DOCUMENT RESUME

ED 067 991 HE 003 416

TITLE PERT and CPM: Workshop Material.INSTITUTION Burroughs Corp., Detroit, Mich.PUB DATE [ 72]NOTE 35p.

EDRS PRICE MF-$0.65 HC-$3.29DESCRIPTORS *Administrator Guides; *Educational Administration;

*Higher Education; Information Syttems; *ManagementInformation Systems; *Management Systems

ABSTRACTThis is a workbook containing problems in PERT

(program evaluation review technique) . It is intended to be used in aworkshop or classroom to train management personnel in the basicmethodology and capability of PERT. This material is not adequate indepth to create an expert in these techniques, but it is felt thatthe material is adequate to provide a working understanding of themethodology as a management tool. It is assumed that this workbook isused under the guidance of an experienced instructor. (Author)

55

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PERT AND CPM:WORKSHOP MATERIAL

A MANAGEMENT SCIENCE SERIES PRESENTATION

Burroughs Corporation 0Detroit.. Michigan 48232

INTRODUCTION

This is a workbook containing problems in PERT tech-niques. It is intended to be used in a workshop or class-room to train management personnel in the basic method-ology and capability of PERT techniques. This material isnot adequate in depth to create an expert in these techniquesbut it is felt that the material is adequate to provide aworking understanding of the methodology as a managementtool. It is assumed that this workbook is used under theguidance of an experienced instructor. A computer is notessential in order to utilize this problem material fortraining purposes. A training course is, however, enhancedif a computer demonstration is integrated with this class-room work.

iii

3

PREFACE

Management decision making, like invention, is no longer amatter of one's individual effort. Project accomplishmentis made through organizations of professional experts inadministration, finance, science, engineering and produc-tion, to list just a few. The complexity of directing andcontrolling programs has challenged conventional manage-ment techniques for years. In our complex and ever ex-panding world of science and industry more effective toolsare required for planning, analyzing and controlling thedevelopment of products.

Courses in PERT (program evaluation review technique)are given regularly. Mountains of literature have beenwritten and published describing its methodology and uses.Undoubtedly, more has been written on the subject of criti-cal path method and PERT-like techniques than on anyother scheduling and controlling tool in all of our industrialhistory. Computer manufacturers have spent hundreds ofthousands of dollars developing software to fill the re-quests of computer hardware users. Our government haspoured millions into proving PERT's validity.

One might say, PERT is industry's better mouse trap.

Let us go back in time to what we might call the birth ofPERT and see how it has evolved through its use of networkand critical path planning.

Work began in January 1957. The basic development wascarried on by Messrs. M. E. Walker and J. E. Kelly, Jr.,of DuPont and Remington Rand UNIVAC Divisionrespectively.

While this technique was being developed, a parallel devel-opment was under way by a program evaluation researchtask force team at the special projects office of the U. S.Navy's Bureau of Ordinance. This project team was direc-

4

ted to research and develop improved methods of planningand controlling the far reaching complex programs fordeveloping our nation's fleet ballistic missiles. Improve-ments in management methods are and have been continu-ally sought. Therefore , this objective was laudable butcertainly not new.

Phase 1 report, issued by the special projects office of theBureau of Naval Weapons, U. S. Navy in July 1958, pre-sented the basic principle and technical parameters ofPERT and outlined the proposed installation pattern. Whilesome modifications to the concept have been made since,the basic concept still remains the same, and so, whatstarted out to be a program evaluation research task forcebecame a program evaluation review technique (PERT).

In its basic format the PERT plan of controlling programsis similar in format to any other type of project controltechnique where a series of tasks are scheduled in a logicalsequence , building events and activities up to achievementof a final objective. Generally, this was done through Ganttcharting. Product performance is specified and resourcesare allocated; then, the achievement of each task and thefinal objective were presented. However, Gantt chartingdoes not depict the dependencies of activities nor does itprovide the manipulative capability necessary in analyzingalternatives and planning and controlling complex projectprograms. Present computer-based network analysismodels whether known as PERT or CPM have added powerto project management.

