method is impractical. It requires
large expenditures of material and manpower resources and time. Therefore it will
hardly be advantageous to perform such experiments. By employing PERT methods,
however, one can utilize another way to solve the assigned problem to find an
optimal variant by modeling the process of response by subunits to a combat alert.
To achieve this end, possible action variants are played out on a constructed and
optimized network model, by feeding in the most probable delays, breakdowns, and
deviations from the designated p1an.
Playing out the process of subunit response to a combat alert and employing PERT
methods, one calculates the critical path, determines time reserves, and spec3.fies
recommendations for eliminating bottlenecks. These recommendations are grounded
on concrete data obtained on the basis of scientific analysis.
Determining the expediency of applying PERT methods, one must take into account
the fact that the groundwork of successful accomplishment of control tasks is laid
during the period of organization of actions, during the period of planning,
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Planning for combat operations (process) with employment of critical-path methods,
the commander thoroughly scrutinizes the forthcoming process, more precisely es-
timates the extent and duration of forthcoming work operations, gains an understand-
ing of the complex interlinkage, logical and process sequence of work operations,
and determines weak areas. This makes it possible to select fram the entire ag-
gregate of work operations the principal ones which determine the total time for
accomplishing the mission, that is, the critical-path work operations.
Thus program evaluation and review technique enables the coumnander knowledgeably
to direct a process, even if he does not possess considerable practical experience.
Scale network schedules greatly facilitate control of a scheduled process. Having~
such a schedule at his disposal, a commander, with knowledge of work operation time
reserves and delay time, will immediately berable to respond to disruption of the
course of work operations.
4. Some Recommendations on Adoption of PERT Methods in Line Units, Military
Educational Institutions and Establishments
- In the era of rapid scientific and technological advance, one of the most pressing
problems is the problem of improving control of complex processes. The question
of improving control has always been at the center of attention of our Communist
Party and Soviet Government. But it has never been so acute as at the present time.
The 24th CPSU Congress stated the task of continuing the policy of improving manage-
ment of the national economy and improving planning.
This congress decision also fully applies to the system of military management and
control. Indeed, in the era of rapid advances in military technology substant3al
changes have taken place in the structure of the Armed Forces, in weaponry, mili-
tary equipment, and views on the character of combat operations have changed.
These factors advance the problem of scientific troop control to the forefront of
- military-scientific problems. PERT methods can lend certain assistance in solving
this problem. These methods contain considerable possibilities for improving ef-
ficiency and effectiveness of control. realization of these possibilities depends
to a significant degree on how c o r r ectly is executed the measure to adopt a
PERT system into the practical activities of staffs, military educational institu-
_ tions, and establishments.
Appropriate training of personnel is a decisive condition for successful adopt~on of
new methods of planning and r~anagement. Experience indicates that suitable train-
ing of personnel in methods of constructing, processing, analyzing and optimizing
network schedules constitutes a base for adoption of a PERT system. Only trained
personnel can utilize in full measure all the advantages offered by the new methods
of planning and management. A superficial acquaintance with program evaluation and
review technique methods and a nonsystemic approach to things leads to pro~ect
discrediting and failure.
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In training cadres, one can combine officer independent study of the appropriate
literature with regular seminars. As experience has shown, however, brief courses
of instruction are the most effective form of teaching PERT methods.
Training should involve not only the immediate executing personnel but also leade~
personnel. Success in adoption of a PERT system depends in large measure on the
attitude of leaders toward the new methods, and this is understandable, for deci-
sions pertaining to practical possibilities of applying PERT measures are made by
top-echelon leaders. In addition, just as any new method, program evaluation and
review technique requires greater attention and support by leader personnel than
existing planning methods.
In the process of training, considerable time should be devoted to practical train-
ing sessions, at which officers should acquire initial skills in working with
schedules and acquire the ability to calculate parameters and optimize networks.
It is also essential to convince officers that critical-path method also promotes
- more precise coordination of the actions of individual executing agencies, improves
organization of work operations, eliminates idle time and reduces the number of
work stoppages. It is important to demonstrate to the trainees that PERT methods
make it possible to establish a precise interlinkage among work operations, which
gives an integral picture of prospects for plan execution and helps each executant
more clearly see and understand his role in the overall program. It is also useful
to convince officers that the new and advanced methods make it possible more fully
to cor~sider the actual capabilities of subunits and correctly to assign tasks to
them, as well as to give initiative to commanders locally in elaborating and im-
plementing measures pertaining to executing the designated program.
More rapid mastery of PERT methods also depends in large measure on correct organ~.za-
tion of work of a psychological nature. Psychological preparation should be
directed primarily toward overcoming conservatism and certain resistance on the part
of so~e iudividuals. Or.e �, ..~i [ = fl~
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N'OR OF FICIAI, I:SF: OtiLI'
- From a comparison of the initial (Figure 66) and optimized (Figure 67) network
schedules we can easily determine the changes which have occurred i.n the initial
(original) plan of action. For example, operation (1, 2) in the initial schedule
is divided into two and in the optimized schedule is represented by two operatio~is
(1, 2) and (2, 4). Operation (2, 3) is carried forward and in the optimized schedule
begins 10 minutes after receipt of the march task, which led to a shortening of the
critical path by 25 minutes. Operation (3, 4) in the initial schedule is shortened,
since in the optimized schedule the battalion commander's deputies and executive
officer are briefed together with the battalion commander, azid therefore it is
sufficient to tell them who is to isaue orders to whom. The work operation with
the code (11, 13) has been separated and in the optimized schedule is represented
by two operations (12, 14) and (14, 17). The latter operation is performed in
parallel with operation (3.4, 16), as a result of which the critical path is shortened
by 15 minutes. At the same time operation (8, 10) in the initial schedule is
replaced by two operations (9, 10) and (9, 11), which in the optimized schedule
are performed in parallel. The total duration of these two operations is equal to
the duration of operation (8, 10) in the initial network schedule.
