PROJECT MANAGEMENT WITH CPMPERT 1 Project Management Project

PROJECT MANAGEMENT WITH CPM/PERT 1

Project Management • Project Definition • Consists of a series of tasks (or activities) with following characteristics • • Starting and ending dates Well-defined objectives Unique endeavor Utilizing resources • Primarily Management Functions • Planning • Organizing • Controlling 2

Project Management Functions l PM functions are to manage l l l Cost and time Human resources Communication Contract/procurement Risk 3

Project Management • When to use • • • Complex projects Several parallel tasks Predefined deadlines and milestones must be met Estimate project completion time Difficult to know when project is in trouble Limited and conflicting resources 4

Examples • • • Building a new airport Expanding a plant Designing a new product Construction projects of all types Maintenance projects R&D projects 5

Project Planning Process l l l l Define project objective(s) Identify activities Establish precedence relationships Make time estimates Determine project completion time Schedule activities Balance resources to meet objective(s) 6

Typical Questions for PM’s l l l What is the total time to complete a project? What are the scheduled start and finished dates for each activity? Which activities are critical and must be completed on time to keep the project on schedules? How long can noncritical activities be delayed before they cause a delay in the project completion time? Is there any way to reduce the project completion time? How much money is needed to expedite the project completion time? 7

Project Management Techniques • Critical Path Method (CPM) • Developed in 1950’s • Planed and control maintenance job of a chemical plant • Reduced length of maintenance shutdown by 40% • Project Evaluation and Review Technique (PERT) • Developed in 1960’s • Planed and control the Polaris missile project • Speeded up project by 2 years 8

Critical Path Method (CPM) • Graphical method of showing relationship of project activities • An activity or task --takes resources and time to complete • Precedence relations (some must be completed before others can start) must be constructed • Critical Path Method is the longest path through the resulting project network 9

Precedence Relations Activity Immediate Predecessor Duration (days) A B C D E (Start) A A A B, C, D 8 6 8 10 4 10

Simple Project Network “Activity on Node” AON representation Precedence relations represented by “arcs” Successor B Predecessor A D E C Project Network 11

Simple Project Network “Activity on Arc” AOA representation 2 B 0 A 6 1 6 C 8 D 10 3 E 4 4 4 12

Activity Start/Finish Times (AON) Activity Name Early Start Time EF ES LS Late Start Time Early Finish Time D LF Late Finish Time Activity Duration 13

Finding the Critical Path B A C C E D 14

Forward Pass 8 B 14 6 0 A 8 8 8 C 16 8 18 E 22 4 8 D 18 105 15

Backward Pass 8 B 14 12 6 18 0 A 8 0 8 8 8 C 16 10 8 18 18 E 22 18 4 22 8 D 18 8 105 18 16

Finding Activity Slack S =EF-ES = LF-EF 8 B 14 S =18 -14=4 14 6 18 S =8 -8=0 0 A 8 0 8 8 Critical Path: Path with zero activity slacks S =22 -22=0 8 C 16 10 8 18 S =18 -16=2 18 E 22 18 4 22 8 D 18 5 8 10 18 S =18 -18=0 17

Example Consider the following activities of a project Activity Predecessors Time (wks) A. none 4 B. none 12 C. B 6 D. A 16 E. A, C 12 F. B 16 G. E, F 10 H. D, G 0 18

Project Network D A Finish E Start C B G F 19

PERT (Program Evaluation and Review Technique) • Similar to Critical Path Method (CPM) • Uncertainty in activity duration • Provides estimates of project duration probabilities • Best used for highly uncertain projects • new product development • first-time projects • R&D projects 20

Dealing with Uncertain Activity Duration l The PERT three-estimate Approach l Most likely estimate (m) l l Optimistic estimate (b) l l estimate of the most likely value of duration estimate of the duration under the most favorable conditions Pessimistic estimate (a) l estimate of duration under the unfavorable conditions 21

A Simple Example Activity Most Optimistic (a) Most Likely (m) Most Pessimistic (b) A 2 8 14 B 3 6 9 C 5 7. 5 13 D 3 10. 5 15 E 2. 5 11. 5 22

Distribution Assumption density Beta distribution a m Expected Time = b a + 4 m + b 6 (b - a)2 Variance = 36 activity duration 23

Expected Duration & Variance Activity A a + 4 m + b 2+4(8)+14 ET = = = 8. 0 6 6 Var = (b - a)2 36 (14 -2)2 = =4 36 24

Expected Duration & Variance Activity Expected Time Variance Critical Path? A 8 4 ? B 6 1 C 8 1. 77 D 10 4 ? E 4 2. 33 ? 25

Probability of Completion Probability that a project will be completed by a specified due date z= Due Date - Expected Completion Date Sum of the Variances on the Critical Path Normal Distribution Expected Completion z Due Date 26

Completion Probability Example What is the probability of completing the project within 24 days? z= 24 - 22 4 + 2. 33 = 0. 624 From a Z-table for standard Normal distributions: Probability of completion = 0. 7324 = 73. 2% 27

Considering Time-Cost Trade-offs • If extra money is spent to expedite the project, what is the least expensive way of attempting to meet the target completion time? • Define Normal and crash points • Normal point shows the time and cost when an activity is performed in the normal way • Crash point shows the time and cost when an activity is fully crashed 28

Time-Cost Relationship • Assumed linear relationship Crash Cost Normal Cost Crash cost/wk= (Crash cost-Normal cost) (Crash time-Normal time) Normal Crash time Normal time 29

Example Time (wk) Activity A B C D E Normal 8 6 8 10 4 Crash 6 5 5 9 3 Cost($1000) Crash 10 7 10 8 7 Normal Max. Red. 8 2 5 1 4 3 6 1 6 2 Cost/wk 2/2=1 2/1=2 6/3=2 2/1=2 1/1=1 30

Crashing An Activity 31

Other Project Mgmt Techniques • Resource leveling • How to schedule resources (equipment, people) to minimizes • Multiple resource scheduling • How to schedule resources when activities can require more than one resource type • Cash flow and budgeting • Combine cash and budget information with project scheduling to track expenditures, project cash flows 32

Problems 1. A project involving the installation of a computer system comprises eight activities. The following table lists immediate predecessors and activity times (in weeks). Activity Immediate Predecessor Time A 3 B 6 C A 2 D B, C 5 E D 4 F E 3 G B, C 9 H F, G 3 z Draw a project network. z What are the critical activities? z What is the expected project completion time? 2. Building a backyard swimming pool consists of nine major activities. The activities, their immediate predecessors, and their time estimates (in days) are shown in the following table. Activity A B C D Immediate Pred. A, B Optimistic 3 2 5 7 Most Probable 5 4 6 9 Pessimistic 6 6 7 10 z Draw a project network. z What are the critical activities? z What is the expected project completion time? z What is the probability that a project can be completed in 25 or fewer days? E B 2 4 6 F C 1 2 3 G D 5 8 10 H D, F 6 8 10 I E, G, H 3 4 5 33

3. Consider the following project. Immediate Time (Weeks) Cost ($1000) Activity Predecessor Normal Crash A 10 8 30 70 B A 8 6 120 150 C B 10 7 100 160 D A 7 6 40 50 E D 10 8 50 75 F C, E 3 3 60 • Develop a project network. • Develop an activity schedule. • What are the critical activities and what is the expected project completion time? • Assume that the project manager wants to complete the project in 6 months or 26 weeks. What crashing decisions do you recommend to meet the desired completion time at the least cost? Work through the network and attempt to make the crashing decisions by inspection. • Develop an activity schedule for the crashed project. • What added project cost is required to meet the 6 -month completion time? 34