Grossly oversimplified, the network planning approachinvolves:

1. The selection of specific, identifiable events whichmust occur to successfully conclude a project.

2. The sequence of these events and the establishmentof interdependencies of events so that a project net-work can be developed.

vi

3. The establishment of time required in doing an activ-ity to achieve an event together with a measurementof the uncertainty involved.

4. Design of an analysis or evaluation procedure toprocess and evaluate data.

5. The establishment of information and communicationchannels to bring actual achievement data and changedata to the evaluation point.

6. The application of electronic data processing equip-ment to the analysis procedure.

. The end product to be a periodic summary evaluationfor each level of management "need to know" whereproblems appear and alternate courses of action willbe presented for consideration.

The basic concepts of project costs as they are associatedwith PERT can only be achieved if Time, Resources andPerformance, are managed and manipulated within a com-mon framework of work elements .

Let's now look at these variables and define them. Sincethe duration of any project is depondent on the times tocomplete the various required activities it is obvious thata range of durations is possible for the project dependingon the selected time allowed each job. This selection oftime also incorporates a selection of costs . The range ofproject duration and costs may be plotted graphically. Thestarting point of the curve is found by taking the normaltime and cost for each job; any shorter duration time for anactivity will result in a higher cost due to premium pay-ments for some or all of the operations necessary inallowing for early completion. Of course, this can only bedone after the initial planning stages have been completedand the project has been optimized to remove slack timewherever possible. In any project there are hundreds ofpossibility combinations for time and cost durations.Through the use of a computer we can examine these rangesand the best duration can be selected.

vii

viii

The basic information generated in a PERT/COST systemcan be summarized in several ways for program manage-ment reporting. The format detail in which this informationis presented will vary depending upon the planning and con-trol requirements of different levels of management.E s s e n t ially , the reports provide managers with thefollowing information in varying degrees of detail:

1. The current project activity plan, time schedule andproject duration

2. Time and cost performance to date with relation tothe plan

3. Time and cost projections of the project objectives.

Identification of the project objectives is the first step inthe PERT/Cost process. These objectives should be spec-ified in terms of the end item that is deliverable. The sub-sequent division of each of these items into its componentparts creates a project work breakdown structure whichthen serves as the framework for planning and controllingthe project. To be most effective a PERT/Cost installationshould begin in the planning phase of a project at the timethe request for proposal is made. The project work break-down structure also serves as the basis for construction ofthe planning network. The configuration and content of thework breakdown structure and its specific work packageswill vary from project to project and will depend on thefollowing considerations:

1. The size and complexity of the project2 . The structure of the organization3. Method for handling the work4. The specific amount of detail desired

The work package formed at the lowest level of breakdownthen constitutes the basic units in the PERT/Cost systemby which actual costs are obtained and compared with es-timates for purposes of cost control.

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In summary, the work breakdown structure represents thefollowing subdivisions of work:

1. Project end items2. End items subdivision3. The work packages4. Activities .

The end item approach to planning and control ensures thatthe total project is fully planned and that all derivativeplans contribute directly to the desired objective . Thelevel of detail to which it is desirable to apply PERT/Costis largely a matter of judgment. For this reason it is un-realistic to specify a predetermined level of detail.

Time and/or Cost overruns are a basic concern to all of in-dustry. The PERT system attempts to provide a reasonabledegree of pertinent project information which will serve asa planning and control vehicle, enabling efforts to be guidedmore economically, purposefully and expeditiously then inthe past.

1A. PROJECT: Paint House

ACTIVITIES: Buy PaintMix PaintPaint HousePaint TrimClean Brushes

1B. PROJECT: Lay Pipe

ACTIVITIES: Dig TrenchLay PipeBackfill

1C. PROJECT: Lay Pipe

ACTIVITIES: Start TrenchFinish TrenchStart Laying PipeFinish Laying PipeStart BackfillFinish Backfill

1

2A.

O

2B.

2C.