Those operations with the code (16, 17) and (17, 18) in the initial sched~ule are
separated and represented in the optimized schedule by three operations (18, 19),
(18, 20), and (18, 21). The new schedule provides for each subunit to proceed by
its own route, which makes it possible to increase speed and consequently to shorten
the critical path by 90 minutes.
Finally, those operations which in the initial schedule bear the codes (18, 19),
(18, 20), and (18, 21) are separated and performed in parallel; in the optimized
schedule they are represented by operations [(19, 22), (22, 25), (22, 28)], [(20,23),
(23, 26), (23, 28)], [(21, 24), (23, 24), (24, 28)]. This shortens the critical
path by an additional 20 minutes.
After optimizing the schedule, we shall calculate its parameters. Table 23 contains
calculation of network schedule parameters. It is evident from Table 23 that the
critical path of the optimized schedule is equal to 525 minutes (8.75 hours). The
directive timetable has been achieved, and therefore there is no further schedule
optimization.
Thus by changing the process technology and parallel performance of work opera-
tions, we have succeeded in shortenjng march preparation and execution time by 150
minutes, fitting it into the directive timetable.
6. Construction of a Scale Network Schedule
Since the optimization process has been completed, on the basis of Table 23 and the
optimized network schedule (Figure 67) we construct a scale network schedule, which
is shown in Figure 68. In this schedule the path from event (18) to the concluding
event separates into three branches. The dashed lines with arrowheads denote
logical links or empty operations. The dashed lines which begin solid-line arrows
c~r are their continuation designate partial or overall work operation reserves
respectively. Types of time reserves of work operations and their magnitude are
indicated below the dashed lines and are designated as follows:

~ Pn 5; Pri 45 and Pn 45,
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where Pn is partial reserve of the first type; Pn partial reserve of the second
type; Pn total work operation reserve.
The numbers after the letters indicate the amount of reserve.
BIBLIOGRAPHY
1. Zukhovitskiy, S. I., and Radchik, I. A., "Matematicheskiye metody setevogo
planirovaniya" [Mathematical Methods of Program Evaluation and Review Technique],
Moscow, Izd-vo Nauka, 1965.
2. Golenko, D. I.; Levin, N. A.; Mikhel'son, V. S., and Naydov-Zhelezov, Ch. G.,
"Avtomatizatsiya planirovaniya i upravleniye novymi metodami" [Automation of
Planning and Management by New MethodsJ, Riga, Izd-vo Zvaygzne, 1966.
- 3. Kazakovtsev, V. S., "Instrument upravleniya" [Management Instrument], Moscow,
Izd-vo Sovetskoye Radio, 1965.
4. Syroyezhin, I. M., "Azbuka setevykh planov. Lektsii po setevomu planirovaniyu"
[Primer of Network Schedules. Lectures on Program Evaluation and Review
Technique], Moscow, Izd-vo Ekonomika, 1966. '
5. Leybkind, Yu. R., and Suvorov, B. P., "Metod setevogo planirovaniya i
upravleniya" [Program Evaluation and Review Technique], Moscow, Izd-vo Ekonomika,
1965.
6. Razumov, I. M.; Belova, L. D.; Ipatov, M. I.; and Proskuryakov, A. V.,
"Setevoye planirovaniye i upravleniye" [Program Evaluation and Review Technique],
Izd. MVTU im. Baumana.
7. "Osnovnyye polozheniya po razrabotke i primeneniyu sistem setevogo planirovaniya
i upravleniya" [Basic Principles of Development and Application of Program
Evaluation and Review Technique Systems], Moscow, Izd-vo Ekonomika, 1965.
8. Mi]:ler, Robert V., "PERT sistema upravleniya" [PERT A Control System],
translated from English, Moscow, Izd-vo Ekonomika, 1965.
9. "Sistema setevogo planirovaniya i upravleniya. Programmirovannoye wedeniye
v PERT" [Program Evaluation and Review Technique System. Programmed Introduc-
tion to PERT], translated from English, Moscow, Tzd-vo Mir, 1965.
10. "Setevoye planirovaniye i upravleniye v promyshlennosti. Materialy seminara"
[Program Evaluation and Review Technique in Industry. Seminar Materials], 1rIDP,
1966.
11. Paraubek, G. E., "Setevoye planirovaniye i upravleniye" [Program Evaluation and
' Review Technique], Moscow, Izd-vo Ekonomika, 1967.
COPYRIGHT: Voyenizdat, 1974
3024
CSO: 8144/1292 END
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