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Quantitative Analysis for Management

Quantitative Analysis for Management. Chapter 13 Project Management. Chapter Outline. 13.1 Introduction 13.2 PERT 13.3 PERT/COST 13.4 Critical Path Method. Learning Objectives. Students will be able to Understand how to plan, monitor, and control projects with the use of PERT.

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Quantitative Analysis for Management

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  1. Quantitative Analysis for Management Chapter 13 Project Management 13-1

  2. Chapter Outline 13.1 Introduction 13.2 PERT 13.3 PERT/COST 13.4 Critical Path Method 13-2

  3. Learning Objectives Students will be able to • Understand how to plan, monitor, and control projects with the use of PERT. • Determine earliest start, earliest finish, latest start, latest finish, and slack times for each activity along with the total project completion time. 13-3

  4. Learning Objectives - continued • Reduce total project time at the least total cost by crashing the network using manual or linear programming techniques. • Understand the important role of software in project management. 13-4

  5. Project Management Models • PERT • PERT/Cost • Critical Path Method 13-5

  6. Questions That May Be Addressed by PERT and CPM 1. When will the project be completed? 2. What are the critical activities or tasks in the project? 3. Which are the noncritical activities? 4. What is the probability that the project will be completed by a specific date? 5. Is the project on schedule, ahead of schedule, or behind schedule? 13-6

  7. Questions - continued 6. Is the project over or under the budgeted amount? 7. Are there enough resources available to finish the project on time? 8. If the project must be finished in less than the scheduled amount of time, what is the best way to accomplish this at least cost? 13-7

  8. Project Planning, Scheduling, and Controlling Project Planning 1. Setting goals 2. Defining the project 3. Tying needs into timed project activities 4. Organizing the team Project Scheduling 1. Tying resources to specific activities 2. Relating activities to each other 3. Updating and revising on regular basis Project Controlling 1. Monitoring resources, costs, quality and budgets 2. Revising and changing plans 3. Shifting resources to meet demands Before Project During Project 13-8

  9. Six Steps Common toPERT and CPM 1. Define the project and all significant activities/tasks. 2. Develop relationships among the activities. Identify precedence relationships. 3. Draw the network. 4. Assign time and/or cost estimates to each activity. 5. Compute the longest time path (critical path) through the network. 6. Use the network to help plan, schedule, monitor, and control the project. 13-9

  10. Advantages of PERT/CPM • Useful at several stages of project management • Straightforward in concept, not mathematically complex • Uses graphical displays employing networks to help user perceive relationships among project activities • Critical path and slack time analyses help pinpoint activities that need to be closely watched 13-10

  11. Advantages - continued • Networks generated provide valuable project documentation and graphically point out who is responsible for various project activities • Applicable to a wide variety of projects and industries • Useful in monitoring not only schedules, but costs as well 13-11

  12. Limitations of PERT/CPM • Project activities must be clearly defined, independent, and stable in their relationships • Precedence relationships must be specified and networked together • Time activities in PERT are assumed to follow the beta probability distribution -- must be verified • Time estimates tend to be subjective, and are subject to fudging by managers • There is inherent danger in too much emphasis being placed on the critical path 13-12

  13. General FoundryPERT 13-13

  14. General Foundry, Inc.PERT Network (Construct Collection Stack) (Install Control System) 4 2 C A (Build Internal Components) F H (Build Burner) E 6 1 7 (Inspect and Test) (Modify Roof and Floor) (Install Pollution Device) G B D 3 5 (Pour Concrete and Install Frame) 13-14