2

0

ACTIVITIES

A 1.2BCDE

A

ACTIVITIES

ABC

ACTIVITIES

O

3A. ACTIVITIES: PlasterInstall PlumbingObtain Plumbing FixturesErect Shell

3B. PROJECT: Build House

ACTIVITIES: Lay FoundationInstall PlumbingObtain Bricks and LumberErect ShellAcquire LotObtain Concrete BlocksSign Closing PapersPaint InteriorObtain Plumbing FixturesPlasterExcavatePaint Exterior

3

4. Calculation of Expected Time (te), Earliest Expected Time(TE), Latest Allowable Time (TL) and Slack.

ActivityFrom To

Opti-misticTime

Most LikelyTime

Pessi-mistic ExpectedTime Time (te)

1 2 1 2 341 3 2 2

2 3 2 4 63 4 1 3 81 4 3 4 6

82 5 2 473 6 1 3

4 6 2 4 95 6 1 1 2

Earliest Expected Latest AllowableTime (TL) SlackEvent Time. {TE)

1

2

3

45

6

4 12

5. PROBLEM: Compute (1) te; (2) TE; (3) TL; (4) Slack

ActivityFrom To

Opti-misticTime

Most LikelyTime

Pessi-mistic ExpectedTime Time (te)

1 2 8 9 16251 3 15 20152 3 8 13

72 4 5 661 5 3 6

3 6 8 8 84 6 3 8 10

64 7 1 5

5 7 11 11 143 8 4 6 8

146 8 3 4147 8 1 9

Event

1

23456

7

8

Earliest Expected Latest AllowableTime (TL) SlackTime (TE)

135

R.

6A. Use of Normal Distribution to Estimate Probability of aGiven Occurrence.

58 60 62 64 66 68 70-30 -20 --la +la +2a +3 Or

Expected Value

Assume: Heights of American females are normally dis-tributed. Average height is 5' 4" or 64 inches.Variance in heights is 4 inches.

58 60 62 64 66 68 70

-30 -20 -la 0 +la -1-217+30

What percentage of females are less than 5' 2" tall?What percentage are more than 5' 8" tall? %What height do 84 % of females exceed ?

6B. Use of Normal Distribution to Estimate Probability ofMeeting Schedule.

- TLook up

Ts

a TE

Ein table.

Ts -147T

TE TE

7. Table of Values of the Standard Normal DistributionFunction

Ts - TE Probability; Ts - TE Probability

Q TE arrE

-3.0 .1 % .1 54.0 %-2.9 .2 % .2 57.9 %-2.8 .3 % .3 61.8 %-2.7 .4 % .4 65.5 %-2.6 .5 % .5 69.2 %

-2.5 .6 % .6 72.6 %-2.4 .8 % .7 75.8 %-2.3 1.1 % .8 78.8 %-2.2 1.4 % .9 81.6 %-2.1 1.8 % 1.0 84.1 %

-2.0 2.3 % 1.1 86.4 %-1.9 2.9 % 1.2 88.5 %-1.8 3.6 % 1.3 90.3 %-1.7 4.5 % 1.4 91.9 %-1.6 5.5 % 1.5 93.3 %

-1.5 6.7 % 1.6 94.5 %-1.4 8.1 % 1.7 95.5 %-1.3 9.7 % 1.8 96.4 %-1.2 11.5 % 1.9 97.1%-1.1 13.6 % 2.0 97.7 %

-1.0 15.9 % 2.1 98.2 %- .9 18.4 % 2.2 98.6 %- .8 21.2 % 2.3 98.9 %- .7 24.2 % 2.4 99.2 %- .6 27.4 % 2.5 99.4 %

- .50'9 %34.5%

2.6 99.5 %- .4 3 2.7 99.6 %- .3 38.2 % 2.8 99.7 %- .2 42.1 % 2.9 99.8 %- .1 46.0 % 3.0 99.9 %

.0 50.0 %

15

8. Calculation of Variance (a 2) and Probability

ActivityFrom To

Opti-misticTime

MostLikelyTime

Pessi-mistic Expected VarianceTime Time (te) (472)

