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- 1. Project Management 1 PROJECT MANAGEMENT: Scheduling of Activities Project: A set of activities, with a definite starting and ending point, that results in a major product or service. Two independent techniques for project management were developed, in mid-50's one by DuPont for their chemical plant maintenance project, which they called the Critical Path Method (CPM). Independently, about the same time the Navy and Booze, Allen and Hamilton Consultants developed the Project Evaluation and Review Technique, popularly referred to as PERT, during the Polaris Missile project. The major difference between the two is: 1. Critical Path Method (CPM): The length of time each activity will take is known with certainty, therefore, the project completion time can be calculated with certainty. 2. Project Evaluation and Review Technique (PERT): The length of time each activity will take is not known with certainty, but estimated, therefore, the project completion time can not be calculated with certainty. Project completion time in this case is probabilistic. The activities that need to be performed for a given project are shown with a Network Diagram. The Network Diagram shows the precedence relationships between activities and also how long each activity will take. Two types of Network Diagrams 1. Activity-on-Arrow (AOA), where activities are shown on arrows 2. Activity-on-Node (AON), where activities are shown by Nodes We will use the AON convention because it is easier and more popular.
- 2. 2 Project Management Draw the AON Network Diagram for the following project Activity Predecessor Start - A Start B Start C A,B D A,B E C F C,D G F Finish G,E
- 3. Project Management 3 Project Scheduling with CPM In the Space Constructors Case, the AON Diagram was as follows: From start to finish there are 4 paths Path Length of Path Start-A-F-Finish 0+3+7+0 = 10 Start-A-D-G-Finish 0+3+5+4+0 = 12 Start-B-G-Finish 0+6+4+0 = 10 Start-C-E-G-Finish 0+2+2+4 = 8 The path with the greatest length is called the Critical Path. Since every activity on it must be completed in order for the project to be completed, the critical path determines the project completion time. For this case, the project completion time is 12 weeks.
- 4. 4 Project Management Crashing This is the practice of doing one or more activities in a shorter than normal time. Questions to be answered: 1. How much does it cost to crash activities? 2. Do the benefits of completing the project in a shorter than normal time outweigh the extra cost of crashing activities? (Recall the story of the Santa Monica Freeway) Sometimes crashing is necessary because an activity gets behind and the project is in danger of being late. Space Constructors Inc. Examples of Crashing Max. Crash NormalNormalCrash Crash Time Cost Cost/ Activity Time Cost Time Cost Red. Increase Week A 3 $ 5,000 2 $10,000 1 $5,000 $5,000 B 6 $14,000 4 $26,000 2 $12,000 $6,000 C 2 $ 2,500 1 $ 5,000 1 $2,500 $2,500 D 5 $10,000 3 $18,000 2 $8,000 $4,000 E 2 $ 8,000 2 $ 8,000 0 F 7 $11,500 5 $17,500 2 $6,000 $3,000 G 4 $10,000 2 $24,000 2 $14,000 $7,000 $61,000 $108,500
- 5. Project Management 5 For small projects finding the critical path can simply be done evaluating all the possible paths in the network. Clearly, for larger projects this would not be feasible. Furthermore, it is necessary to find the amount of slack on the non-critical activities. All of this is accomplished by calculating the following for each activity. Early Start (ES): The earliest that you can start an activity. ES is equal to the largest EF of the activity's immediate predecessors. Early Finish (EF): The earliest you can finish an activity. EF is equal to ES + Activity Time. ES and EF times for activities are calculated by moving from start to finish, referred to as forward pass. Late Start (LS): The latest you can start an activity yet not delay the completion of the project. LS is equal to the LF - Activity Time. Late Finish (LF): The latest you can finish an activity yet not delay the completion of the project. LF is equal to the smallest LS of the activity's immediate successors. LS and LF times for activities are calculated by moving from finish to start, referred to as backward pass. Slack: Slack is equal to LF - EF or LS - ES Activities on the critical path have the least slack. Usually it is zero. This is one way in which critical activities are identified.
- 6. 6 Project Management Calculating ES, EF, LS, LF and Slack times for the Case. Activity Predecessor Activity Time (in Weeks) Start - 0 A Start 3 B Start 6 C Start 2 D A 5 E C 2 F A 7 G B,D,E 4 Finish F,G 0 The AON Diagram for the Case:
- 7. Project Management 7 Project Scheduling with PERT PERT requires three time estimates for each activity to calculate the expected activity time E(T), the variance of activity time (σ2) and the standard deviation of the activity time (σ). In this case, the project completion time will have a probability distribution. On theoretical grounds, this is normal distribution. The normal distribution is used to calculate various probabilities of completing the project in any given period of time. a the optimistic time m the most likely time b the pessimistic time a<=m<=b Install Equation Editor and double- click here to view equation. Install Equation Editor and double- click here to view equation. Install Equation Editor and double- click here to view equation. For example for activity A the time estimates are: a=14, m=26, b=32 (days) et = (14 + 104 + 32)/6 = 25 σ2 = [(32 - 14)/6]2 = 9 σ=3 If a = m = b, then the solution becomes similar to using the CPM technique, variance becomes zero.
- 8. 8 Project Management Example with PERT technique. A Hospital Moving Project requires the following activities: Activity Description A Select administrative and medical staff B Select site and do site survey C Select equipment D Prepare final construction plans and layout E Bring utilities to the site F Interview applicants and fill positions in support staff G Purchase and take delivery of the equipment H Construct the hospital I Develop an information system J Install equipment K Train staff Activity Predecessor a m b et σ2 σ Start - 0 0 0 0 0 0 A Start 11 14 17 14 1 1 B Start 5 8 17 9 4 2 C A 4 10 16 10 4 2 D B 8 9 10 9 0.1 0.3 E B 13 25 37 25 16 4 F A 6 9 18 10 4 2 G C 24 36 48 36 16 4 H D 31 40 49 40 9 3 I A 10 13 28 15 9 3 J E,G,H 1 4 7 4 1 1 K F,I,J 5 6 7 6 0.1 0.3 Finish K 0 0 0 0 0 0
- 9. Project Management 9 The Diagram is shown below: The Critical Path is: A-C-G-J-K Expected Project Completion Time = 70 days
- 10. 10 Project Management The Critical Path: Activity a m b et σ2 A 11 14 17 14 1 C 4 10 16 10 4 G 24 36 48 36 16 J 1 4 7 4 1 K 5 6 7 6 0.1 ____ Total 22.1 The variance of the critical path is equal to the sum of the variances of the activities on the critical path. Therefore, σ2Critical Path = 22.1 σCritical Path = 4.7 (≈5)
- 11. Project Management 11 What is the probability of completing the project: a. within 70 days? b. within 80 days? c. within 65 days? d. between 60 and 75 days? e. between 70 and 85 days? What is the probability of the project completion time exceeding: a. 70 days? b. 65 days? c. 60 days? d. 100 days? e. 75 days?

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