PERT and CPM Networks

Chapter 5Scheduling the Project

Copyright 2005 John Wiley & Sons, Inc.

PERT AND CPM NETWORKS


MEM 612 Project Management

HistoryLate 1950sProgram Evaluation and Review Technique (PERT)U.S. Navy, Booz-Allen Hamilton, and Lockeheed AircraftProbabilistic activity durationsCritical Path Method (CPM)Dupont De Nemours Inc.Deterministic activity durations



The Language of PERT/CPMActivitytask or set of tasksuse resourcesEventstate resulting from completion of one or more activitiesconsume no resources or timepredecessor activities must be completed



The Language of PERT/CPM continuedMilestonesevents that mark significant progressNetworkdiagram of nodes and arcsused to illustrate technological relationshipsPathseries of connected activities between two events



The Language of PERT/CPM concludedCritical Pathset of activities on a path that if delayed will delay completion of projectCritical Timetime required to complete all activities on the critical path



Building the NetworkAOA NetworkAON Network



Table 5-1 A Sample Set of Project Activities and Precedences


Task

Predecessor

a

--

b

--

c

a

d

b

e

b

f

c, d

g

e


Figure 5-1 Stage 1 of a Sample AON Network



Figure 5-2 Stage 2 of a Sample AON Network



Figure 5-3 A Completed Sample AON Network



Figure 5-4 Stage 1 of a Sample AOA Network



Figure 5-5 Stage 2 of a Sample AOA Network



Figure 5-6a A Completed Sample AOA Network



Figure 5-6b A Completed Sample AOA Network Showing the Use of a Dummy Task



Table 5-2 A Sample Problem for Finding the Critical Path and Critical Time


Activity

Predecessor

Duration

a

--

5 days

b

--

4

c

a

3

d

a

4

e

a

6

f

b, c

4

g

d

5

h

d, e

6

i

f

6

j

g, h

4


Figure 5-7 Stage 1 of a Sample Network



Figure 5-8 A Complete Network



Figure 5-9 Information Contents in an AON Node



Figure 5-10 The Critical Path and Time for Sample Project



Calculating Activity SlackSlack or FloatLST - EST = LFT - EFT = Slack



Figure 5-11 An MSP Version of PERT/CPM Network



Figure 5-12 A Modified Version of MSP Network


PROJECT UNCERTAINTY AND RISK MANAGEMENT



Calculating Probabilistic Activity TimesThree Time Estimatespessimistic (a)most likely (m)optimistic (b)



Figure 5-13 The Statistical Distribution of all Possible Times for an Activity



Activity Expected Time and Variance



95 Percent LevelTask will be a or lower 5 percent of the timeTask will be b or greater 5 percent of the time



90 Percent LevelTask will be a or lower 10 percent of the timeTask will be b or greater 10 percent of the time



95 Percent Level (Alternative Interpretation)Task will be between a and b 95 percent of the time



90 Percent Level (Alternative Interpretation)Task will be between a and b 90 percent of the time



Figure 5-14 An AON Network



Figure 5-15 An MSP Version of a Sample Problem Network



Figure 5-16 A Pert/CPM Network for the Day Care Project



Figure 5-17 An MSP Calendar for the Day Care Project, 4/16/00 to 5/27/00



The Probability of Completing the Project on Time=NORMDIST(D,,,TRUE)



Figure 5-18 The Statistical Distribution of Completion Times of the Path a-b-d-g-h



Selecting Risk and Finding DNORMINV(probability,,,TRUE)


SIMULATION



Traditional Statistics Versus SimulationSimilaritiesmust enumerate alternate pathsDifferencessimulation does not require assumption of path independence


THE GANNT CHART



Figure 5-23 A Gantt Chart of a Sample Project



Figure 5-24 A Gantt Chart of Sample Project Showing Critical Path, Path Connections, Slack, EST, LST, EFT, and LFT



Figure 5-25 A Gantt Chart of a Day Care Project Showing Expected Durations, Critical Path, Milestone, and Resource Requirements



Figure 5-26 A Progress Report on a Day Care Project Showing Actual Progress Versus Baseline


EXTENSIONS TO PERT/CPM



Precedence DiagrammingFinish-to-start linkageStart-to-start linkageFinish-to-finish linkageStart-to-finish linkage



Figure 5-27 Precedence Diagramming Conventions



Other MethodsGraphical Evaluation and Review Technique (GERT)combines flowgraphs, probabilistic networks, and decision treesallows loops back to earlier events and probabilistic branching



CopyrightCopyright 2005John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information herein.


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PERT and CPM Networks