reid & sanders, operations management © wiley 2002 project management 17 c h a p t e r

Reid & Sanders, Operations Management© Wiley 2002

Project Management 17C H A P T E R


Learning Objectives

• Describe the project life cycle• Describe the critical path method (CPM)• Describe the program evaluation & review technique

(PERT)• Distinguish Activity-on-Arrow (AOA) & Activity-on-

Node Diagrams• Estimate the completion time of a project• Identify critical activities that cannot be delayed

without delaying the project• Calculate the amount of available slack for non-

critical activities


Definitions

• Project:– An endeavor with specific objectives & multiple

activities with defined precedence relationships, to be completed within a limited duration

• Activities:– Specific tasks that must be completed & require

resources

• Precedence relationships:– A natural order between activities, where some

tasks must be complete before others can begin


Project Life Cycle

• Conception

• Feasibility analysis or study

• Planning

• Execution

• Termination


Network Planning Techniques

• Critical Path Method (CPM):– Developed to coordinate maintenance projects in

the chemical industry– A complex undertaking, but individual tasks are

routine (tasks’ duration = deterministic)

• Program Evaluation & Review Technique (PERT):– Developed to manage the Polaris missile project– Many tasks pushed the boundaries of science &

engineering (tasks’ duration = probabilistic)


Both CPM & PERT

• Graphically display the precedence relationships & sequence of activities

• Estimate the project’s duration

• Identify critical activities that cannot be delayed without delaying the project

• Estimate the amount of slack associated with non-critical activities


Notation

• Activity-on-Arrow (AOA):– Each arrow represents an activity & its

precedence relationship(s)– May require the use of “dummy” arrows if the

activity has more than one successor task– Nodes used only as end-points for arrows

• Activity-on-Node (AON):– Uses nodes to represent the activity– Uses arrows to represent precedence

relationships


AOA & AON Comparison


Example

Activity DescriptionImmediate

PredecessorDuration (weeks)

A Develop product specifications None 4B Design manufacturing process A 6C Source & purchase materials A 3D Source & purchase tooling & equipment B 6E Receive & install tooling & equipment D 14F Receive materials C 5G Pilot production run E & F 2H Evaluate product design G 2I Evaluate process performance G 3J Write documentation report H & I 4K Transition to manufacturing J 2


AOA Diagram


AON Diagram


Add Activity Durations


Identify Unique Paths


Calculate Path Durations

• The longest path (ABDEGIJK) limits the project’s duration (project cannot finish in less time than its longest path)

• ABDEGIJK is the project’s critical path

Paths Path durationABDEGHJK 40ABDEGIJK 41ACFGHJK 22ACFGIJK 23


Calculating the Slack of Non-Critical Activities

• All activities on the critical path have zero slack

• Slack defines how long non-critical activities can be delayed without delaying the project

• Slack = the activity’s late finish minus its early finish (or its late start minus its early start)


Calculate Activities’Early Starts & Finishes


Calculate the Activities’Late Starts & Finishes


Calculate Slack

ActivityLate

FinishEarly Finish

Slack (weeks)

A 4 4 0B 10 10 0C 25 7 18D 16 16 0E 30 30 0F 30 12 18G 32 32 0H 35 34 1I 35 35 0J 39 39 0K 41 41 0


Revisit Example UsingProbabilistic Time Estimates

Activity DescriptionOptimistic

timeMost likely

timePessimistic

timeA Develop product specifications 2 4 6B Design manufacturing process 3 7 10C Source & purchase materials 2 3 5D Source & purchase tooling & equipment 4 7 9E Receive & install tooling & equipment 12 16 20F Receive materials 2 5 8G Pilot production run 2 2 2H Evaluate product design 2 3 4I Evaluate process performance 2 3 5J Write documentation report 2 4 6K Transition to manufacturing 2 2 2


Use Beta Distribution to Estimate Expected Task Durations

6

cpessimistilikelymost 4optimistic timeExpected


Expected Task Durations

ActivityOptimistic

timeMost likely

timePessimistic

timeExpected

timeA 2 4 6 4B 3 7 10 6.83C 2 3 5 3.17D 4 7 9 6.83E 12 16 20 16F 2 5 8 5G 2 2 2 2H 2 3 4 3I 2 3 5 3.17J 2 4 6 4K 2 2 2 2

6

cpessimistilikelymost 4optimistic timeExpected


Build AOA Network& Identify Paths


Estimate Path Durations

• ABDEGIJK is the expected critical path & the project has an expected duration of 44.83 weeks

Activities on paths Expected durationABDEGHJK 44.66ABDEGIJK 44.83ACFGHJK 23.17ACFGIJK 23.34


The End

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reid & sanders, operations management © wiley 2002 project management 17 c h a p t e r

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