Critical path analysis for development administration [Reprint 2019 ed.] 9783110811612, 9789027921741

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CRITICAL PATH ANALYSIS FOR D E V E L O P M E N T A D M I N I S T R A T I O N

PUBLICATIONS OF THE I N S T I T U T E OF SOCIAL STUDIES

PAPERBACK SERIES VII

PROCUL CERNENS

INTERNATIONAAL INSTITUUT VOOR S O C I A L E S T U D l f i N - ' S - G R A V E N H A G E 1972

CRITICAL PATH ANALYSIS FOR DEVELOPMENT ADMINISTRATION

by

PHILIP C. P A C K A R D

1972 MOUTON THE HAGUE - PARIS

© Copyright 1972 Institute of Social Studies, The Hague, The Netherlands. No part of this book may be translated or reproduced in any form, by print, photo-print, microfilm, or by any other means, without written permission from the Institute. The responsibility for works published in the series "Publications of the Institute of Social Studies" rests with the authors; publication of a work in this series does not commit the Institute of Social Studies to any opinions stated therein.

LIBRARY OF CONGRESS CATALOGIC CARD NUMBER: 72-85842

Printed in the Netherlands by N.V. Zuid-Hollandsche Drukkerij

PREFACE

These notes have been written for a set of lectures which I delivered at the Institute of Development Studies, University of Sussex, in November 1969. I wish to thank the participants of the Seminar on "Implementing Development Plans", and in particular the Director of the Seminar, Dr. B. B. Schaffer, for helping me to advance my ideas on the uses of network analysis for underdeveloped countries. I wish to thank the Institute of Social Studies for providing the necessary leisure to set down the following ideas. Philip C. Packard La Pena Rubia, Cala Ratjada, Mallorca

CONTENTS

Preface

5

Introduction

9

I.

The Project Model

13

II. Event and Activity Times

27

III. The Critical Path

36

IV. Resource Allocation

46

V.

64

CPA and Development Administration

VI. Speculations on CPA for Development Planning . . . .

69

Select Bibliography

80

INTRODUCTION

The literature on Critical Path Analysis and its variants within the family of network planning is so large that it may seem superfluous to devote more attention to the topic. My first reason for pursuing the topic, therefore, is that the subject has been relatively neglected for planning other than for what is sometimes termed "planning" in industrial situations. In particular, though interest is expressed in network planning techniques within the underdeveloped countries, little attention has been devoted to discussing CPA or its variants in relation to conditions in these countries. A second reason has to do with the connexions between economic principles and practices embodied in the trade of economic planning and administrative systems and practices in the underdeveloped countries. It is only recently that "public" administration has been reviewed and given rise within the genus to the new species "development administration". Whatever definition one may care to give to development administration, it is and must be concerned with management practices. Management leads on to economics, for the problems facing the underdeveloped countries are those which fall within the domain of the discipline. It is still the case, unfortunately, that most expositions of economic planning touch very lightly if at all on public administration. This may be and seems to be changing, but the greater weight and prestige given to the older (academic) field of economics tends to maintain the rigidity of the economic approach to planning. As is well known, a great deal of the body of economic planning assumes the existence of management or administrative functions considered necessary for effective planning. In a sense this is still true for the discipline of

10

INTRODUCTION

economics itself, owing its origin as it does to that period in history and those countries in which institutions emerged and human action grew to manage resources within the economic system which is the subject of investigation of the discipline. Finally, the set of techniques which comprise CPA seem to me to be not only especially relevant for those involved in government in the underdeveloped countries, but may also serve as a bridge for understanding the ways in which economists have looked at planning and the different administrative practices which do exist at present. The exposition of the concepts of CPA in the first chapters proceeds in the usual way from construction of the network through resource scheduling. A few points can be made here about the differences in treatment of the subject when CPA is applied within underdeveloped countries and those differences in emphasis which seem important. Anyone who learns his economics or is exposed to the subject with a development "slant", almost invariably thinks in terms of the structure of an economy and how that structure can be altered. The "macro" approach is favoured. The structured conceptions of macro economics also serve to organize the data — i.e., information — on the economy. These data form the building blocks for such summaries as the national accounts and the like. This is certainly not the place to criticize emphases within economics or to disparage efforts at understanding structure and operation of underdeveloped economies. The point is merely that the experience of those directly involved in government activities can be quite different from what is summarized, for example, in the national accounts. It is quite probable that macro economic notions are relegated to the dustbin of "theory" by the "practical" man. (He may even be trained in economics.) The exposition develops from the project model which is described as a "logic" model. This approach is designed to bring out the "theoretical" character of planning for a project. In effect, the model is drawn up and eventually "tested" through its operation. Moreover, by concentrating on the project approach, appeal is made directly to the experience and interests of those who work in government. The further elaborations of the CPA method con-

INTRODUCTION

11

tinually stress the "efficiency" concept, with the object of relating the project at a later stage to development planning. The stress is also on "management", and the exposition tries to develop the meaning and relevance of "control" for projects and within the process of development planning. The literature on CPA is of course biased in terms of the environment in which the set of techniques has been developed: industrial projects for the most part in the industrialized countries. Even where the literature deals extensively with construction projects, the underlying assumptions are those of an industrial environment. The effect is that attention is for the most part devoted to the calculations and analyses of the critical path and resource scheduling to bring out the importance of managing a project. The underlying definition of the "jobs" associated with the activities is not dealt with so extensively in this literature. One great defect with projects — and government projects in underdeveloped countries — is that the newness of these projects calls for careful job definition. I have continually stressed the resource "bottle-neck" problem, which arises firstly within organizations when resource uses in relation to activities are not well defined. Moreover, overuse of skilled resources for less skilled tasks is a common phenomenon of these projects. By stressing job definition I have tried to approach the estimates of duration times as dependent in a meaningful way upon the amounts and qualities of resources to be allocated to the various activities. Therefore, the emphasis is not on such mathematically sophisticated methods for estimating duration times as those statistical methods developed for PERT, for example. Resource bottlenecking arising from joint-project resource use is dealt with in a literary way in the last chapter on development planning. There, the potentialities of CPA are discussed, though no quantitative methods (such as the RAMPS method) are presented. The attempt is to avoid jumping to sophisticated methods which must depend upon data processing equipment without first carrying out the detailed and laborious work of constructing project models and analyzing them in terms of time and resources. The emphasis is on improvement throughout, rather than upon one set of techniques as the panacea for development planning or project

12

INTRODUCTION

planning. In this regard, the last chapter discusses "efficiency" in a somewhat philosophical way, but with the intention of focussing upon the practical role of management. I have tried to bring out what I think the link should be between "managers" of projects and development planning and the criteria problems which have been dealt with so extensively in the literature on economic planning. This treatment of the subject can be at most an introduction. I have added a bibliography as an aid to those who wish to pursue the subject and adapt the CPA concepts to their own environments and uses.

I THE PROJECT MODEL

STEPS IN PLANNING

When we plan, we prepare a plan for action. In the language of Critical Path Analysis, we draw up the project model and then schedule the project. This distinction between model building and preparation for carrying out the project via scheduling time and resources is a most important one. A great deal of planning suffers from the confusion of the two activities, with the result that planning as a whole becomes ineffective. The secret of CPA is that it separates the two activities and systematically develops the project model as the basis for later action.

EVENTS AND ACTIVITIES

To prepare a plan for "action" means that we are looking towards the future. In other words, we are concerned with time. In drawing up the project model, we divide time into events which are points in time, and into activities which occur through time. Events divide time into discrete units and these units of time between events are taken up by one or more activities. We can illustrate events and activities with a simple example. Let us suppose that four men leave a place at the same time with the object of meeting as soon as possible at a common point some distance away. The starting place is given by the circle with "1" inside it. The "1", in other words, stands both for the geographical place and for the event in time which is the starting point for their journey. The four men

14

THE PROJECT MODEL

walk to point "2", and then separate into two groups: one man walking along road B to point "4", and the other three walking together to point "3". From point "3", each man chooses a separate road (D, E and F), each of which leads to point "4". The question which now interests us is this: when or at what time will the four men meet at point "4"? The times for walking are given under each section of the road network. We can therefore determine that it takes 5 hours between events 1 and 2, 10 hours along road B and 4, 3 and 5 hours to walk D, E and F, respectively. Therefore, the earliest time at which the four men can meet is 15 hours from the start of their journey. Event 4 can occur at the earliest at 15 hours after the time of the starting event, which is event 1. B

We can notice from the road network that event 3 occurs in time at 10 hours after the start of the journey. Therefore, the man who walks along road D can arrive at point 4 in 14 hours; similarly, the man who walks along road E can arrive at point 4 in 13 hours. However, the other two men cannot arrive at point 4 until 15 hours have passed. The path for one of these men is from event 1 to 2 to 4; for the other, his path is from event 1 to 3 to 4. Both of these paths take 15 hours to walk. It is therefore the case that, for the roads D and E, the time for starting from point 3 could be delayed: by one and two hours, respectively. If the man walking D left point 3 after eleven hours, he would still arrive at point 4 in 15 hours, similarly, the man walking road E could leave after 12 hours and

THE PROJECT MODEL

15

still arrive at point 4 in 15 hours. What this illustrates is that we could schedule the times at which the men walk roads D and E in such a way that there is variation in their start and finish times. For the "project" as a whole, we must schedule the walking times so that the four men meet at point 4 in 15 hours. The project constitutes the plan for the four men between events 1 and 4. This project is made up of activities, each of which comprises one or more men walking a segment of the road network. From this example a number of conclusions can be drawn. The road network is of course one way of showing geographical relations in space. What is important for us, however, is that the network shown graphically is a set of logical relations. The project model, in other words, is composed of activities which have certain relations one to another. For example, logically, roads D, E and F follow road C. In order to walk from point 1 to point 4 along roads C and D, one must pass through point 3. In terms of our project, the road network is looked at in terms of time for walking. The logical interrelations of the activities in our project result in an overall time for walking by diverse routes from point 1 to point 4. Our project is also based on men who walk. We can and shall refer to men in this sense as resources, and to the activity which is based on walking as a job. In other words, the object of the project is to meet at point 4 for the four men, and this is accomplished by the various "jobs" of walking the sections of the road network. Notice that if we gave each man a bicycle, the time for meeting at point 4 would undoubtedly be shortened. Each activity, therefore, is based upon its relation to the project as a whole and to the ways in which the activity is carried out. In the case of adding bicycles, we have changed the nature of the "job" by changing the resources necessary for carrying out the activity. The project model is therefore a "logic" model based on a definable starting point in time and an ending point in time. We develop the logical interrelations of activities which are conceived of as "jobs". We have to be careful in defining activities to have understanding of the resources necessary for carrying out each of the activities. This does not mean that these resources are present in prescribed amounts. What it does mean is that an activity is

16

THE PROJECT MODEL

defined in terms of specific resources for doing the "job". The amounts of resources needed for each activity is the problem of scheduling, which is the separate step in planning that follows the construction of the project model.

RULES FOR DRAWING UP A PROJECT MODEL

Once the project has been assigned a definable beginning and end event, and once the activities have been drawn up on the basis of jobs to be performed, the logic of activity interrelations can be established. We can use the following rules for determining this logic: 1. For a given activity, what other activities (jobs) must be completed before this activity (job) can start? 2. What other jobs can start at the same time as this job? 3. What jobs cannot start until after this job is finished? For the previous example of our road network and the project based on it, we could analyze the logic in the following way. For activity A (the section of the road network) we find that, following rules 1 and 2, no activity precedes nor starts at the same time. Therefore, A is the first activity of the project. Following rule 3, we find that activities B and C cannot start until A is finished. For B and C, following rule 2, we find that B and C can start at the same time. For C, we find that activities D, E and F cannot start until C is finished. Finally, D, E and F can start at the same time. We should notice that the logic of activity interrelations that we establish is developed in terms of the activities of the project. Each of these activities has a start and end event. It may be the case that an event has more than one activity preceding it or emanating from it. In this case, different activity times allow for variations in scheduling activities. We shall use the differences in event and activity times to schedule the activities and carry out the project.