1 2 1 2 3

1 3 2 2 42 3 2 4 6

3 4 1 3 8

1 4 3 4 6

2 5 2 4 8

3 6 1 3 7

4 6 2 4 9

5 6 1 1 2

Earliest Expected Variance Scheduled Proba-Event Time (TE) (0,2) Time bility

123456

8

16

7

13

9. PROBLEM:

Ac tivityFrom To

Compute (1) a2 ; (2) Probability

Opti- Most Pessi-mistic Likely mistic Expected VarianceTime Time Time Time (te) (a2)

1 2 8 9 161 3 15 20 252 3 8 13 152 4 5 6 71 5 3 6 63 E 8 8 84 6 3 8 104 7 1 5 6

145 7 11 113 8 4 6 86 8 3 4 147 8 1 9 14

Earliest Expected Varignce ScheduledEvent Time (TE)

1234567

8

(Q) Time

; 17

24

30

35

Proba-bility

9

2

10. Calculation of PERT Output without Network Diagram.

A. Sort activities into topological sequence.B. To compute Earliest Expected Times:

1. Enter 0 as TE for first event(s).2. Take activities one by one in forward sequence.3. Add te for an activity to TE for its beginning event.

If the result is greater than the TE for its endingevent, enter it as the TE for its ending event.

C. To compute Latest Allowable Times:1. Enter TE (or TD, if there is one) as TL for last

event(s).2. Take activities one by one in backward sequence.3. Subtract te for an activity from TL for its ending

event. If the result is less than the TL for its begin-ning event,enter it as the TL for its beginning event.

Activity Expected Activity ExpectedFrom To Time (te) From To Time (te)

7 8 8.54 6 7.51 3 20.04 7 4.51 2 10.01 5 5.55 7 11.53 8 6.03 6 8.02 3 12.56 8 5.52 4 6.0

Earliest Expected Latest AllowableEvent Time (TE) Time (TL) Slack

12345678

10 18

11. PROBLEM: Given standard PERT input, produce standardPERT output report.

ActivityFrom

STANDARD PERT INPUTINTERMEDIATECALCULATIONS

To

Opti-misticTime

MostLikelyTime

Pessi-mistic Expected VarianceTime Time (te) (a2)

1 2 2.0 4.0 9.08.01 3 3.0 7.0

1 4 3.0 6.0 9.02 4 5.0 5.0 5.0

10.03 4 2.0 3.02 5 6.0 8.0 10.04 5 10.0 12.0 20.03 6 1.0 9.0 17.0

10.04 6 1.0 4.05 6 5.0 6.0 7.03 7 4.0 7.0 7.05 7 6.0 15.0 18.0

12.06 7 1.0 5.0

Directed Delivery Time (TD) for Project = 39.0Scheduled Time (Ts) = 39.0 for Event 7 and 10.0 for Event 4

STANDARD PERT OUTPUT

Earliest Latest Sched- Vari-Expected Allowable uled ange Proba-

Event Time (TE) Time (TL) Slack Time (a') bility

1234567

12. Calculation of CPM Activity-Oriented Output.

A. Earliest Start for an activity is equal to the TE of itsbeginning event.

B. Latest Finish for an activity is equal to the TL of itsending event.

C. Earliest Finish for an activity is equal to its EarliestStart plus its Expected Duration.

D. Latest Start for an activity is equal to its Latest Finishminus its Expected Duration.

E. Float for an activity is equal to its Latest Start minusits Earliest Start (or Latest Finish minus EarliestFinish).

PERT COMPUTATIONS

Earliest Expected Latest AllowableEvent Time (TE) Time (TL) Slack

1 , 0.0 0.0 0.0 *2 2.0 2 . 0 0.0 *3 6.0 6.0 0.0 *4 9.5 9.5 0.0 *5 6.3 7.7 1.46 14.0 14.0 0.0 *

CPM COMPUTATIONS

ActivityFrom To

Expected Earliest Latest Earliest LatestDuration Start Start Finish Finish Float

1 2 2.01 3 2.32 3 4.03 4 3.5

4.21 44.32 5

3 6 3.34 6 4.5

1.25 6

12

20

r. 13. PROBLEM: Given PERT event times, produce standardCPM activity-oriented output report.

x.

