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Chapter 10 Project Scheduling: PERT/CPM Critical Path Scheduling Project Scheduling with Uncertain Activity Times PERT and CPM PERT (program evaluation and review technique) – U.S. Navy Special Projects Office (1958) – Polaris missile project CPM (critical path method) – J. E. Kelly of Remington-Rand and M. R. Walker of Du Pont (1957) – Scheduling maintenance shutdowns of chemical processing plants Precedence Relationships Predecessor and Successor Activities Activity A is called a predecessor of activity B if activity A needs to be completed before activity B can be started. In this case, activity B is called a successor of activity A. Note: An activity may have more than one predecessor and/or more than one successor. Example: Development of a Compact Recording Device A : Design device B : Build prototype C : Evaluate assembly equipment D : Test prototype E : Write methods specification report F : Write assembly equipment evaluation report G : Write final report Precedence Relationships: Recording Device Development Immediate Activity Predecessor(s) A - B A C A D B E C, D F C, D G E, F Precedence Relationships: Recording Device Development Activities C and D are the immediate predecessors of activity E. What are all of the predecessors of activity E? We call activity E an immediate successor of both activities C and D. How many immediate successors does activity C have? What are all of the successors of activity C?

Chapter 10 Project Scheduling: PERT/CPMutminers.utep.edu/solis/qmb 3301/QMB 3301 su05/Project Scheduling.pdfChapter 10 Project Scheduling: PERT/CPM zCritical Path Scheduling zProject

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Page 1: Chapter 10 Project Scheduling: PERT/CPMutminers.utep.edu/solis/qmb 3301/QMB 3301 su05/Project Scheduling.pdfChapter 10 Project Scheduling: PERT/CPM zCritical Path Scheduling zProject

Chapter 10

Project Scheduling: PERT/CPM

Critical Path SchedulingProject Scheduling with Uncertain Activity Times

PERT and CPMPERT (program evaluation and review technique)

– U.S. Navy Special Projects Office (1958) – Polaris missile project

CPM (critical path method)– J. E. Kelly of Remington-Rand and M. R. Walker

of Du Pont (1957)– Scheduling maintenance shutdowns of chemical

processing plants

Precedence RelationshipsPredecessor and Successor Activities• Activity A is called a predecessor of activity B if

activity A needs to be completed before activity B can be started.

• In this case, activity B is called a successor of activity A.

Note: An activity may have more than one predecessor and/or more than one successor.

Example: Development of a Compact Recording Device

A : Design deviceB : Build prototypeC : Evaluate assembly equipmentD : Test prototypeE : Write methods specification reportF : Write assembly equipment evaluation report G : Write final report

Precedence Relationships: Recording Device Development

ImmediateActivity Predecessor(s)

A -B AC AD BE C, DF C, DG E, F

Precedence Relationships: Recording Device Development

Activities C and D are the immediate predecessors of activity E. What are all of the predecessors of activity E? We call activity E an immediate successor of both activities C and D.How many immediate successors does activity C have? What are all of the successors of activity C?

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Precedence Relationships: Recording Device Development (cont.)

Does activity A have an immediate predecessor?Does activity G have an immediate successor?

Estimating Activity DurationEstimated duration for each activity stated in terms of specified time unit– months, weeks, or days

Usually difficult in practiceIn certain instances, multiple time estimates are used– optimistic– most likely– pessimistic

Activity Duration Estimates: Recording Device Development

Immediate EstimatedActivity Predecessor(s) Duration (weeks)

A - 12B A 5C A 7D B 2E C, D 4F C, D 7G E, F 2

Prerequisites for Critical Path Analysis

A project must have:

well-defined jobs or tasks whose completion marks the end of the project;

independent jobs or tasks; and

tasks that follow a given sequence.

Steps in the CPM with Single Activity Time Estimate

1. Activity Identification2. Activity Sequencing and Network Construction3. Determination of the Critical Path

– From the critical path all of the project and activity timing information can be obtained

Activity on Node (AON)Network RepresentationNetwork consists of nodes & arcs

A CB

Arc(precedencerelationshipbet. activities)

Node(activity)

2 4 3

Activity time estimate

Page 3: Chapter 10 Project Scheduling: PERT/CPMutminers.utep.edu/solis/qmb 3301/QMB 3301 su05/Project Scheduling.pdfChapter 10 Project Scheduling: PERT/CPM zCritical Path Scheduling zProject

Activity on Arrow (AOA)Network Representation

1 32Construct forms Pour concrete

Arcs represent activities

AON vs. AOA Network Representation

In AON, nodes represent activities & arcs show precedence relationships.In AOA, arcs represent activities & nodes are ‘events’ (completion or beginning of an activity).Difference between AOA and AON only in form. AOA and AON are conceptually equivalent.We use AON.

AON Network Diagram: Necessary Elements

Nodes representing activitiesArcs representing precedence relationships between activitiesActivity time estimates (single or multiple)

Constructing the Network Diagram: Our Conventions

Predecessor node must be drawn to the left of its successor node/sSuccessor node must be drawn to the right of its predecessor node/sNo vertical arcs No arcs moving from right to leftThus, network clearly flows from left to rightDraw arrowheads on arcs

Network Diagram : Recording Device Development

A,12

B,5

C,7

D,2

F,7

E,4

G,2

‘Forward Pass’: Earliest Times

ES = earliest time activity can startForward pass starts at beginning of CPM/PERT network to determine ES timesUsually set ES = 0 for beginning activityEF = ES + t

• ES = largest EF of immediate predecessors• Why?

Page 4: Chapter 10 Project Scheduling: PERT/CPMutminers.utep.edu/solis/qmb 3301/QMB 3301 su05/Project Scheduling.pdfChapter 10 Project Scheduling: PERT/CPM zCritical Path Scheduling zProject

‘Backward Pass’: Late Times

LS = latest time activity can start & not delay projectBackward pass starts at end of CPM/PERT network to determine LS timesUsually set LF = EF for last activityLS = LF – t

• LF = smallest LS of immediate successors• Why?

Activity Slack, S

SlackS = LS - ES = LF - EF

Activity is a critical activity if ES=LS & EF=LFS = 0

Activity is not critical if it has positive slackS > 0

Critical Path

Path: sequence of connected activities running from start to end node in network.Critical path: path consisting entirely of critical activities.Critical path has longest duration among all paths on network.

Critical Path

Duration of critical path = earliest project completion time. Project cannot be completed in less than length (duration) of critical path.Activity slack: meaning?Critical path in project control: significance?Is critical path unique?

Critical Path Scheduling with 3 Activity Time Estimates

Reflect uncertainty of activity timesBeta distribution is used in PERT

a = optimistic time estimatem = most likely time estimateb = pessimistic time estimate

where

64 : time(expected)Mean bmat j

++=

22

6 :Variance ⎟

⎠⎞

⎜⎝⎛ −

=ab

Example

2.52.01.5F, HI

5.04.03.0GH

7.03.53.0B, DG

3.02.01.0EF

1.51.00.5B, DE

2.52.01.5CD

3.02.01.0-C

6.02.52.0AB

2.52.01.5-A

PessimisticMost LikelyOptimisticPredecessor/sActivity

Time (weeks)Immediate