Chapter 16 Project Management Operations Management by R.
Chapter 16 Project Management Operations Management by R. Dan Reid & Nada R. Sanders 2nd Edition Wiley 2005 PowerPoint Presentation by R.B. Clough - UNH Project Management Applications What is a project? Any endeavor with objectives With multiple activities With defined precedent relationships With a specific time period for completion Examples? A major event like a wedding Any construction project Designing a political campaign
Five Project Life Cycle Phases Conception: identify the need Feasibility analysis or study: costs benefits, and risks Planning: who, how long, what to do? Execution: doing the project Termination: ending the project Network Planning Techniques Program Evaluation & Review Technique (PERT): Developed to manage the Polaris missile project Many tasks pushed the boundaries of science & engineering (tasks duration = probabilistic)
Critical Path Method (CPM): Developed to coordinate maintenance projects in the chemical industry A complex undertaking, but individual tasks are routine (tasks duration = deterministic) Both PERT and CPM Graphically display the precedence relationships & sequence of activities Estimate the projects duration Identify critical activities that cannot be delayed without delaying the project Estimate the amount of slack associated with non-critical activities Network Diagrams Activity-on-Node (AON):
Uses nodes to represent the activity Uses arrows to represent precedence relationships Step 1-Define the Project: Cables By Us is bringing a new product on line to be manufactured in their current facility in some existing space. The owners have identified 11 activities and their precedence relationships. Develop an AON for the project. Activity A B C D E F G H I J K Description Develop product specifications Design manufacturing process Source & purchase materials Source & purchase tooling & equipment Receive & install tooling & equipment Receive materials Pilot production run Evaluate product design Evaluate process performance Write documentation report Transition to manufacturing
Immediate Duration Predecessor (weeks) None 4 A 6 A 3 B 6 D 14 C 5 E&F 2 G 2 G 3 H&I 4 J 2 Step 2- Diagram the Network for Cables By Us Step 3 (a)- Add Deterministic Time Estimates and Connected Paths
Step 3 (a) (Continued): Calculate the Path Completion Times Paths ABDEGHJK ABDEGIJK ACFGHJK ACFGIJK Path duration 40 41 22 23 The longest path (ABDEGIJK) limits the projects duration (project cannot finish in less time than its longest path) ABDEGIJK is the projects critical path Some Network Definitions
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 activitys late finish minus its early finish (or its late start minus its early start) Earliest Start (ES) = the earliest finish of the immediately preceding activity Earliest Finish (EF) = is the ES plus the activity time Latest Start (LS) and Latest Finish (LF) depend on whether or not the activity is on the critical path ES, EF Network LS, LF Network Calculating Slack Activity A B C D E F G H I J K Late Finish 4 10
0 0 0 Earliest Start Gantt Chart A B C D E F G H I J K 0 5 10 15 20 25 30 35 40
45 Latest Start Gantt Chart A B C D E F G H I J K 0 5 10 15 20 25 30 35 40 45
Revisiting Cables By Us Using Probabilistic Time Estimates Activity A B C D E F G H I J K Description Develop product specifications Design manufacturing process Source & purchase materials Source & purchase tooling & equipment Receive & install tooling & equipment Receive materials Pilot production run Evaluate product design Evaluate process performance Write documentation report Transition to manufacturing Optimistic time 2 3 2
6 2 Using Beta Probability Distribution to Calculate Expected Time Durations A typical beta distribution is shown below, note that it has definite end points The expected time for finishing each activity is a weighted average optimistic 4 most likely pessimistic Exp. time 6 Calculating Expected Task Times optimistic 4 most likely pessimistic Expected time 6 Activity A B C D E F G H I
J K Optimistic time 2 3 2 4 12 2 2 2 2 2 2 Most likely time 4 7 3 7 16 5 2 3 3 4 2 Pessimistic time 6
10 5 9 20 8 2 4 5 6 2 Expected time 4 6.83 3.17 6.83 16 5 2 3 3.17 4 2 Network Diagram with Expected Activity Times Estimated Path Durations through the Network Activities on paths ABDEGHJK ABDEGIJK ACFGHJK
ACFGIJK Expected duration 44.66 44.83 23.17 23.34 ABDEGIJK is the expected critical path & the project has an expected duration of 44.83 weeks Estimating the Probability of Completion Dates Using probabilistic time estimates offers the advantage of predicting the probability of project completion dates We have already calculated the expected time for each activity by making three time estimates Now we need to calculate the variance for each activity The variance of the beta probability distribution is: 2
p o 6 2 where p=pessimistic activity time estimate o=optimistic activity time estimate Project Activity Variance Activity Optimistic Most Likely Pessimisti c Variance A 2 4 6 0.44
B 3 7 10 1.36 C 2 3 5 0.25 D 4 7 9 0.69 E 12
16 20 1.78 F 2 5 8 1.00 G 2 2 2 0.00 H 2 3 4
0.11 I 2 3 5 0.25 J 2 4 6 0.44 Variances of Each Path through the Network Path Number Activities on Path Path Variance (weeks) 1
A,B,D,E,G,H,J, k 4.82 2 A,B,D,E,G,I,J,K 4.96 3 A,C,F,G,H,J,K 2.24 4 A,C,F,G,I,J,K 2.38 Calculating the Probability of Completing the Project in Less Than a Specified Time When you know: The expected completion time Its variance
You can calculate the probability of completing the project in X weeks with the following formula: specified time path expected time DT EFP z 2 path standard time P Where DT = the specified completion date EFP = the expected completion time of the path P 2 variance of path Example: Calculating the probability of finishing the project in 48 weeks Use the z values in Appendix B to determine probabilities E.G. for path 1 48 weeks 44.66 weeks z 4.82 1.52
Path Number Activities on Path Path Variance (weeks) z-value Probability of Completion 1 A,B,D,E,G,H,J,k 4.82 1.5216 0.9357 2 A,B,D,E,G,I,J,K 4.96 1.4215
0.9222 3 A,C,F,G,H,J,K 2.24 16.5898 1.000 4 A,C,F,G,I,J,K 2.38 15.9847 1.000 Reducing the Time of a Project (crashing) Activit y Normal Time (wk) Normal Cost ($)
Crash Time Crash Cost ($) Max. weeks of reduction Reduce cost per week A 4 8,000 3 11,000 1 3,000 B 6 30,000
5 35,000 1 5,000 C 3 6,000 3 6,000 0 0 D 6 24,000 4 28,000 2
2,000 E 14 60,000 12 72,000 2 6,000 F 5 5,000 4 6,500 1 1500 G 2
6,000 2 6,000 0 0 H 2 4,000 2 4,000 0 0 I 3 4,000 2 5,000
1 1,000 J 4 4,000 2 6,400 2 1,200 Crashing Example: Suppose the Cables By Us project manager wants to reduce the new product project from 41 to 36 weeks. Crashing Costs are considered to be linear Look to crash activities on the critical path Crash the least expensive activities on the critical path first (based on cost per week)
Crash activity I from 3 weeks to 2 weeks $1000 Crash activity J from 4 weeks to 2 weeks $2400 Crash activity D from 6 weeks to 4 weeks $4000 Recommend Crash Cost $7400 Will crashing 5 weeks return more than it costs? Crashed Network Diagram Chapter 16 HW Assignment Problems 1 8, 13 - 16
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