THE PROJECT MODEL

17

NUMBERING EVENTS

Each of the events in the previous example is represented by a circle. When we come to analyze the project model, it will be helpful if we can refer to each activity by a number designation. Moreover, activities can be analyzed more readily if they are numbered in such a way that each has a number for its start event less than the number of its end event. Therefore, it is customary to number the events of the network (the project model) in such a way that no number is assigned to an event until the start events of all activities preceding that event have received a number. For example, we could have the following:

We can assign the number "2" to the end event of either A or D. We cannot assign an event number to the end events of B, C, E or F until the end events of A and D both have numbers. The event numbers we have are therefore such that each activity has an event number for its start event less than the number for its end event (in the case, above, we could have the end event for A numbered "3", and the end event for D numbered "2", with no violation of the general rule about numbering events). It should be pointed out, however, that in complex networks with a great many activities, or in networks which have been altered in their original logic, activities may not be numbered so that the start event has a lower number than the end event for an activity. One solution is to leave "gaps" in the numbers assigned to events, for example, number them 1, 10, 20, 30, etc. so that the addition of new activities or the alteration in the logic of the network will not affect the general way of numbering activities. In any case, it is not wrong that an activity has its start event numbered higher than its

18

THE PROJECT MODEL

end event; it is merely more convenient to observe the general rule for later analysis.

DUMMIES AND LOGICAL ERRORS

One difficulty exists in assigning numbers to activities when activities can start at the same time or go on in time together. These concurrent activities will have the same event numbers. To avoid this ambiguity, we introduce what is called a "dummy" activity. On the network it is shown as a dotted arrow. For example, for our project based on the road network, we would introduce dummies in the following fashion: B

©

Now it is the case that each activity can be identified unambiguously by its event numbers: each activity has at least one event number unique to that activity. The dummy activity has no time duration and it does not use resources. Since a project is defined by its start and end events, each activity must be related logically to other activities between these two events. One logical error that can occur is referred to as "dangling" arrows, as exemplified by or

In each of these cases, the activity C is unrelated to the project as a whole. We have to check on the relation of C to other activities and eliminate it as a "dangling" arrow.

THE PROJECT MODEL

19

Another logical error may arise from "looping". This is shown in the following way:

With a loop of this kind, it is impossible to move from the start event of the project to the end event. Loops must be eliminated by changing the logical interrelations of the activities of the network. When a network becomes complex, it is quite possible to fall into logical errors in drawing up the network. Complexity may give rise to the following situation. For the network below, the first thing we can notice is that a dummy arrow is necessary to give activities B and C at least one event unique to each of these activities. Notice, also, that the dummy occurs at the end event of activity A, rather than at the end event of activity B. The dummy could occur in either position, but it is placed before the start of activity B to bring out the logic that both B and C precede activity E. In other

Activity

Logical Interrelations

A A A B B C C D D E E E F F G

precedes B precedes C precedes D follows A precedes E follows A precedes E follows A precedes F follows B follows C precedes G follows D precedes G follows E and F

Activities E and F are concurrent

20

THE PROJECT MODEL

words, activity E is dependent logically on both B and C. The logical interrelations specified above indicate that F follows D, or to put it another way, F is dependent on D. On the other hand, activities E and F are concurrent (can start at the same time in this case). This is indicated by a dummy arrow coming from the end event of B and C and going to the end event of D. The use of the dummy arrow in this way brings out the logic that, whilst E is dependent on both B and C, and F is dependent on D, E and F are concurrent activities. In other words, E and F share a common start event. As in the previous example, the dummy activity has no time duration nor does it use resources. "DELIVERY" ACTIVITIES

Any "job" to be carried out does depend upon the availability of resources. In order to bring out this dependance, it may be necessary to add activities which are referred to as "delivery" activities. For example it may be necessary to provide equipment as an activity that precedes the use of this activity on the "job". Similarly, arrangements may have to be made for employing labour of various kinds, and this would therefore be put in the form of an activity. For many activities of government, it is necessary to obtain authorization to proceed, either with a project or with some action that affects the project. As an example, budgetary authorizations could be put in the form of a "delivery" activity. If targets are assigned to a project, they may act as constraints either to one or more activities or to the project as a whole.

21

THE PROJECT MODEL

Delivery activities can therefore be constraint activities which are not easily controlled through the application of resources. We shall have to be particularly aware of activities that can constrain a project and affect its actual carrying out.

ACTIVITY SUB-DIVISION

Let us suppose that we have the following two activities from a project:

O

COLLECT DATA

p.

ANALYZE DATA

^ T ^ - '

By analyzing the character of these activities, we find that they can be divided into the following new activities: START FINISH C O L L E C T D A T A Y C O L L E C T DATA V V 3 j 3 X . START A FINISH p. ANALYZE D A T A * ^ A N A L Y Z E D A T A ' 1 ^ 4 4

The effect of these new activities is to change the logic of activity interrelations and to shorten the overall time for carrying out the "jobs" which were entailed in the two original activities. This subdivision of activities is possible when it is found that the "job" for each activity is itself a series of tasks which can be carried on in series — i.e., one task after another. Sub-divisions of activities show also the definitional character of any activity. We choose the activity and can therefore divide it at will if the character of the "job" allows for it. The sub-division of activities is usually possible in administrative situations, such as the work carried on within governments. The desirable result is that we do shorten the time for carrying out the project without affecting the quality of work necessary for making the project effective.

EXCESS DUMMIES

The use of dummies to establish a unique number system for

22

THE PROJECT MODEL

activities can lead to the over use of dummies. For example, we might have the following:

We can eliminate the excess dummies without changing either the logic of the network or interfering with the numbering system of

the activities. Excess dummies do not alter the logic of the network, but they may make for unnecessary complications and should be eliminated.

THE STATISTICAL SURVEY PROJECT

We can illustrate the character of a project model by presenting a project drawn up in the Central Statistical Office (of an underdeveloped country). This project has as its object the carrying out of a "survey". The project was first conceived in terms of a number of important events, which were thought to be part of a statistical survey. They were the following: 0 1

Start Project Start Sample

THE PROJECT MODEL

2 3 4 5

23

Start Interviews Start Analyze Returns Start to Prepare Final Document End Project

These events mark "stages" in the project. It is therefore possible to develop the activities between the events by both asking what must follow an event or precede it in the way of activities. In Figure 1 we have the network (project model) for the Statistical Survey Project. The important events are given (in triangles) directly above the corresponding events on the network. Most projects start with an activity which might be called "lead" time or "preparation" or the like. In this case we have the first activity called "Discuss Survey within Department". At the end of the project, we have the final activity, which stands for the ultimate objective of the project: "Prepare Final Document". A number of characteristics of government projects are seen from this network. In the first place, we have the three activities concerned with deliveries of equipment, supplies and typing clerks (0-18, 0-19 and 0-20). Each of these can become a constraint to the project so that their inclusion is necessary as activities. Another type of "delivery" constraint occurs in the activity "Obtain Budget Authorization". This is a common type of constraint for government projects and therefore it is important to include it as a delivery constraint activity. One very common type of activity for government projects of the kind represented by the Statistical Survey Project is "Send Questionnaires to Ministries for Reply". This is an activity which seeks information, the resulting information to be incorporated into the content of activities of the project. In other words, an activity of this kind influences the character of what the project "produces": the final survey. It is possible to define this activity carefully by drawing up the questionnaire in an unambiguous way. The difficulty is that the time for this activity is difficult to estimate in that the "reply" to the questionnaire is dependent upon what goes on in the various ministries. We shall come back to this problem of estimating duration times for activities in the next chapter.

24

THE PROJECT MODEL

The degree of activity detail is related to the character of the project and to what has been found to be important for past projects. In other words, experience with other projects leads to the inclusion of certain detailed activities. In the case of the Statistical Survey Project, a number of detailed activities have been included: (13-16) (16-17) ( 9-17)

Arrange Schedule for Supervisors Make Bookings for Supervisors Arrange per diem Expenses for Enumerators

Each of these activities is necessary for carrying out the activity "Supervised Interviews" effectively. The degree of activity detail is also affected by the "pilot project" which precedes the important activity "Sample". The activities necessary for "Sample" are, among others, "Prepare Preliminary Sample Frame" (4-5), "Pilot Survey" (5-6), and "Prepare Final Sample Frame" (6-7). Finally, we can notice from the network that the training of Statistical Clerks and Enumerators gives rise to a number of pre-

A

A PREVIOUS " V SURVEYS I I SEND QUESTIONPREPARE N A I R E S TO -Q PRELIMINARY SAMPLE FRAME '-'MINISTRIES FOR' REPLY PREPARE .! PRELIMINARY A mnrtFT

OBTAIN

PREPARE AND SEND BUDGET REQUEST

CALCULATING

PREPARE

•0> PHOT ffl

EQUIPMENT

OBTAIN BUDGET AUTHORIZATION

AllTHnni7ATir»H

AND

MATERIALS ARRANGE OBTAIN

FOR TYPING

TYPEWRITERS

Fig. 1.

AND

CLER SUP

Statistica

THE PROJECT MODEL

25

ceding activities. These should be all included in the project model along with those activities which are more closely related to the technical character of statistical sampling as such. We can now see that the "logic" of a project model is based on activity interrelations in such a way that we ensure through the model's logic that each activity can be carried out. Not only do we need resources to do a "job", but we also must make sure that each activity has been properly prepared for before it actually is scheduled to take place. This is the reason for including delivery constraint activities and such preparatory activities as "Arrange per diem Expenses for Enumerators". We can notice from the network that each event has been numbered in such a way that its end event has a higher number than its start event. The project model has now been prepared for analysis. The next steps are to assign times to the activities, to determine the critical path, and to schedule the resources for carrying out the project. We shall come to each of these steps for the Statistical Survey Project in later chapters.

A TIST1CAL

CLERKS

GESTIONNAIRE ARRANGE

SCHEDULE

FOR S U P E R V I S O R S PER DIEM EXPENSES

iirvey project

ARRANGE BOOKINGS FOR " ^ SUPERVISORS ENUMERATORS

A A A

26

THE PROJECT MODEL

SUMMARY

The steps in developing the project model can be summarized in the following way: 1. Decide on character of project (its "objective") 2. Define "jobs" (activities) in such a way that it is clear how an activity can be carried out 3. Develop logic of activity interrelations using the three rules (presented above) 4. Sub-divide activities where possible 5. Be careful to add "delivery" activities 6. Eliminate excess dummies 7. Eliminate "dangling" arrows and "loops". The strength of the CPA method is that it refines thinking about the project. By adhering carefully to the steps given above, the project model will be a firm basis for carrying out the project. Drawing up the project model is the key to success in CPA!