PERT COMPUTATIONS

Earliest Expected Latest AllowableEvent Time (TE) Time (TL) Slack

1 0.0 0.0 0.0 *2 10.0 10.0 0.0 *3 22.5 22.5 0.0 *4 16.0 23.0 7.05 5.5 16.0 10.56 30.5 30.5 0.0 *7 20.5 27.5 7.08 36.0 36.0 0.0 *

STANDARD CPM OUTPUT REPORT

Activity Expected Earliest Latest Earliest LatestFrom To Duration Start Start Finish Finish Float

1 2 10.01 3 20.02 3 12.52 4 6.01 5 5.53 6 8.04 6 7.54 7 4.55 7 11.53 8 6.06 8 5.57 8 8.5

2113

14. Types of Activity Float and Their Significance in Scheduling.

TE = 13TL = 17

TE =14TL = 15

Total Float: The maximum time that is available to do ajob, mimus its expected duration.

Activity TotalFrom To Float

13 1414 1613 1613 1515 16

Free Float: The float available to an activity if all activitiesare started as early as possible.

Activity FreeFrom To Float

13 1414 1613 1613 1515 16

Independent Float: The float available to an activity if allpreceding activities are started as late as possible andall succeeding activities are started as early as possible.

14

/15. Examination of the Tradeoff Between Time and Cost Con-

siderations in Planning a Project.

ActivityFrom To

NormalTime

NormalCost

CrashTime

Crash IncrementalCost Cost per Week

1 2 3 $ 500 2 $10001 3 7 $ 800 4 $26002 3 5 $1000 4 $14002 4 8 $ 850 6 $14503 4 4 $1000 2 $2400

al 15

16. Examination of the Tradeoff Between Time and Cost Consider-ations in Planning a Project.

Project Direct Indirect TotalDuration Costs Costs Cost

8 $1100

9 $1400

10 $1850

11 $2750

12 $3850

10,000

9,000

8,000

7,000

Cost 6,000

in 5,000

Dollars 4,000

3,000

2,000

1,000

0

16

7 8 9 10 11 12

Duration in Weeks

2,4

AIM

17A. Projected Requirements for a Given Resource for Activitiesin a Project.

ActivitY

Time Data FromNetwork

Requirements for Resource )0Cby Month

is EarlyStart

LateStart

1 2 3 4 5

1 - 2 2 0 0 8 8

1 - 3 2 0 4 2 1

2 -3" 4 2 2 2 3 4 4

1 - 4 4 0 5 1 2 3 2

3 -4 3 6 6 6 6 2

2 - 5 4 2 8 1 2 3 3

3 - 6 3 6 11 1 2 1

4 - 6 5 9 9 2 1 3 3 2

5 - 6 1 2 6. 12 II 4 5

17B. Projected Financial Requirements for Activities in a Project.

Activ-Time Data Financial Requirements by Month

($000)Totality

ts Sched.Begin 1 2 3 4 5

1- 2 2 9 9 18

1 -3 2 3 2 5

2 - 3 4 2 3 5 3 13

1 - 4 4 2 3 4 21

11

3 - 4 3 9 5 2 16

2 - 5 4 1 2 2 8

3 - 6 3 2 2 2 6

4 - 6 5 1 2 1 2 4 10

5 - 6 2 3 4 7

C'g 17

18A. PROBLEM: Compute the projected monthly requirementsfor Resource XX, assuming that each activity begins on itsEarliest Start.

Activity EarlyStart

Project Month

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 - 2 0

1 - 3 0

2 - 3 2

1 - 4 0

3 - 4 6

2 - 5 2

3 - 6 6

4 - 6 9

5 - 6 6

Total

18B . Graphical Presentation of Monthly Requirements for ResourceXX.

Man-Months

18

1110

9876543210

1 2 3 4 5 6 7 8 9 10 11 12 13 14Project Month

.--- 26

19A. PROBLEM: Schedule activities in the project so as to levelthe monthly requirements for Resource XX.

ActivitySchedStart

Project Month

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 - 21 - 32 - 31 - 43 - 42 - 53 - 64 - 65 - 6Total

19B. Graphic ilresentation of Monthly Requirements for Resource)0C.

