Project Management: PERT/CPM Chapter 9 Project Management: PERT/CPM

Project Planning & Scheduling Projects consist of numerous separate jobs Managers schedule/coordinate activities for on time completion of the project Interdependence of activities make this difficult Answer questions such as: Total time to complete the project Start and finish dates Critical activities Delay of noncritical activities before they become critical

Elements Of Project Planning Define project objective(s) Identify activities Establish precedence relationships Make time estimates Determine project completion time Compare project schedule objectives Determine resource requirements to meet objective 5

Project Scheduling What to do? Critical Path Method (CPM) DuPont & Remington-Rand (1956) deterministic task times activity-on-node network construction (AON) Project Evaluation & Review Technique (PERT) U.S. Navy, Booz, Allen & Hamilton multiple task time estimates (probabilistic) activity-on-arrow network construction (AOA)

PERT/CPM Develop a network model Determine activity times Uncertain times use an estimating method Certain times use CPM Analyze Network Find critical path Variability Time/Cost Trade offs

Networks and PERT/CPM Network analysis Simple PERT analysis Shortest route problem Minimal spanning tree Maximum flow Algorithm Simple PERT analysis Finding critical path using CPM Sensitivity analysis critical/gating activities time/cost tradeoffs

PERT/CPM CPM Shortest Route problem Minimal Spanning Tree Maximal Flow minimizes the distance from an origin to a destination Minimal Spanning Tree most economical way to find a connecting route transportation networks computer/communication networks distribution networks Maximal Flow problems involving restrictions on flow between nodes

Monitoring & Gantt Charts Popular tool for project scheduling Graph with bar for representing the time for each task Provides visual display of project schedule shows both planned and completed activities against a time scale Shows slack for activities (amount of time activity can be delayed without delaying project) 7

A Gantt Chart 4 10 6 8 3 1 5 7 9 Month Activity 2 Design house and 4 10 6 8 3 1 5 7 9 Month ½ Activity Design house and obtain financing Lay foundation Order and receive Materials Build house Select paint Select carpet Finish work 8

Critical Path A path is a sequence of connected activities running from the start to the end node in a network The critical path is the path with the longest duration in the network A project cannot be completed in less than the time of the critical path 13

Network Construction In AON, nodes represent activities & arrows show precedence relationships In AOA, arrows represent activities & nodes are events for points in time An event is the completion or beginning of an activity A dummy shows precedence for two activities with same start & end nodes 11

Precedence Table Job Precedence Time 1 Contact Client - 4 2 Write Proposal 3 Obtain Approval Complete Programming 12 5 Complete Industry Review 10 6 Write Final Draft 4, 5 7 Complete Oral Report 11

Project Network/Precedence Diagram Complete Industry Review Complete Oral Report 5 7 Complete Programming Write Proposal 1 2 4 6 Contact Client 3 Write Final Draft Obtain Approval 12

Early Start Times ES - earliest time activity can start Forward pass starts at beginning of network to determine ES times EF = ES + activity time ESj = maximum (EF) EFi = ESi + ti ES1 = 0 EF1 = ES1 + t1 = 0 + 4 = 4 days 16

Computing Early Times ES2 = max (EF1) = 4 days EF2 = ES2 + t2 = 4 + 2 = 6 days EF3 = ES3 + t3 = 6 + 3 = 9 days EF4 = ES4 + t4 = 9 + 12 = 21 days 17

Earliest Start Times Table Job ES EF 1 Contact Client 4 2 Write Proposal 6 3 Obtain Approval 9 Complete Programming 21 5 Complete Industry Review 10 Write Final Draft 27 7 Complete Oral Report 26 11

Late Times LS - latest time activity can start & not delay project Backward pass starts at end of network to determine LS times LF - latest time activity can be completed & not delay project LSi = LFi - ti LFi = minimum (LS) 18

Computing Late Times LF7 = 27 days LS67 = LF7 - t6 = 27 - 5 = 22 days LF5 = minimum (LS6, LS7) = min(21,22) = 21 days LS5 = LF5 - t5 = 21 - 10 = 11 days 19

Latest Start Times Table Job LS LF 1 Contact Client 4 2 Write Proposal 6 3 Obtain Approval 9 Complete Programming 21 5 Complete Industry Review 11 Write Final Draft 27 7 Complete Oral Report 22 11

Activity Slack Activities on critical path ES = LS EF = LF slack = 0 Activities not on critical path have slack Si = LSi - ESi or Si = LFi - EFi S5 = LS5 - ES5 = 11 - 0 = 11 days S7 = LS7 - ES7 = 27 - 26 = 1 day 21

1--->2--->3--->4--->6 The Critical Path The critical path is the path with the longest duration in the network A project cannot be completed in less than the time of the critical path Therefore, 1--->2--->3--->4--->6 is the critical path for the project 13

Project Crashing Shorten durations of critical tasks by adding more resources ($) or changing task scope Crashing refers to analyzing the tradeoff of compressing the duration of tasks versus cost to compress those tasks Managers use this technique to balance project time constraints with project budget constraints