II EVENT AND ACTIVITY TIMES

DURATION TIMES

In order to determine how long the project will take, we must estimate the duration time for each activity. On the basis of these estimates, we will be able at a later point to schedule the activities of the project. Each activity is defined in terms of a "job". By identifying the resources which are necessary for carrying out the project, we can assign a "job time" for each of these activities. We should be careful to keep in mind that we are not talking at this point about the availability of resources for each job; we are merely estimating the time for carrying out each activity if the resources are available. Experience with similar jobs in the past provides a good deal of the information necessary for estimating duration times. In the absence of appropriate experience, what is called for is understanding of the "job". This is why the development of the project model in as careful a fashion as possible is so necessary for success of the project. EVENT TIMES

Once duration times have been estimated, we can proceed to assign event times to the network. Using our road network project as an example once more, we start out with event 1 and assign it the earliest start time of zero. This time zero is not as yet related to calendar time. What we are doing is to assign zero as a "reference" time for the start of the project. When we come to scheduling the resources and carrying out the project, the time zero will also be related to calendar time. Event 2 can occur at the earliest at 5 hours

28

EVENT AND ACTIVITY TIMES

(which is 5 hours after the start of the project at time zero). This earliest time for event 2 is determined by adding the duration time of activity A to the earliest start time of event 1. Since there is only one activity between events 1 and 2, there is no confusion over the earliest time for event 2 to occur. Similarly, the earliest time at which event 3 can occur is 10 hours. For event 6, the earliest time of its occurrence is affected by the four activities which precede it: B, D, E and F. If we keep in mind that an event can only occur after all its preceding activities have been completed, we find that the earliest time for occurrence of event 6 is 15 hours. This is determined by both activity B from event 2 and by activity F from event 3. In both cases, 15 hours is necessary to complete these activities. On the other hand, activities D and E can be completed before 15 hours. This is shown explicitly for E, in that it occurs at the earliest at 13 hours. For activity D it is not so obvious, since its end event has assigned to it the earliest time of 15 hours. We shall come back to analyzing activity times below. Each of the earliest times for events is shown by a circle O beside the appropriate event on the network. ® 0 CD—

©

m

A

5

We now wish to determine the latest time at which an event can occur. For event 6, if we wish the project to be completed in the shortest overall time possible, we must assign the latest time of 15 hours to event 6. Now we can work backwards in time through the project to determine the other latest event times. Event 4 can occur at the latest at 15 hours. This is the case as the dummy which connects events 4 and 6 has no time duration. For event 5, we assign similarly the latest time of 15 hours. When we come to event 3, we are faced with the fact that 3 activities emanate from it: D, E and F. The latest time at which event 3 can occur, therefore, is determined by the activity with the longest time duration: in this case, activity

29

EVENT AND ACTIVITY TIMES

F. The latest event time for event 3 is 10 hours. There is the possibility that we assign the latest time to event 3 by subtracting the duration time of either activity D or E from its respective latest end event time. Thus, for D we would have 15 hours minus 4 hours, which gives us a latest event time for event 3 of 11 hours. For E, we would obtain the latest time for event 3 of 12 hours. This would, however, be wrong! If event 3 has either a latest event time of 11 or 12 hours, the network cannot finish until either 16 or 17 hours. This is due to the fact that the duration time of activity E is 5 hours, and since event 6 cannot occur until all the activities that precede it are finished, the time of event 6 is dependent upon activity E (also in this case, activity B). The latest time for event 2 is determined both by the duration time of activity B and activity C. This latest time is 5 hours. Thus we reach event 1 and find that it must start at the latest at time zero in order that the project be completed in 15 hours. These latest event times are shown by squares • beside the appropriate event. ACTIVITY TIMES

The activity times can now be derived from the event times. What we are interested in is the comparison between the times at which events can occur and the variations in the start and finish times of activities. For our road network project, we can summarize activity times in the following way: Activity i-j

Duration D

ES Earliest Start

LS Latest Start

EF Earliest Finish

LF Latest Finish

Float

1-2 2-3 2-6 3-4 3-5 3-6

5 5 10 3 5 4

0 5 5 10 10 10

0 5 5 12 10 11

5 10 15 13 15 14

5 10 15 15 15 15

0 0 0 2 0 1

Each activity is now listed by two numbers: an "i" number to mark its start event and a "j" number to mark its end event. Looking at the column labeled Earliest Start, we see that activity

30

EVENT AND ACTIVITY TIMES

1-2 starts at the earliest at time zero. This start time is based on the fact that event 1 can occur at the earliest at time zero. Similarly, activity 2-3 can start at the earliest at 5 hours. The earliest event time for event 2 is 5 hours. We can follow through this column and determine the earliest start times for all activities based on the earliest times at which their respective start events can occur. For the column labeled Earliest Finish, activity times are determined by adding the duration time of each activity to the respective activity start time. Thus, for example, activity 2-6 has an earliest finish time of 15 hours, which is the sum of its earliest start time of 5 hours and its duration time of 10 hours. The Latest Finish for each activity is given by the latest time at which its end event can occur. This is read directly from the network. Finally, we determine the figures in the column labeled Latest Start by subtracting the duration time of an activity from its latest finish time. Thus, for example, for activity 3-4, its latest start time is 12 hours, which is 15 hours (latest finish time) minus duration time (3 hours). We can notice from the above table that four out of the six activities have the same time for earliest and latest start and the same time for earliest and latest finish. For these activities, there is no possibility of variations in their scheduling if the project is to finish in the shortest overall possible time of 15 hours. On the other hand, the activities 3-4 and 3-6 have differences between their earliest and latest start times and differences between their earliest and latest finish times. These activities can either begin later or finish earlier up to some amount of time. In the case of activity 3-4, this variation in time is 2 hours; for activity 3-6, the variation is one hour. These variations are summarized in the table under the heading "Float". For all those activities which have no variation possible in their schedules, floats are zero. On the other hand, for activities 3-4 and 3-6, their floats are 2 and 1, respectively. FLOAT

Float measures the possible variation in scheduling activities for the project. In this sense it measures the differences between activity

31

EVENT AND ACTIVITY TIMES

and event times for the project. In using float, we will find that we have to be careful in its use so that scheduling is carried out properly. We can therefore refine the notion of float into three particular kinds of float which may occur for the activities of a

10 ©

d

n

20

•(ST © M

project. To take an example, we have a portion of a network shown with earliest and latest event times, and duration times for the activities. If we now think of float in terms of earliest and latest event times we can have the following table.

Activity i-j

Duration D

11-17 11-19 11-21 17-21

5 20 10 5

Total float jL-iE-D 10 0 10 10

Free float jE-iE-D 0 0 10 10

Independent float jE-iL-D 0 0 10 0

The "float" that we have been referring to is now called Total Float. It is calculated by subtracting from the latest finish time of the end event the earliest event time of the start event and the duration time of the activity. What total float measures, therefore, is the maximum variation in scheduling time for any activity. In contrast, Free Float is the difference on the one hand of the earliest event time of the end event and the sum of the earliest event time for the start event and the activity duration time. What free float measures, therefore, is the variation in scheduling for an activity with no effect upon the floats of subsequent activities that immediately follow it. Thus, for

32

EVENT AND ACTIVITY TIMES

example, activity 11-17 has a Total Float of 10 but a Free Float of zero. On the other hand, activity 17-21 has 10 for both Total and Free Float. Activities 11-17 and 17-21 share the total float of 10. If activity 11-17 should use this total float, it would reduce the total float available to 17-21 to zero. This is indicated by having the free float for 11-17 equal to zero. In scheduling, therefore, the using up of float of one activity may affect the float available to other activities. The reduction in float available to any activity reduces the variation possible in its scheduling. Finally we have the particular kind of float known as Independent Float. This is calculated by subtracting from the earliest event time of the end event the latest time of the start event and the duration time of the activity. Independent float measures, therefore, the float of any activity which does not affect subsequent or preceding activities. Thus, activity 11-21 has an independent float equal to 10. All this float can be used (for example by starting activity 11-21 at time 40 instead of time 30) without affecting floats of other activities or affecting the overall time for project completion.

THE STATISTICAL SURVEY PROJECT

The earliest and latest event times have been calculated for the Statistical Survey Project. They are found beside each event in Figure 2, earliest event times represented by circles O and latest event times by squares • . Each activity is now represented by a letter (which is given in Table 1). From these event times we can calculate the activity times and total float for the activities. We should remember that the determination of duration times for activities is based upon experience with similar activities in the past and also upon thorough analysis of the "job" characteristics of an activity. For our Statistical Survey Project, a number of activities present difficulties with respect to their duration times. For activity C ("Send Questionnaires to Ministries for Reply") we face the difficulty that the time for this activity is not based clearly on a "job" which is within the control of our project. In other words, no matter how many resources we apply to activity C, it is

EVENT AND ACTIVITY TIMES

33

TABLE 1 Designations for Activities in Statistical Survey Project Activity Number

Letter

Name

0- 1 0-18 0-19 0-20 1- 2 1- 3 1- 4 3- 8 4- 5 5- 6 6- 7 7- 9 8- 9 9-10 9-11 9-12 9-13 9-15 9-17

A Y Z B-B B D C H E F G J I K L N O M T

Discuss Survey with Department Obtain Calculating Equipment and Supplies Arrange for Typing Clerks Obtain Typewriters and Supplies Review Previous Surveys Prepare Preliminary Budget Request Send Questionnaires to Ministries for Reply Prepare and Send Budget Request Prepare Preliminary Sample Frame Pilot Survey Prepare Final Sample Frame Decide on Survey Obtain Budget Authorization Hire Statistical Clerks Hire Enumerators Arrange for Instructors Sample Arrange for Classrooms Arrange per diem Expenses for Enumerators

34 Number 13-14 13-16 14-15 15-17 15-18 16-17 17-18 18-20 20-21

EVENT AND ACTIVITY TIMES

Letter P R

Q u V

s

A-A W X

Name Make up Questionnaire Arrange Schedule for Supervisor Mail Questionnaires Train Enumerators Train Statistical Clerks Arrange Bookings for Supervisor Supervised Interviews Analyze Returns Prepare Final Document

still the case that the time for this activity is largely beyond our control. Information activities of this kind, therefore, have to be looked at in terms of their importance for the content of the project. By assigning the time of 5 weeks to activity C, what we in effect do is to say that we will proceed with the activities of the network after this activity has been "completed", even though not all ministries have replied or replied in adequate ways in terms of the provisions of the questionnaire. For activity I ("Obtain Budget Authorization"), difficulties may arise in somewhat similar fashion. It is still possible to assign a time to activity I based on past experience. There is also a difference between activities C and I in the sense that C is not necessarily an activity that must be met by the ministries in question. In other words, activity C, from the ministerial point of view, may not be required. On the other hand, such activities as activity I are found within an administrative system which binds organizations and individuals to a greater or lesser degree to carry out the activities. Table 2 lists all the activity times and floats for the various activities. Dummy activities have been omitted as they do not have time duration. We see from Table 2 that the "delivery" activities Y, Z and B-B all have very large floats. We have to be careful in dealing with these activities to be sure that what is meant by each activity is the arrival (of equipment, supplies or typists) rather than merely the arranging for their arrival. In other words, the times for these activities are based on the "jobs" of both arranging and verifying that the deliveries occur within the estimated duration times. This has to be the case to make scheduling these

35

EVENT AND ACTIVITY TIMES

TABLE 2 Activity

Times and Floats for Statistical

Survey

Project

Activity

Duration

ES

LS

EF

LF

Float

0- 1 0-18 0-19 0-20 1- 2 1- 3 1- 4 3- 8 4- 5 5- 6 6- 7 7- 9 8- 9 9-10 9-11 9-12 9-13 9-15 9-17 13-14 13-16 14-15 15-17 15-18 16-17 17-18 18-20 20-21

1 30 3 5 2 2 5 2 2 3 3 1 5 3 4 5 2 4 1 1 1 1 15 20 2 40 12 4

0 0 0 0 1 1 1 3 6 8 11 14 5 15 15 15 15 15 15 17 17 18 20 20 18 35 75 87

0 45 84 82 4 6 1 8 6 8 11 14 10 17 16 15 16 16 34 18 32 19 20 55 33 35 75 87

1 30 3 5 3 3 6 5 8 11 14 15 10 18 19 20 17 19 16 18 18 19 35 40 20 75 87 91

1 75 87 87 6 8 6 10 8 11 14 15 15 20 20 20 18 20 35 19 33 20 35 75 35 75 87 91

0 45 84 82 3 5 0 5 0 0 0 0 5 2 1 0 1 1 19 1 15 1 0 35 15 0 0 0

activities on the bases of their floats possible. The information provided in Table 2 can now be used to calculate the critical path for the Statistical Survey Project. This is the next step in the analysis of the project model before we come to scheduling and resource allocation.