1110

987

Man- 6

Months 543210

1 2 3 4 5 6 7 8 9 10 11 12 13 14Project Month

19

20A. PROBLEM: Compute the projected financial requirementsfor the project, using Table 17B and the schedule developedin Table 19A.

ActivitySchedStart

Project Month

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 - 2

1 - 32 - 31 - 43 - 42 - 53 - 64 - 65 - 6Total

Cumulative Total

20B. Graphical Presentation of Financial Requirements of Project.

1110

987

Dollars 6(000) 5

43210

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14Project Month

28,

21A. Table showing financial status of activities in the project atthe end of the tenth month.

Activity

Actuals Reported by Month Actualto

Date

Latest Estimates Totalto

Compl1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 - 2 7 8 7 22 22

1 - 3 1 2 3 3

2 - 3 3 2 2 5 12 12

1 - 4 2 4 1 4 11 11

3 - 4 7 2 1 10 10

2 - 5 2 2 6 2 3 15

3 - 6 3 3 1 5 12

4 - 6 2 4 3 3 6 18

5 - 6 4 5 9

Total 7 8 7 6 8 3 9 7 2 3 60 9 7 8 8 7 11 110

Cumul.Total 7 15 22 28 36 39 48 55 57 60 69 76 84 92 99 110

21B. PROBLEM: Produce basic PERT /COST Management Sum-mary Report.

PERT/COST MANAGEMENT SUMMARY REPORT

Work Performed to Date Totals at Completion

ActivityFrom To

1 21 32 31 43 42 5

3 64 65 6

Total

ActualValue Cost

Over- Planned Latest Over-Run Cost Estimate Run

21

22A. PROBLEM: Tabulate planned, actual and latest estimates ofproject costs, using cumulative totals from Tables 20A and21A.

Project Month

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Planned

Actual

LatestEstimate

22B. Graphical Presentation of PERT/COST Data.

120

100

80

60Dollars

(000) 40

20

0

0

22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Project Month

30

BIBLIOGRAPHY

Churchman, C. W.: Introduction to Operations Research,John Wiley & Sons , Inc., New York, 1957.

Clark, C.: "The Optimum Allocation of Resources amongthe Activities of a Network," Journal of Industr i a lEngineering, January-February, 1961.

Cost Reduction through Better Management in the FederalGovernment, Executive Office of the President, Bureauof the Budget, April, 1963.

DOD/NASA PERT/COST Guide, U. S. Government PrintingOffice, Washington, D.C., June, 1962.

Forrester, J. W.: Industrial Dynamics, The M .I.T.Press , Massachusetts Institute of Technology ,

Cambridge, Mass., 1961.Kelly, J. E., Jr.: "Critical Path Planning and Scheduling:

Mathematical Basis," Operations Research, vol. 9, pp.296-320, May-June , 1961.

Malcolm, D. G.: "Extensions and Applications of PERT asa System Management Tool," Operations Research, Inc.,Silver Springs, Md., March, 1961.

Miller, Robert W.: "How to Plan and Control with PERT,"Harvard Business Review, March-April, 1962.

Miller, Robert W.: Schedule, Cost, and Profit Control withPERT, McGraw-Hill Book Company, Inc., 1963.

Packard, K.: "Probabilistic Forecasting of ManpowerRequirements," IRE Transactions on Engineer ingManagement, vol. EM-9, no. 3, September, 1962.

Pearlman, Jerome: "Engineering Program Planning andControl through the Use of PERT," IRE Transactions onEngineering Management, vol. 7, pp. 125-134, 1960.

"PERT/COST Output Reports," Supplement No. 1, DOD/NASA PERT/COST Guide, 1963.

"PERT Guide for Management Use," U. S. GovernmentPrinting Office, August, 1963.

Roseboom, J., C. Clark, W. Fazar and D. Malcolm:"Application of a Technique for Research and DevelopmentProgram Evaluation," Operation s Research, vol. 7,no. 5, September-October, 1959.

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/NOTES

En

NOTES

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