  15. Beta Probability Distribution with Three Time Estimates 13-15

  16. General Foundry, Inc. Time Estimates a m b E(t) 2 Activity 2 A B C D E F G H 1 2 1 2 1 1 3 1 2 3 2 4 4 2 4 2 3 4 3 6 7 9 11 3 2 3 2 4 4 3 5 2 3 - 1 1 æ ö = ç ÷ 6 9 è ø 2 4 - 2 1 æ ö = ç ÷ 6 9 è ø 2 3 - 1 1 æ ö = ç ÷ 6 9 è ø 2 6 - 2 4 æ ö = ç ÷ 6 9 è ø 2 7 - 1 9 æ ö = ç ÷ 6 9 è ø 2 9 - 1 16 æ ö = ç ÷ 6 9 è ø 2 11 - 3 16 æ ö = ç ÷ 6 9 è ø 2 3 - 1 1 æ ö = ç ÷ 6 9 è ø Total: 25 weeks 13-16

  17. General Foundry, Inc.PERT Network - with E(t) t=2 4 2 C t=3 A F t=2 H t=4 E 6 1 7 t=2 t=3 G t=5 B D 3 5 t=4 13-17

  18. General Foundry, Inc.PERT Network ES/EF, LS/LF 2 4 2 4 4 7 10 13 0 2 0 2 13 15 13 15 4 8 4 8 8 13 8 13 0 1 1 4 3 7 4 8 t=2 4 2 C t=3 A F t=2 H t=4 E 6 1 7 t=2 B G t=3 t=5 D ES EF LS LF 3 5 t=4 13-18

  19. General Foundry, Inc.PERT Network - Critical Path 4 2 C A F H E 6 1 7 G B Total time: 15 D 3 5 13-19

  20. General FoundrySchedule & Slacks 13-20

  21. General Foundry Meeting a Deadline Project Standard Deviation, T = Project Variance Due Date - Expected Completion Date Z = T 16 - 15 = = 0.57 1.76 0.57 Standard Deviations Probability (T  16 Weeks) is 71.6% 15 16 Time - weeks 13-21

  22. PERT Provided • Project expected completion date: 15 weeks • Probability of finishing in 16 or fewer days: 71.6% • Identity of activities on critical path: A, C, E, G, and H • Identity of activities with slack: B, D, and F • Detailed schedule of start/finish dates 13-22

  23. General FoundryPERT - Use of Dummy 13-23

  24. General Foundry, Inc.PERT Network - with Dummy (Construct Collection Stack) (Build Internal Components) (Install Control System) 4 2 C F A H (Build Burner) E Dummy 6 1 7 (Inspect and Test) (Install Pollution Device) G B (Modify Roof and Floor) D 3 5 (Pour Concrete and Install Frame) 13-24

  25. General Foundry, Inc.PERT Network - with Dummy t=2 4 2 C t=3 A F t=2 H t=4 Dummy t=0 E 6 1 7 t=2 t=3 G t=5 B D 3 5 t=4 13-25

  26. PERT - Sensitivity Analysis 13-26

  27. General Foundry, Inc. PERT & Budgeting Total Budgeted Cost Budgeted Cost per Week Earliest Start (ES) Latest Start (LS) Expected Time, t Activity 0 0 2 3 4 4 8 13 0 1 2 4 4 10 8 13 2 3 2 4 4 3 5 2 $22,000 $30,000 $26,000 $48,000 $56,000 $30,000 $80,000 $16,000 $11,000 $10,000 $13,000 $12,000 $14,000 $10,000 $16,000 $ 8,000 A B C D E F G H Total $308,000 13-27

  28. General FoundryBudget Ranges 13-28

  29. General FoundryMonitoring & Controlling 13-29

  30. Critical Path MethodSteps in Project Crashing 1. Find normal critical path and identify critical activities. 2. Compute crash cost per week for all activities. 3. Select critical activity with smallest crash cost per week. Crash this activity 4. Check to make sure critical path is still critical. If not, find the new one. Return to step 3. 13-30

  31. General FoundryNormal/Crash Costs & Times 13-31

  32. Crash & NormalTimes and Costs Crash Cost Crash Cost - Normal Cost Crash Cost = - per Week Normal time Crash time Activity Cost 34000 - 30000 = 3 - 1 $34,000 $33,000 $32,000 $31,000 $30,000 Crash 4000 = = 2000 per week 2 Normal Normal Cost Time (Weeks) 1 2 3 Crash Time Normal Time 13-32

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