Ill THE CRITICAL PATH

THE CONCEPT OF THE CRITICAL PATH

We have determined the event and activity times for a project with the result that we can distinguish between the various activities of the project. Those activities which, taken together, determine the shortest overall possible time of the project we call the critical path for the project. To take another simple example, we have the following network. In the table below, we have the earliest and latest times for the activities and their floats: Activity

Duration

ES

LS

EF

LF

TF

FF

IF

1-2 1-3 2-3 2-4 3-4 3-5 4-5

4 2 8 5 3 6 4

0 0 4 4 12 12 15

0 10 4 10 12 13 15

4 2 12 9 15 18 19

4 12 12 15 15 19 19

0 10 0 6 0 1 0

0 10 0 6 0 1 0

0 10 0 6 0 1 0

From this table, we can see that a number of activities have the same times for their earliest and latest start times and the same times for their earliest and latest finish times. Each of these activities has a total float equal to zero. The significance of zero total float for these activities is that there is no possible variation in their scheduling times. If we want the project to finish in the shortest overall time possible, we must schedule these activities in con-

37

THE CRITICAL PATH

formity to the times shown in the table. On the other hand, all activities with positive total float can have some variation in their start and finish times. We can use these floats to take advantage of schedule variation. We shall see that this is important for resource allocation. We should notice also that the critical activities have zero float for both Free Float and Independent Float.

©0

© OE

The critical activities of a project focus upon the management problem of any project. Obviously, our first concern is with these activities since they affect directly the project's overall completion time. This does not mean that we can neglect the non-critical activities. What it does mean is that those responsible for carrying out the project can delegate responsibility for the non-critical activities to others. Management is therefore the focussing upon critical activities and the setting out of responsibility for the other activities of the project. Once the critical path has been determined, it is desirable to review the project model before resources are assigned and scheduled. Review involves questioning the character of each activity in the following way : 1. What is the function of the activity within the project? 2. Does the activity occur within the "logic" model at the appropriate time? 3. Is the sequence of the activity appropriate? 4. Has the activity been defined carefully in terms of the resources necessary to carry it out? 5. Has responsibility been set for carrying out the activity?

38

THE CRITICAL PATH

Each of these questions contributes to refinement of the project model and may alter the logic of the model, change resources needed for each activity and change the overall time for completion of the project. By making this check for the project, we enhance the possibility that the project can actually be carried out according to its "plan": the project model.

THE CRITICAL PATH AND CONSTRAINTS

The calculation of the critical path depends upon what time we set for the shortest overall completion time of the project. To this point, we have taken this time to be that determined by the logical interrelations of the project activity and the estimated duration times for the activities. It may be the case that constraints are imposed on the project, either by those responsible for the project, by administrative decision or by particular "delivery" constraints which are found to affect government actions. Let us suppose that, for the above project, it has been decided within the administrative system that the project must be completed in 17 time units instead of the 19 time units estimated. Decisions of this kind arise, for example, from within the administrative system where a particular ministry or agency of government must "produce" its results within a prescribed time. In other words, these ministries or agencies of government function within an administrative system which sets rules and targets for their activities. The effect of this "target" of 17 time units is to alter the event times of the project. We now assign 17 as the latest event time for event 5 and work backwards through the network to reach the latest time at which event 1 can occur. We find that this time is —2, which means in effect that the project must be shortened by 2 time units for one or more of its critical activities in order that the new completion time of 17 time units be achieved. We have the following table for activity times and total floats. The effect of the "target" is to make the floats for the critical activities negative. Each of these activities now has a float of —2. At the same time, activity 3-5 now has a float equal to — 1. There-

39

THE CRITICAL PATH

Activity

Duration

ES

LS

EF

LF

TF

1-2 1-3 2-3 2-4 3-4 3-5 4-5

4 2 8 5 3 6 4

0 0 4 4 12 12 15

-2 8 2 8 10 11 13

4 2 12 9 15 18 19

2 10 10 13 13 17 17

-2 8 -2 4 -2 -1 -2

©

©mi

fore, by imposing this target upon the project, we make the floats of a number of activities negative. The critical activities have floats which are the most negative. If we are to meet the target, we must reduce activity times. Moreover, no activity can be left with a negative float. If the network is to be carried out, the floats of its activities must be equal to or greater than zero. It is quite possible, of course, that by reducing activity times, we change the critical path for the project. Let us suppose that we change the activity times of activities 1-2 and 2-3, so that they have 3 and 7 times units, respectively. We therefore have the following table for the readjusted project model: Activity

Duration

ES

LS

EF

LF

TF

1-2 1-3 2-3 2-4 3-4 3-5 4-5

3 2 7 5 3 6 4

0 0 3 3 10 10 13

0 8 3 8 10 11 13

3 2 10 8 13 16 17

3 10 10 13 13 17 17

0 8 0 5 0 1 0

40

THE CRITICAL PATH

The effect of shortening these two activity times is to eliminate all negative floats. Now the critical activities have zero floats. For activity 3-5, its float has changed from —1 to 1. This is the result of reducing the earliest event time of event 10 from 12 to 10 time units. Now it is the case that activity 3-5 can begin at 10 and finish at 16 (or, alternatively, begin at 11 and finish at 17 time units). It is not always the case that activities such as 3-5 which are non-critical without the imposition of a target, will have zero or positive floats for target imposed projects once the activity times along the critical path have been shortened appropriately. It is necessary to eliminate all negative floats to make the project feasible in terms of the target time. ©on

© m

®®

© 03

One other type of constraint can occur for a project which affects its overall completion time. In the project below, we have the main activities which are necessary for carrying out a project within an economic plan. This is a typical example of a constraint which arises from the need to finance a project through the foreign exchange of the country in question. Activity 1-5 ("Authorization to Use Foreign Exchange") is based on the underlying administrative system, where, for example, the Ministry of Finance or the Central Bank must authorize foreign exchange funds for projects. This kind of activity can become a constraint in that, by the time event 5 is reached through the two paths 1 - 2 - 3 - 5 or 1 - 2 - 3 - 4 - 5 , activity 1-5 has not been completed. It may be extremely difficult to assign a time for duration to activity 1-5. This kind of constraint illustrates the difficulties of carrying out projects according to estimated times based on the project model. It is the kind of difficulty that can be ascribed to weaknesses in the administrative system in which government projects are formulated and carried out. We can treat an activity such as 1-5 in the same way we treat

THE CRITICAL PATH

41

any other critical activity : we focus our attention on it and try to bring resources to bear in such a way that we meet the estimated time of the activity or even reduce its estimated time. What we OBTAIN

FOREIGN

EXCHANGE

have to keep in mind is that certain activities of the network are more amenable to control — i.e., we can, through the application of resources, predict more accurately their duration times. Activities such as 1-5 reduce the reliability of the predicted overall completion time of the project. Alternatively, the constraint in the above project could take the form of a specific time imposed for event 5. For example, it might be the case that foreign exchange is not available except at a specific later date related to the budgetary process of government. Therefore, event 5 becomes a calendar time. If the activities in the two paths 1 - 2 - 3 - 5 and 1 - 2 - 3 - 4 - 5 have as their overall combined times less time than is needed to start the project "now", their floats will be positive, and it will be possible to delay the start of the project. If event 5 will occur at the earliest at time 100 (from "now"), and if these two paths have combined times of 70 and 80, respectively, the project can be started at time 20. In other words, the project can be delayed — event 1 can occur at the latest — by 20 time units. Imposition of calendar time to an event is a target which can be called a Milestone Event. We should be careful to distinguish between milestones which are imposed from outside the project and targets assigned either to the overall project or to an event by those responsible for managing the project. In virtually every case, targets assigned to a project which reduce its necessary overall completion time, and which are met by reducing

42

THE CRITICAL PATH

one or more of the duration times of critical activities, call for increased resources applied to these activities. It may be necessary to redefine the "job" in order to carry out any activity in a reduced time. "CRITICALITY" AS A MANAGEMENT TOOL

The concept of the critical path leads to focussing upon that set of activities which must be scheduled and carried out with no variations in their start and finish times. These activities are less than the total number of activities of any project, so that a division of labour can arise for the management task of carrying out the project. This division of labour rests upon delegating to others the responsibility for overseeing the non-critical activities and leaving to the "manager" or those directly responsible for the project concern for the critical activities. Any system or organization of delegated responsibility has to be looked at carefully within the context of the CPA method. It makes no sense to divide the activities into critical and non-critical and delegate responsibility if delegation will not be effective. It is true of course that the critical path concept is of great potential use to managers in that they can perceive the project more clearly. However, the great gains in efficiency arise from being able to concentrate one's attention on a portion of the network at any given time rather than the whole complex of activities which make up the network. Efficiency means in this sense planning and carrying out the project in the shortest overall time possible and with a minimum use of resources for each "job". In other words, efficiency is the savings on time and resources to carry out the objective of the project. It is therefore the case that the CPA method depends for its effectiveness upon the organizational methods which exist for identifying and assigning responsibility for carrying out the various activities of the project. CPA can identify organizational weaknesses, and it may lead to review of the ways in which "jobs" are carried out, both within projects and within the organization as a whole.

43

THE CRITICAL PATH

THE CRITICAL PATH OF THE STATISTICAL SURVEY PROJECT

The critical path of the statistical survey project is given in Figure 2, each critical activity marked by a "/" through its respective arrow. The time for completion of the project is 91 weeks. For this project, the logic of activity interrelations was examined and it was found that activity "Train Statistical Clerks" could start at the event which is the start event for "Supervised Interviews" and be concurrent with this activity. The change in logic is such that the activity "Train Enumerators" comes before "Train Statistical Clerks". The effect of this change in logic is to reduce the time for "Train Enumerators" from 15 to 7 weeks. What has been done is to reallocate teaching by the instructors in such a way that teaching is concentrated on the enumerators, reducing their time for instruction. The time for training statistical clerks is now 25 weeks, but since this activity is concurrent with "Supervised Interviews" which has a duration time of 40 weeks, the activity "Train Statistical Clerks" has a float of 15 weeks. The changes in the network are given in Figures 3 and 4 and Tables 3 and 4. The effect of this change in logic is to reduce the overall completion time of the project from 91 to 83 weeks, based on the reduced time for the critical activity 15-17. It should be noticed that the change in the logic of activities has affected the numbering system of the events. These events have been renumbered from the original network (in Figure 1). We should reiterate that the number system for events can be based on ©@ }r STATIST!CAL *

CLERKS

©m (g) T R A I N

ENUMERATORS

ARRANGE

FOR

TYPING

CLERKS

@

j^]

Times in Weeks. Fig. 3. Change in critical path overall time: Statistical survey project

44

THE CRITICAL PATH

Times in weeks. Fig. 4. Shortened critical path: Statistical survey project TABLE 3 Duration and Activity Times for Shortened Critical Path: Statistical Survey Project Activity

Duration

ES

LS

EF

LF

Float

0-19 0-20 0-21 9-10 9-11 9-12 9-13 9-15 9-17 13-14 13-16 14-15 15-17 16-17 17-19 18-19 19-21 21-22

30 3 5 3 4 5 2 4 1 1 1 1 7 2 40 25 12 4

0 0 0 15 15 15 15 15 15 17 17 18 20 18 27 27 67 79

37 76 74 17 16 15 16 16 26 18 24 19 20 25 27 42 67 79

30 3 5 18 19 20 17 19 16 18 18 19 27 20 67 52 79 83

67 79 79 20 20 20 18 20 27 19 25 20 27 27 67 67 79 83

37 76 74 2 1 0 1 1 11 1 7 1 0 7 0 15 0 0

THE CRITICAL PATH

45

TABLE 4 Renumbered Activities for Shortened Critical Path: Statistical Survey Project Activity Number

Letter

Name

0-19 0-20 0-21 17-19 18-19 19-21 21-22

Y Z B-B A-A V W X

Obtain Calculating Equipment and Supplies Arrange for Typing Clerks Obtain Typewriters and Supplies Supervised Interviews Train Statistical Clerks Analyze Returns Prepare Final Document

"gaps" in numbers assigned so that changes in logic do not affect the desired sequence of event numbers where the start event of an activity has a lower number than the head event of an activity. This may not always be possible for complex networks. The statistical survey project has now been analysed in such a way that resources can be allocated to the project. This is the next step for carrying out the project plan.

IV RESOURCE ALLOCATION

RESOURCE SCHEDULING

Each activity in the network has assigned to it resources which are necessary to carry it out. In this sense each activity is a "job", having a duration time estimated on the basis of resources necessary for the "job". To take a simple example, we have the network (below) which has been analyzed for its critical path, so that we have the division between critical and non-critical activities. For each activity on the network, we find the amount of resources necessary, given in the triangle A attached to each arrow. The table below gives the activity times and the various kinds of floats for the activities of the network. The resources needed for each activity are the same kind, so that we can add the resources used for each activity in each time period to determine the total number of resource units needed in each time period. We now schedule resources in the following way. Each activity

47

RESOURCE ALLOCATION

is listed in the first column in ascending order based on the number of its start event. Activity

Duration

ES

LS

EF

LF

TF

FF

IF

1-2 1-3 1-4 2-4 2-5 3-4 4-6 4-7 5-7 6-7

3 2 4 8 6 4 8 10 5 3

0 0 0 3 3 2 11 11 9 19

0 5 7 3 11 7 11 12 17 19

3 2 4 11 9 6 19 21 14 22

3 7 11 11 17 11 19 22 22 22

0 5 7 0 8 5 0 1 8 0

0 0 7 0 0 5 0 1 8 0

0 0 7 0 0 0 0 1 0 0

The next column gives the duration time for each activity, followed by subsequent columns which are the periods of time in which the project will take place. If we have sufficient resources available, we will be able to complete the project in the estimated shortest overall completion time of 22 time units. Each activity is scheduled to start at its earliest start time. We show an activity's schedule by drawing a horizontal line which has the length of the number of time units of its duration. For example, activity 1-2 begins at time "1", and has the duration of 3 time units; activity 3-4 begins at time "3", and continues for 4 time units. Notice that 1-2 must begin at the beginning of time "1", as its earliest and latest start times are identical: it is a critical activity. On the other hand, 3-4 has as its earliest start time the beginning of time "3", but its latest start time is the beginning of time "8". (In order to avoid confusion, we can think of an activity's start time as the end of the event time, which is identical to the beginning of the next time period.) For each activity, we list the resources needed in the column for the time period in which the activity occurs. For example, activity 1 -2 uses 5 units of resources for each of the 3 time periods in which it occurs. Since it is scheduled for the first 3 time periods, a number "5" is placed in each of the first 3 columns. We now add the resources used by each activity for each time period and give the total

48

RESOURCE ALLOCATION

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57

RESOURCE ALLOCATION TRAIN

v

STATISTICAL

CLERKS

Times in weeks. Fig. 5. Change in network 'Logic': Resource constraint Statistical survey project TABLE 9 Duration and Activity Time for Resource Constraint: Statistical Survey Project Activity

Duration

ES

LS

EF

LF

Float

0-20 0-23 0-24 9-10 9-11 9-12 9-13 9-15 9-17 13-14 13-16 14-15 15-17 16-17 17-18 17-21 17-23 18-19 21-22 22-23 23-24 24-25

3 30 5 3 4 5 2 4 1 1 1 1 5 2 8 15 20 8 13 12 12 4

0 0 0 15 15 15 15 15 15 17 17 18 20 18 25 25 25 33 40 53 65 77

74 35 72 17 16 15 16 16 24 18 22 19 20 23 32 25 45 45 40 53 65 77

3 30 5 18 19 20 17 19 16 18 18 19 25 20 33 40 45 41 53 65 77 81

77 65 77 20 20 20 18 20 25 19 23 20 25 25 40 40 65 53 53 65 77 81

74 35 72 2 1 0 1 1 9 1 5 1 0 5 7 0 20 12 0 0 0 0

58

RESOURCE ALLOCATION

are given in Table 10). The basis of this change in logic is the attempt to stay within the availability of 1 unit of Resource 1. By reviewing the character of interviews, it has been found that we can have three groups of enumerators such that the interviews are conducted in series: in groups A, B and C, each group supervised successively by the Head, Statistical Survey (1 unit of Resource 1). Each group of enumerators is trained prior to its carrying out interviews. Thus, we have 17-21 dependent on 15-17, 21-22 dependent on 17-18, and 22-23 dependent on 18-19. By dividing the enumerators into groups, not only have we been able to stay within the resource constraint of Resource 1, but we have also reduced the overall completion time of the project from 83 to 81 weeks.

TABLE 10 Renumbered Activities for "Resource Constraint": Statistical Survey Project ACTIVITY Number

Letter

Name

0-20 0-23 0-24 15-17 17-18 17-21 17-23 18-19 21-22 22-23 23-24 24-25

Z Y B-B U-A U-B A-A-A V U-C A-A-B A-A-C W X

Arrange for Typing Clerks Obtain Calculating Equipment and Supplies Obtain Typewriters and Supplies Train Enumerator Group A Train Enumerator Group B Supervised Interviews Group A Train Statistical Clerks Train Enumerator Group C Supervised Interviews Group B Supervised Interviews Group C Analyze Returns Prepare Final Document

Table 11 now lists the renumbered activities with the resources necessary to carry out the activities. Based on the new set of activity interrelations represented in Figure 5, the resource schedule is given in Table 12. Starting with week 21, the activities are scheduled so that the project is completed with the available resources in 81 weeks (activity 15-17, "Train Enumerators Group A", is on the critical path and immediately precedes event 17). It should be

59

RESOURCE ALLOCATION

noticed from Table 12 that Resources 6, 7 and 8 have either been arranged for by preceding activities in the network, or resources have been "produced" through the operation of the project. This is the case for the enumerators and statistical clerks who are trained for their "jobs" in the project. We have now carried through all the steps prior to actually carrying out the project. At each step we built upon the previous one, with the result that the project model was refined. The effect of this refinement was to reduce the duration times of critical activities thereby reducing the overall completion time of the project; and to stay within the resources available to the project. All of these steps were carried out before actual project implementation. In other words, what we did was to simulate the project in its operation before it actually came into operation. Therefore, what we have done is to divide planning into a series of conceptual steps with the object of preparing the best plan for action possible. The statistical survey project can now be carried out.

TABLE 11 Resource Needs for Renumbered Activities Based on "Resource Constraint": Statistical Survey Project RESOURCES Activity

1

2

3

4

15-17 17-18 17-21 17-23 18-19 21-22 22-23 23-24 24-25 Resources

5

6

7

o.k. o.k. o.k.

o.k. o.k. o.k. o.k. o.k. o.k. o.k. 1 2 3 4

Head Statistical Survey Statisticians Accountant Assistant Accountant

5 Clerks 6 Statistical Clerks 7 Enumerators 8 Instructors

60

RESOURCE ALLOCATION

TIME VS. COST IN CPA

The method used above for resource scheduling is what is called a "trial and error" method. By experimentation it was found that activities can be rescheduled on the bases of their floats so that it is possible to stay within resource constraints in some cases. On the other hand, in our earlier example, it was found that by reducing the available resource units from 10 to 8, the completion time for the project was extended from 22 to 24 time units. "Trial and error" means that it is quite possible that two people might develop two different patterns of resource scheduling. This is not so surprising when we think back to the construction of the project model itself. This project model must be constructed by someone (who is responsible for the project model), and, therefore, the amount of information collected, the experience that exists for constructing project models, and perhaps the distinctive abilities of those who construct project models enter into the various steps in planning the project. What is similar about projects prepared using the methods of CPA is that we can expect them to be improvements, and usually significant improvements, over projects which have not been planned in such systematic ways. In other words, by using the methods of CPA, a project is most likely to be more efficient: it will take less time for completion and use less resources as compared to an unplanned or unsystematically prepared project. However, to come back to "trial and error" methods, it may be the case that in complex projects comprising a great many activities, the manual methods of resource scheduling we have used will not lead to the "best" result. Complexity of detail and complexity of network information call for the use of data processing equipment. It is, however, the case that in a great many government projects, similar to that of the Statistical Survey Project we have given, the number of activities is sufficiently small to allow for the use of "trial and error" methods in resource scheduling. Resource scheduling, in conjunction with construction of the project model and the determination of the critical path, is a powerful tool for planning and managing projects. We shall come back to the possible uses of data processing equipment later on.

T A B L E 12 Resource schedule for weeks 21 through

T I M E I N WEI Activity

Duration

0-20

3

0-23

30

0-24

5

9-17

1

13-16

1

15-17

5

16-17

2

17-18

8

17-21

15

17-23

20

18-19

8

21-22

13

22-23

12

23-24

12

24-25

4

Needed Resource

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

1

1

1

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

I

1

1

1

1

1

1

1

1 1

1

1

3

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

4

0

0

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

5

1

1

1

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

6

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

7

0

0

0

0

—

—

—

—

0 —

o.k.

—

o.k. Resources Available 1:1 unit 2 : 3 units 3 : n o units 4 : 1 unit 5:1 unit (with the exception that 3 units are available for activity 24-25) 6: Supplied by activity 17-23 7: Supplied by activities 15-17, 17-18 and 18-19 8:Supplied by activity 9-12

—

—

—

—

0

0

0 —

0

0

5

ABLE 12 7 through 81: Statistical Survey Project 3 IN WEEKS 48 49

50

51

52

53

54

55

56

57

58 59

60

61

62

63

64

1 1 0 1 0 0

1 1 0 1 0 0

1

1 1 0 1 0 0

1 1 0 1

1 1 0 1 0 0

1 1 0 1 0 0

1 1 0 1 0 0

1 1 0 1 0 0

1 1 0 1 0 0

1 1 0 1 0 0

1 1 0 1 0 0

1

1 1 0 1 0 0

1

-

0

1 1 0 1 0 0

0 1 0 0

0 0

1 0 1 0 0

0 1 0 0

65

66

67

68

69

1 0 0 0

3 0 0 0

1 3 0 0 0

1 3 0 0 0

1 3 0 0 0

0

0 0

0 0 0 0 —_

-

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

—

0 0

0 0

70

3 0 0 0 — o.k. 0 0 0 0

71 72

1 3 0 0 0

1 3 0 0 0

—

0 0

73

74

75

76

77

3 0 0 0

3 0 0 0

3 0 0 0

3 0 0 0

1 3 0 0 0

0 0

0 0

—

0 0

0 0

—

0 0

78 79

1 3 0 0 3

80

81

1 3 0 0 3

1 3 0 0 3

1 3 0 0 3

0 0

0 0

—

0 0

0 0

—

0 0

82

RESOURCE ALLOCATION

61

What is the "best" result for a project we plan? If we review briefly the steps in planning the project, we see that all of the subsequent analysis we carried out to determine the critical path, determine activity times and floats and to schedule resources, was based on the project model. The project model in turn was the result of our developing the logic of activity interrelations. Each activity was also conceived to be a "job", requiring time and resources to carry out the activity. The project model, therefore, is based on information which we combine in systematic ways for planning. If we think of a project based on information in this fashion, it is possible to imagine that if we continued to collect information, the nature of activities and "jobs" in the project model would be subject to continual refinement. In a very practical sense, however, information is not collected "forever". Information is "costly": it consumes time and resources in its collection. Therefore, there is some point at which we stop collecting information and draw up the project model. This point is based inevitably on judgement and upon organizational requirements. It is therefore possible that, even though our "trial and error" methods for resource scheduling give us only one possible result, a conflict exists between time and resources. In other words, it may be necessary either to extend the completion time of the project with limited resources, or to increase resources in order to meet the estimated shortest overall completion time. The imposition of a target time, shorter than the estimated overall completion time, does call for increases in resources to meet the target. A target is based on what can be called a criterion or set of criteria for choosing a specific combination of time and resources. In other words, a target enables us to decide whether we should or should not increase resources in any given instance. If we are to decide in those cases where time and resources conflict, we must have either targets which are specific 01 general criteria for choice. In economic planning, this problem of possible conflict between time and "costs" (resources) is resolved conceptually by using criteria based on the notion of "profitability". In the economic sense of "profitability", therefore, time is given a "cost" comparable to the "costs" of other resources. By "discounting" time, it is

62

RESOURCE ALLOCATION

possible conceptually to decide between resource and time conflicts that may arise through the use of the CPA method. What "profitability" enables the economist to do is to decide the present worth for each of the two possibilities: limited resources and extended completion time for the project: or increased resources and completion in the estimated shortest overall time for the project. Each of these two possibilities has a present worth which is obtained by discounting the "costs" as they occur through time and deducting them from the discounted "benefits" as they occur in time. The alternative with the highest net present worth is chosen. The notion of present worth rests upon this idea: the further away in time a "cost" or a "benefit" will occur from the present, the lower its present worth. Therefore, in deciding upon resource and time conflicts, the addition of resources increases the present worth of "costs", but by incurring extra costs the project is completed in a shorter overall time with the result that its benefits have a higher present worth. The criterion of "profitability" therefore enables us to choose: if the present value of benefits less the present value of "costs" is higher through the application of more resources as compared to staying within the constraint of limited resources with a longer project completion time, we choose to increase resources for the project. The difficulty with the economic concept of "profitability" is that it is related quite closely to "values" in markets. In other words, present worth can be calculated most easily by using the market prices for resources to determine their "costs", and by using prices for goods and services produced as the bases for calculating "benefits". These market prices are measurable in terms of money, so that "profitability" is a quantifiable concept and therefore present worths of alternatives can be compared quantitatively. For many government projects, on the other hand, "benefits" are not easily quantifiable. This is obviously the case for the Statistical Survey Project. The project "produces", i.e., it gives rise to a "service" which has usefullness within the economy, the administrative system and also within the society at large. However, it is unlikely that this "service" will be sold for what it is "worth", corresponding to a market price for a service to be sold. Moreover,

RESOURCE ALLOCATION

63

even though we try to asses the "benefits" of the statistical survey by analogy with market prices, in the sense that we ask what it might sell for, it is extremely difficult to agree upon a quantity of "benefits" to be assigned to the project. In practice, decisions about such projects as statistical surveys are made administratively, and not on the basis of present worth derived from the economic concept of "profitability". If decisions about resource and time conflicts are to be resolved by reference to the criterion of "profitability", government projects must be constructed and carried out within a framework of development planning. In other words, we can only use the concept of "profitability" if we have a broad enough context for decisions which enables us to decide to allocate resources for all projects in such a way that the present worth of the projects we choose is the highest value possible. What development planning means, therefore, is that there is a framework for choosing projects and allocating resources which is broader than the organizations which exist within government. Development planning can only be effective, therefore, if ministries and other agencies of government are subject to administrative controls which are consistent with development planning. In the absence of effective development planning, methods such as the CPA method are what are called in economics "second best solutions". If each government project is carried out without effective interconnexions with other government projects, there exist no fully consistent ways to decide upon resource and time conflicts. The CPA method is therefore applied at a lower level than is the case for development planning, assuming that it exists. Once we have said this, however, we should again emphasize the very great practical importance of CPA. By planning systematically with this method, resources are used more efficiently and projects are completed in shorter overall times as compared to unplanned or unsystematically planned projects. We can stress the fact that CPA allows us to plan more effectively. It is an improvement, and usually a substantial improvement, over unmethodical and unsystematic planning procedures.

V CPA AND DEVELOPMENT ADMINISTRATION

ADMINISTRATION AND MANAGEMENT

The term "development administration" has been developed as a contrast to the older terms "administration" or "public administration". By adding the word "development", we imply more than what is conventionally ascribed to the activities and actions of government. To take the latter, administration has the connotation of either prescribed ways of carrying on activities or that prescribed activities are carried out. Moreover, these activities are usually conceived to be of a repetitive or maintenance character. ¡I By contrast, "development" implies change and innovation. It also calls for what can be termed a "management" approach. Management rests upon the following main factors : 1. 2. 3. 4.

Perceived objectives Systematically prepared projects The scheduling (allocation) of resources Continued control over the project

All these factors depend in a very general way upon the desire to achieve the objectives (of the project) as efficiently as possible. Development administration, therefore, must be management oriented. It is true, of course, that any dichotomy between "administration" and "management" oriented actions may be misleading in that the government and organizations within government are based upon some mixture of the two approaches. This should not obscure the

CPA AND DEVELOPMENT ADMINISTRATION

65

fact that innovative activity, to be effective, must at some point be management oriented. Moreover, it is the possible conflict between the two approaches which may result in weaknesses in government actions and thereby lead to ineffective projects. In terms of the CPA method outlined, we can list some of these major weaknesses: 1. 2. 3. 4.

Little or no perception of a project plan in its totality Imprecise notion of project time Imprecise notion of jobs to be performed Imprecise notion of project's objective(s)

For the first point, it is the case that, for repetitive or maintenance functions of government, a project need not be perceived in its totality. A well-established administrative system constitutes a set of rules or rests upon habitual actions in such a way that there is no necessity either for those who "manage" or for those who participate to think of the project as a whole. This is true also for the other three main points listed: established ways of doing things and established non-changing activities do not in fact call for any conscious awareness of purpose, time or resources by those w h o t a k e

part in any project. However, whenever anything new is to be accomplished, conscious planning is invariably necessary to make that planning effective. The CPA method constitutes one important way of making planning effective.

ADVANTAGES OF CPA

With respect to the weaknesses listed above, we can outline briefly the advantages to be expected from a systematic planning method such as CPA. In the first place, when planning is separated into a number of conceptual steps, later confusions over time and resources can be largely avoided. The preparation of the "logic" model puts off to a later point the analyses of time and resources for a project. In effect, we construct a "plan", and then analyze further the requirements for putting the plan into operation. In this

66

CPA AND DEVELOPMENT ADMINISTRATION

process, we incorporate as much valid knowledge as possible (within the constraints of the "costs" of information), as well as any consciously imposed constraints such as the various kinds of "targets". In the second place, the "logic" model itself rests upon careful definition of "jobs" to be performed in carrying out the activities. One of the persistent difficulties with projects in this regard is that imprecise definitions of "jobs" lead to resource bottlenecks. In the absence of resource scheduling, at some point in carrying out the network one or more resources will be seen to be "scarce" — i.e., there will be inadequate units of these resources available to enable the network to be carried out in conformity to any predicted time schedule. An additional difficulty with inadequate job definition is that unforeseen resource "scarcities" can lead to a reduction in the quality of results: the project's objectives are not only delayed in time but are imperfectly realized. A more subtle difficulty with lack of proper job definition is that "skilled", "scarce", or "highly valuable" resources are used for activities which call for less skill, training or experience. This is a particular kind of difficulty which shows itself in recurring "bottlenecks" throughout a project's operation. Related to improper job definition is the problem of inadequate delegation of responsibility for the activities to be carried out. Along with job definition should go estimates of the kinds and amounts of resources needed and the character of supervision over the activity called for. Delegation of responsibility in this sense has to do with the ways jobs and activities are formulated. The character of supervision of a "job" can range between complete autonomy for those who carry it out in terms of the job's requirements, or complete direction of details of the job by someone who falls within the management function of the organization or management of the project. It is obviously a question of job definition as to how autonomy or the lack of it is conceived; but, from our previous discussion of the critical path as a management tool, its success depends upon delegation of responsibility in some fashion in order to make the CPA method effective. It should be clear from our earlier discussion that the success of CPA depends upon its being viewed as based upon the importance

CPA AND DEVELOPMENT ADMINISTRATION

67

of information for all the steps in project planning. When one comes to construct a "logic" model, to define jobs, to assign duration times and to schedule resources, the information needed must come from diverse sources, both within the organization as well as from outside it. If the project is to be perceived in its totality in a meaningful way, it must rest on valid knowledge which allows for its being carried out in conformity to the predicted overall completion time. Therefore, the "resources" which are necessary for the various "jobs" must "understand" the network from their points of view. In other words, the people involved in carrying out the various jobs must understand what they are to do and the relations of their particular jobs to the project as a whole. The project, to be effective, must be based on cooperative effort which is only effective through understanding. Understanding does not of course guarantee that the jobs will be carried out according to the "logic" model, but understanding is one necessary ingredient for success of the project. A great deal of the literature on CPA dealing with industrial situations stresses the fact that the CPA method can lead to a "learning process" in such a way that organizational efforts at project planning become more efficient through time. In other words, by cooperating in projects with the understanding of what a project is, people become more adept in the use of the principles of CPA. There seems to be no reason to suppose otherwise for projects carried on within government. What is required is the appreciation of systematic planning methods and the conscious attempts to apply them in practice.

THE LIMITATIONS O F THE CPA M E T H O D

We should recognize that any such method as CPA is nothing more than a set of techniques. Both its strengths and weaknesses arise from this fact. With any technique of this kind, we cannot expect that objectives, policies, or any set of desired results can be derived mechanistically by use of the technique. Objectives must be derived outside the technique: they depend upon criteria which are found within some context. The extent of this context determines in im-

68

CPA AND DEVELOPMENT ADMINISTRATION

portant ways the consistency or validity of the criteria used to formulate objectives — to choose projects. In similar fashion, criteria for carrying out projects — efficiency criteria — depend upon context. This is certainly the case for those conflicts which may arise between time and resources for carrying out projects. Only a broad enough context such as development planning would enable us to decide what to do in situations of this kind. Moreover, it is important to remember that development planning, to be effective, must be carried out administratively. Any instance of "bottlenecking" is more amenable to control if it occurs for resources directly under the control of those responsible for the project. What control means, therefore, is that those who manage the project can predict more accurately the behaviour of resources within the organization and plan through resource scheduling the elimination or reduction of bottlenecks. Notice that this can be likened to an information concept, in that resources and their behaviour within an organization are understood more fully than those outside the organization. It may therefore be the case that resource bottlenecks develop in general outside a number of projects simultaneously in operation without the understanding of those who manage the individual projects. This is again the problem of the context in which plans are constructed and carried out. If development planning is to be effective, it must collect information in relation to diverse projects and supply those responsible for the various projects with information which arises from mutual project operations. For a particular project, we have seen this problem arise in the specific form of "delivery" activities which do not lend themselves to effective control by those responsible for the project itself. Finally, it should be clear that ill-defined objectives, improper delegation of responsibility and resource bottlenecking within organizations are management weaknesses which are not solved simply or directly by appeal to the CPA method. What CPA can do is to outline these weaknesses. It cannot as a technique eliminate their causes.

VI SPECULATIONS ON CPA FOR DEVELOPMENT PLANNING

CONCEPT OF THE ENVIRONMENT

We have characterized a project as made up of activities and events logically interrelated in the project model. By scheduling resources and "managing" these resources during the project's operation, we attempt to meet the overall completion time predicted for the project. We have made the point, moreover, that "control" over the project means that those who manage the project can predict the times for activities on the bases of the information embodied in the network, including the predicted behaviour of resources. By contrast, lack of control means that activity times cannot be predicted well, even with greater and greater applications of resources to particular activities. What control means in another sense, therefore, is that resources can be managed in such a way that their uses are allocated in time. The intensity or quality of resource "output" is largely taken as a datum in the project model. In a very general way, we can identify events and activities which occur through time which are not subject to conscious management from our point of view. These activities and events may be of recurrent pattern, though we should expect that, as time goes on, "change" occurs in the sequences and times and in the character or quality of activities and events. We can speak of these phenomena as processes which occur in the environment. These environmental processes are the broad context in which projects are conceived and will take place. The same can be said for development planning. Environment processes have a history: their "origins" lie in the past; and it is on the basis of understanding their history that we

70

SPECULATIONS ON CPA FOR DEVELOPMENT PLANNING

attempt to predict what will happen in future. Prediction in this sense is the reading of history to gain insight into regular patterns or constellations of events and activities which can be expected to persist through time. When we construct a project model, we do so on the basis of our understanding of the "logic" of activity interrelations which we consider necessary for achieving the results or objectives desired for the project. Any particular activity, with its associated "job", may or may not be new to the environment. If it is new, it may involve a combination of resources and a time for the completion of the activity not found before in the environment. Its newness may also be attributed to the unique context in which the activity is found: the project model. In either case, newness can be expected to lead to some influence over the environmental processes in such a way that activity and event times are altered. If we imagine that the project is "small" relative to the environment, in other words that its activities and the resources they use have little impact upon the processes in the environment, "management" means simply the capacity to allocate resources under direct "control" so that the occurrence of activities and events of the project meets the predicted overall completion time. However, since the "control" over resources is most likely to be limited for any one project, we may speak of the project as being primarily adapted to its environment. In other words, the project conforms to the broad environmental processes occurring and does not influence them in any significant way. As we extend the number of projects under our conscious control, we can expect that they come to affect the environment by a process that we can refer to as "feedback". If we imagine that the number and scope of government projects increase through time, interrelations among these projects will come to exist and can be brought under "control". This control can manifest itself both through changes in the project models and resource uses at the project level and through an increasing perspective on the set of projects operating in the environment. For the latter, we are approaching what we have called development planning. At the project level, "feedback" becomes influential when the times and qualities of resources are affected and the activities altered. We can illustrate

SPECULATIONS ON CPA FOR DEVELOPMENT PLANNING

71

this by referring once again to the difficult type of activity we have called a "delivery" activity. If, through project planning, activities within one organization, which are also necessary within a project in another organization, become more susceptible to prediction in terms of their duration times, all projects which depend in part on this activity will become more reliable in terms of their predicted overall completion times. If we think over the character of the CPA method in this regard, we can also expect that greater activity time reliability affects resource use and the critical paths within particular projects. "Feedback" can also be "planned", in the sense that a perspective on the interrelations among projects leads to attempts to allocate resources to relieve bottlenecks which are affecting a number of projects simultaneously. Thus, for example, a realized resource scarcity which has developed because two or more projects need that resource can be dealt with by rescheduling projects, similar to the way in which we discussed scheduling resources within projects. Moreover, "feedback" can be used to create additional or new resources through the carrying out of projects which have as their "output" these resources. As we move from the individual project which is adapted to its environment to the set of projects which have been or are being brought under "control", we are moving towards the broader context of development planning. The effect is that we come to "control" the environment in the sense that we can predict more accurately activity times and resource uses for the various "jobs". Moreover, we come, as we did for the individual project, to have a greater capacity to set the times for resource uses. One important difference exists between the project and development planning in this regard. Development planning is more than the extension of the idea of altering times for activities and events in the environment. It can also, through its operation, alter the amounts and qualities of resources available. This is what we might mean by speaking of planned growth. THE DEVELOPMENT PLANNING NETWORK

Following our notions derived from the CPA method, we can

72

SPECULATIONS ON CPA FOR DEVELOPMENT PLANNING

characterize development planning as based, in most countries concerned with planning, on key events we can call National Plans. Between the events which mark the beginning and end of a national plan we can identify more detailed planning activities. Thus, for example, the national plan may be divided into sectors which have detailed plans developed for specific categories of activities. We think of sectors as based on industry, agriculture, education and so on. The distinctive characteristic about these sectors is that they are administrative concepts. They are ways of organizing activities in the environment in terms of the existing organization of government. Moreover, these administrative divisions are the bases for carrying on the planning process. They are the organizational units for carrying out the intent of the national plan. If the administrative framework for development planning is such that we have both national and sector plans, we can represent the development planning network initially in the following simplified way. In Figure 6 we have five sectors, each with an administrative organization responsible for the activities in these sectors. The first activity is the preparation of the national plan, followed by the preparation of sector plans and the preparation and implementation of sector projects. This may be considered a "logic" model, similar to the one we have drawn up for a government project itself. After the end event of the preparation of the national plan, the other concurrent "activities", which are in effect complexes of a great many other "projects" in the form of sector plans and sector projects, are shown as dependent upon the activity for preparing the national plan. If we carry through the subsequent steps of CPA, we would assign activity and event times, determine the critical path, and schedule resources for the development planning network. Our knowledge of the environment and our understanding of CPA are such that we can expect that this "logic" model does not include the interconnexions among projects of the various sectors. If the sector plans are drawn up in isolation from each other, the predicted time of the network will be greater and the available resources will not be used as "efficiently" as possible. Moreover, resource bottlenecks are likely to occur. We can illustrate the possible interrelations of projects across sectors in the following

SPECULATIONS ON CPA FOR DEVELOPMENT PLANNING

o

- o -

0

0

* 0 — - O c

0

0

Ò Fig.

Development planning network

74

SPECULATIONS ON CPA FOR DEVELOPMENT PLANNING

way. In Figure 7 we have, for the first two sets of activities, one activity preceding three other concurrent activities. If we compare these two sets of activities, we see that a dilemma exists for the planning process. In the first case, the activity "Transport and Communications" (the sector) precedes the activity "Power" (the sector), as well as the two other sector activities. In the second case, "Power" precedes "Transport and Communications". We resolve this conflict in the third case in Figure 7 by dividing the sectors into their respective projects and constructing a network of sector projects in such a way that the sectors are interrelated not only in terms of the prior activity of preparing the national plan but also in terms of the mutual interactions of the sectors within the planning process. The effect is that we can expect that the overall time for carrying out the network will be reduced. We can also expect to be able to schedule projects to minimize resource bottlenecks. This latter characterization of development planning calls for a framework in which project information is developed and "fed" back to those responsible for "managing" the national plan. Development planning is therefore a complex form of management of many projects. It can be seen that it can only function well if the organizational units — the administrative divisions of government — that draw up projects are "controlled" in ways similar to those we have outlined for resources at the project level. Those responsible for managing the national plan must be able to predict project times and resource uses and to allocate specific times to these resources. In other words, they must be able to schedule projects. We can characterize development planning, therefore, as made up of a hierarchy of managements, from the specifics of the resources having autonomous control over their "jobs", in terms of the jobs' requirements, to more detailed supervision of complexes of activities as we ascend from project management through administrative divisions to those responsible for development planning. All this management activity depends for its success upon proper delegation of responsibility, similar to delegation within any project itself. Moreover, understanding of one's "job" within the context of development planning seems a necessary ingredient for success.

SPECULATIONS ON CPA FOR DEVELOPMENT PLANNING POWER

•o

AGRICULTURE

TRANSPORT

TRE

"O

COMMUNICATIONS

INDUSTRY

-*o

TRANSPORT AND COMMUNICATIONS

O

POWER

O

AGRICULTURE

a

TRANSPORT PROJECT I

^Y

I I I

A POWER PROJECT Ï ^ V

IAGRICULTURE^A p R o i F r T iI PROJECT

Fig. 7.

O

-*o

INDUSTRY

INDUSTRY PROJECT I

75

- o

INDUSTRY PROJECTH

O

TRANSPORT PROJECT n

>

AGRICULTURE PROiFr.T n PROJECT E

p

)

^

Sector and project networks

RESOURCE BOTTLENECKS

The concept of a resource "bottleneck" is that an activity cannot be carried out on a time schedule without affecting the overall completion time of the project. The additional difficulty is that bottlenecking may cause deterioration in the quality of the results of the project. Where any resource is subject to joint-project use, solutions

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to bottlenecking can take place only if there is appeal to a context which is broader than the two projects. Moreover, this context must be one where "control" can be exercised in such a way that the decision on the allocation of the resource sets specific contexts for each project. We should notice that resource bottlenecks may not be consciously understood by those who manage individual projects. To refer to our CPA approach, we draw up the "logic" model and the associated "jobs" for the activities. Resources subject to joint-project use can therefore be "predicted" as available for each project, taken as a separate project, but if both projects attempt to operate simultaneously, "scarcity" results. The solution to the conflict over resource use lies in a perspective on the set of projects and criteria for deciding on resource allocation. CPA can be extended to cover joint-project resource use. These methods are too complex for the "trial and error" methods of resource scheduling we developed earlier. They call in most instances for the use of data processing equipment. In terms of a set of techniques, therefore, there is no insuperable difficulty in using CPA for development planning, or at the very least, for complexes of projects which can be expected to utilize the same categories of resources and which therefore call for scheduling of projects in sequence. We can argue in economic terms that the use of data processing equipment is one important way to "save" on scarce resources — in particular, scarce management resources which tend to be used for "jobs" for which they are overqualified. Management will be more "efficient" if it is freed to prepare and oversee projects rather than be absorbed into the detail of carrying out specific activities of any network. Beyond the use of techniques lies the more fundamental problem of developing a perspective on the set of projects operating in the environment. Solutions to resource bottlenecks must begin with the detail of project plans, which are the information raw materials for development planning. BUDGET RESTRAINTS

Administrative organizations, like other organizations, are subject to budgetary controls. When we come to develop the notion of

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development planning, however, there are differences that arise with respect to budgetary practices of government and those found outside government in the "economic" sectors of the economy. Government as a whole can borrow and can tax. Both constitute sources of funds for carrying out government projects. Within government, however, funds for various projects are most likely to be allocated according to procedures based on estimates of past and expected expenditures of the various administrative divisions of government. The budgetary process is therefore largely an administrative process which bears no necessary close relation to the requirements of development planning. The effect of this budgetary process can be that bottlenecks arise in the financing of projects. If we conceive of project planning and the carrying out of projects as a continual process within the administrative organizations of government, the budget of any administrative organization occurs as an event in this process. In terms of CPA, one method of coping with such an event (a kind of "delivery" affecting a number of projects) is to arrange the projects in sequence so that there will be minimum interruption in the flows of activities which make up all the steps of preparing and carrying out projects. However, to look at the budgetary process in this way is to give a particular weight or value to the continual flow of project activity. It is to apply a criterion for deciding among the various projects that are candidates for financing. Other criteria which assign different weights or values to different projects might result in a different sequence of projects and interruptions in the flow of project activity. When we view development planning as the interconnexions of projects across sectors, budgets as events are seen clearly as restraints upon the planning process. We should distinguish between the amounts of funds available to finance all government projects and the distribution of these funds among administrative organizations. These administrative organizations will have in some cases deficits — a shortage of funds — in terms of development planning, whilst others will have surpluses — funds unused for carrying out projects. This situation is equivalent to that of resource bottlenecks. To make development planning effective, funds must be allocated in relation to "control" by management — which means that those re-

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sponsible for development planning must also allocate — i.e., schedule — funds, similar to the scheduling of resources. We might speculate that the budgetary allocation of funds could be supplemented by an institutional system within government whereby surplus funds from one administrative organization were "loaned" to organizations having deficits. This would be a system analogous to that found within financial systems of industrial countries. Any distribution or redistribution of funds, however, to be effective for development planning, must be related to some overall development planning network composed of the individual projects of the national plan or the development planning process.

THE CONCEPT OF EFFICIENCY

We have used the word "efficiency" in a narrow and a much broader sense in our discussions on the CPA method. In its narrow sense at the individual project level, efficiency means either achieving a "target" time for a project with the least use of resources, or completing a project in the shortest overall possible time with the fixed resources available. The use of a "target" time is based on a criterion for choice, as is that situation where we attempt to minimize project time with fixed resources. General criteria for choosing combinations of project completion times and resources to be used depend, as we have indicated, on a context which comprises all projects which use all available resources. The use of adjusted "prices" (sometimes called "shadow prices") in economic planning rests conceptually on such a context for resource use. We should emphasize once again that any context for development planning which does not embrace the allocation of all resources either directly or through a set of projects which indirectly influences the environment, can be expected to lead to "second best solutions". In this sense, therefore, development planning can be looked upon as ideally typical though not fully existing in practice. If this is the case, as it is found in reality in underdeveloped countries, development planning is at best a closer approximation to efficiency as compared to projects conceived and carried out in isolation from

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each other. This does not mean that the differences are insignificant: development planning, if it is effective, is more "efficient", and considerably more efficient than planning at the individual project level. What we can emphasize is that "efficiency" is in its most general sense the achievement of objectives with the least time and resources. The character of development planning is such that the "feedback" process affects objectives, alters duration times for activities and their environmental sequences and alters the qualities and times at which resources are available. In other words, "efficiency" is not something to be defined once and for all but a process itself which does or does not exist in the environment. As a process it exists or comes to exist when planning is conscious — when objectives are formulated and ways found to carry out those objectives. In terms of conscious planning, efficiency can be measured against some fixed standard for a period of time. The "feedback" process alters the standard through time by which efficiency is measured. When we equate efficiency with conscious planning, we are raising once again the importance oí management. Behind management must lie the motivation to "control". Control does not mean the minute direction of actions which make up the various "jobs". It means at the most altering time sequences, where possible, to minimize project completion time or resource use, or both. Management "control" is therefore of a regulatory nature, a balancing of activities and the resources necessary for their "jobs". This notion of regulation permeates conscious planning from the detailed level of a "job" to the management function of those responsible for development planning. Management is carried on to achieve objectives, but "control" is itself a process of adjustment among "conflicts", "restraints", "targets", "bottlenecks" and the like. If "efficiency" is an ideal, or more appropriately, a scale which can for a period of time measure performance, we can emphasize once again the use of a planning method such as CPA at any level of planning. The conscious attempt to "manage" leads towards efficiency even without the framework necessary for effective development planning. Even without this framework, we can apply CPA for "second best solutions".

SELECT BIBLIOGRAPHY

Archibald, R. D. and R. L. Villoría, Network-Based Management Systems (London: John Wiley & Sons Inc., 1967). Battersby, A., Network Analysis for Planning and Scheduling (London: Macmillan & Co. Ltd., 1967, Second Edition). British Productivity Council, Critical Path Analysis, Eighteen Case Histories (London, 1966). Collins, F. T., Network Planning and Critical Path Scheduling (Berkeley, Cal.: Know How Publications, 1964). Lockyer, K. G., An Introduction to Critical Path Analysis (London: Sir Isaac Pitman & Sons Ltd., 1967). Lowe, C. W., Critical Path Analysis by Bar Chart (London: Business Publications Ltd., 1968). Morris, L. N., Critical Path, Construction and Analysis (London: Pergamon Press, 1967). Martino, R. L., Finding the Critical Path (Volume I of Project Management and Control [New York: American Management Association, 1964]). Reynaud, C. B., The Critical Path, Network Analysis Applied to Building (London: George Godwin Ltd., 1967). Shaffer, L. R., J. B. Ritter and W. L. Meyer. The Critical Path Method (New York: McGraw Hill Co. Inc., 1965). Woodgate, H. S., Planning by Network (London: Business Publications Ltd., 1967, Second Edition). Articles J. G. Barmby, "The Applicability of PERT as a Management Tool", IRE Transactions on Engineering Management (September, 1962), 130-1. B. M. Christensen, "Network Models for Project Scheduling", Machine Design, Part I - Planning Phase (10 May 1962), 114-24. Part II - Preliminary Scheduling Phase (24 May 1962), 173-78. Part III - Advanced Scheduling Phase (7 June 1962), 132-40. Part IV - Preparation of Network Model (21 June 1962), 155-62. Part V - Preparing Computer Data (5 July 1962), 105-14. Part VI - Choosing a Plan (19 July 1962), 136-42. R. E. Cooke-Yarborough, "Critical Path Planning and Scheduling", Review

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of Marketing and Agricultural Economics 32 (1964), 36-48. A. K. Giles and L. G. Bennett, "Network Analysis, A Technique of Work Planning in Agriculture and Horticulture", Agriculture 73, No. 6, 284-90. J. E. Kelley Jr. and M. R. Walker, "Critical-Path Planning and Scheduling", 1959 Proceedings of the Eastern Joint Computer Conference (December 1959), 160-73. J. E. Kelley Jr., L. D. Wilson and H. Berman, "Using Critical Path Programming", Automation (November 1962), 90-95. R. K. Levy, G. L. Thompson and J. D. Wiest, "The ABCs of the Critical Path Method", Harvard Business Review (September-October 1963), 98-108. J. J. Moder, "Without A Computer", Engineering News-Record (14 March, 1963), 31-36. G. Nevill and D. Falconer, "Critical Path Diagramming", International Science and Technology (October 1962), 43-49. (No Author), "Using Pert for New-Product Production", Management Review (June 1966), 67-71.

CHAPTERS I, II and III Lockyer, K. G., Critical Path Analysis, Problems and Solutions (London: Sir Isaac Pitman & Sons Ltd., 1966). Articles R. D. Archibald, "Pert/CPM Management System for the Small Subcontractor", Technical Aids for Small Manufacturers (March-April 1964), 1-4. E. L. Buesnel, "Using Network Planning in the Office - A Review of Problems and Possibilities", Office Management (Spring 1967), 24-37. G. B. Davis, "Network Techniques and Accounting - With an Illustration", National Association of Accountants Bulletin (May 1963), 11-18. W. Dusenburg, "Applying Advanced Science to Marketing and Ad Plans", Printers Ink 292 (September 1965), 15-21. W. B. Glassford, "Critical Path Scheduling", Plant Administration and Engineering 21, No. 10 (October 1961), 59-62. J. Hollingum, "Production Planning with PERT", Metalworking Production (20 March 1963), 53-57. J. N. Kennedy, "Network Scheduling of Accounting Operations", Financial Executive (June 1963), 15-21. H. Walton, "Critical Path Method - How to Start?" Chemical and Process Engineering (April 1964), 183-90. T. G. Wyant, "Critical Path Network Analysis of a Course", Technical Education and Industrial Training (October 1965), 456-58. (No Author), "Production Planning and Evaluation", Mechanical Engineering (June 1964), 48-52. (No Author), "Critical Path Analysis, A Tool for the Management Accountant", The Accountant (9 December 1967), 750-53.

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CHAPTER IV Archibald, R. D. and R. L. Villoría, Network-Based Management Systems (London: John Wiley and Sons, 1967). Chapter 6, "Cost and Manpower", 119-37. Morris, L. N., Critical Path Analysis, Eighteen Case Histories (London 1966). Chapter 7, "Allocation of Resources", 63-84. Shaffer, L. R., J. B. Ritter and W. L. Meyer, The Critical Path Method (New York: McGraw Hill, 1965). Chapter VII, "Resource Scheduling: CPM-I", 89-109. Articles A. R. Burgess and J. B. Killebrew, "Variation in Activity Level on a Cyclical Arrow Diagram", The Journal of Industrial Engineering XIII, No. 2, 76-82. W. Cosinuke, "The Critical-Path Technique for Planning and Scheduling", Chemical Engineering (25 June 1962), 113-18. H. S. Woodgate, "Network Planning Techniques as an Aid to Management", Systems and Communications, Part I (November 1965), 34-39; and Part II (December 1965), 34-37.

CHAPTER V Archibald, R. D. and R. L. Villoría, Network-Based Management Systems (London: John Wiley and Sons, 1967). Chapter 8, "Organizing the Integrated System", 161-73. Articles C. E. Law and D. C. Lach, "Implementing the Critical Path Method in a Large Organization", CORS Journal 4 (1966), 35-47. W. S. Ryan, "Network Analysis in Forming a New Organisation", CAS Occasional Paper Number 3 (H M Treasury, London, HMSO, 1967). P. P. Schoderbek and L. A. Digman, "Third Generation, PERT/LOB", Harvard Business Review (September-October 1967), 100-110.

CHAPTER VI Archibald, R. D. and R. L. Villoría, Network-Based Management Systems (London: John Wiley and Sons, 1967). Chapter 12, "Multiproject Integration", 214-33. Lambourn, S., Resource Allocation (An Introduction to the Allocation of

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Limited Resources to Projects Described by the Network Analysis Method of PERT, Critical Path Method, etc.) (London: Industrial & Commercial Techniques Ltd., September 1965). Articles R. M. de Baun, "Switching Network Analysis Methods", Chemical and Engineering News 42 (22 June 1964), 84-90. D. G. Boulanger, "Program Evaluation and Review Technique", Advanced Management (July-August 1961), 8-12. E. Grasberg, "Network Analysis: Development Project Formats - A Design for Maximum Information", Development Digest V, No. 2 (July 1967), 1-30. S. Lambourn, "Resource Allocation and Multi-Project Scheduling (RAMPS) A New Tool in Planning and Control", Computer Journal 5 (1963), 300-304. A. A. McGee and M. D. Markarian, "Optimum Allocation of Research/Engineering Manpower Within a Multi-Project Organizational Structure", IRE Transactions on Engineering Management (September 1962), 104-108. J. N. Noettl and P. Brumbaugh, "Information Concepts in Network Planning", Journal of Industrial Engineering (July 1967), 428-35. N. Stahl, "Information Networking", Mechanical Engineering (December 1964), 34-38. B. O. Szuprowicz, "Network Planning and Economic Development", New Scientist 345 (27 June 1963), 728-30.

MATHEMATICAL REFERENCES Articles J. A. Carruthers and A. Battersby, "Advances in Critical Path Methods", Operational Research Quarterly 17, No. 4, 359-80. C. E. Clark, "The Optimum Allocation of Resources Among the Activities of a Network", The Journal of Industrial Engineering 12, No. 1, 11-17. R. A. Bildson and J. R. Gillespie, "Critical Path Planning - Pert Integration", Operations Research 10 (November/December 1962), 909-15. D. R. Fulkerson, "Expected Critical Path Lengths in Pert Networks", Operations Research 10 (November/December 1962), 808-17. S. E. Elmaghraby, "An Algebra for the Analysis of Generalized Activity Networks", Management Science 10, No. 3 (April 1964), 494-514. S. E. Elmaghraby, "On the Expected Duration of Pert Type Networks", Management Science 13, No. 5 (January 1967), 299-306. R. J. Freeman, "A Generalized Network Approach to Project Activity Sequencing", IRE Transactions on Engineering Management EM-7 (1960), 103-8. D. R. Fulkerson, "A Network Flow Computation for Project Cost Curves", Management Science 7 (January 1961), 167-78. W. R. King and T. A. Wilson, "Subjective Time Estimates in Critical Path Planning - A Preliminary Analysis", Management Science 13, No 5,

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(January 1967), 307-20. R. M. Oliver and A. H. Samuel, "Reducing Letter Delays in Post Offices", Operations Research 10 (November/December 1962), 839-92. A. A. B. Pritsker and W. W. Happ, "GERT: Graphical Evaluation and Review Technique", The Journal of Industrial Engineering 17, No. 5, 267-301.

MISCELLANEOUS REFERENCES Articles R. T. Boverie, "The Practicalities of PERT", IEEE Transactions on Engineering Management (March 1963), 3-5. D. E. Greene, "PERT for Materials Handling", Mechanical Handling 50, (August 1963), 442-47. H. W. Paige, "How PERT/Cost Helps the General Manager", Harvard Business Review (November/December 1963), 87-95. J. W. Pocock, "Pert as an Analytical Aid for Problem Planning - Its Payoff and Problems", Operations Research 10 (November/December 1962), 893-903. D. D. Roman, "The PERT System: An Appraisal of Program Evaluation Review Technique", Journal of Advanced Management (April 1962), 57-65. T. V. Sobszak, "A Look at Network Planning", IRE Transactions on Engineering Management (September 1962), 113-16.