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Project Management CPM/PERT Professor Ahmadi

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Learning Objectives Understand how to plan, monitor, and control projects using PERT/CPM. Determine earliest start, earliest finish, latest start, latest finish, and slack times for each activity. Understand the impact of variability in activity times. Understand important role of software such as Microsoft Project in project management.

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**Project Planning Specific questions that are considered:**

What is goal or objective of project? What are various activities (or tasks) that constitute project? How are these activities linked? What are precedence relationships between activities? What is time required for each activity? What other resources (such as labor, raw materials, and machinery) are required for each activity?

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**Project Scheduling Questions to be answered:**

When will project be completed? What is schedule for each activity? What are critical activities in project? What are non-critical activities in project? By how much can a non-critical activity be delayed without affecting completion time of entire project? If variability in activity times is considered, what is probability project will be completed by a specific deadline?

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Project Controlling Control of large projects involves close monitoring of schedules, resources, and budgets. Questions to be answered: At any particular date or time, is project on schedule, behind schedule, or ahead of schedule? At any particular date or time, is money spent on project equal to, less than, or greater than budgeted amount? Are there enough resources available to finish project on time? If project is to be finished in shorter amount of time, what is best way to accomplish this at least cost?

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**Gantt Chart for a New Voice Recognition System**

Project Activities Apr. May June July Aug. a. Design System b. Build Prototype c. Test Prototype d. Estimate Material Costs e. Estimate Labor Costs f. Refine Design g. Build the final Product h. Demonstrate the product i. Market the Product

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**Drawing Project Network**

There are two major approaches for drawing a project network -- Activity on Node (AON), and Activity on Arc (AOA). Although both approaches are popular in practice, many project management software packages, including Microsoft Project 2000, use AON networks. Focus is on AON networks.

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**CPM and PERT Network techniques Developed in 1950’s**

CPM by DuPont for chemical plants (1957) PERT by Booz, Allen & Hamilton with the U.S. Navy, for Polaris missile (1958) Consider precedence relationships and interdependencies Each uses a different estimate of activity times

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CPM/PERT CPM stands for Critical Path Method. It is Project Scheduling with Known Activity Times (CPM) PERT stands for Program Evaluation Review Technique. It is Project Scheduling with Uncertain Activity Times (PERT) PERT/CPM is used to plan the scheduling of individual activities that make up a project. PERT/CPM can be used to determine the earliest/latest start and finish times for each activity, the entire project completion time and the slack time for each activity.

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Project Network A project network can be constructed to model the precedence of the activities. The nodes of the network represent the activities. The arcs of the network reflect the precedence relationships of the activities. A critical path for the network is a path consisting of activities with zero slack.

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**Determining the Critical Path**

Step 1: Make a forward pass through the network as follows: For each activity i beginning at the Start node, compute: Earliest Start Time = the maximum of the earliest finish times of all activities immediately preceding activity i. (This is 0 for an activity with no predecessors.) Earliest Finish Time = (Earliest Start Time) + (Time to complete activity i. The project completion time is the maximum of the Earliest Finish Times at the Finish node.

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**Determining the Critical Path**

Step 2: Make a backwards pass through the network as follows: Move sequentially backwards from the Finish node to the Start node. At a given node, j, consider all activities ending at node j. For each of these activities, (i,j), compute: Latest Finish Time = the minimum of the latest start times beginning at node j. (For node N, this is the project completion time.) Latest Start Time = (Latest Finish Time) - (Time to complete activity (i,j)).

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**Determining the Critical Path**

Step 3: Calculate the slack time for each activity by: Slack = (Latest Start) - (Earliest Start), or = (Latest Finish) - (Earliest Finish). A critical path is a path of activities, from the Start node to the Finish node, with 0 slack times.

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**Uncertain Activity Times**

In the three-time estimate approach, the time to complete an activity is assumed to follow a Beta distribution. An activity’s mean completion time is: t = (a + 4m + b)/6 Each activity’s completion time variance is: S2 = ((b-a)/6)2 a = the optimistic completion time estimate b = the pessimistic completion time estimate m = the most likely completion time estimate The variance of the critical path is: 2 = S2

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**Uncertain Activity Times**

In the three-time estimate approach, the critical path is determined as if the mean times for the activities were fixed times. The overall project completion time is assumed to have a normal distribution with mean equal to the sum of the means along the critical path and variance equal to the sum of the variances along the critical path.

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**Network for construction of a new building Example 1**

A project comprises of the following activities and their predecessors. Activity Description Predecessor A Survey site -- B Initial design -- C Obtain approval A,B D Select architect C E Establish budget C F Finalize design D,E G Obtain financing E H Hire contractor F,G Draw a network for this project.

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**Critical Path Method (CPM) Example 2**

A project comprises of the following activities and their predecessors. Immediate Expected Activity Predecessor time (days) A - 2 B - 6 C A 4 D B 3 E C, D 1 a. Draw a network and determine the critical path. How long will it take to complete the project? b. Provide a detailed activity schedule for the project.

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**Program Evaluation and Review Technique (PERT) Example 3**

For the following activities and their predecessors and the three time estimates (days): Activity Predecessor Optimistic (a) Most Probable (m) Pessimistic (b) A B C A 4 5 6 D B 7 8 9 E C, D a. Compute the expected completion time for each activity. b. Draw a network and determine the critical path based on the expected completion times. c. What is the probability of finishing the project in less than 19 days? d. What is the probability of finishing the project in less than 23 days?

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**Network for construction of a new building Refer to Example 1-Your turn**

A project comprises of the following activities and their predecessors. Activity Description Predecessor Time (Days) A Survey site B Initial design C Obtain approval A,B 24 D Select architect C 8 E Establish budget C 12 F Finalize design D,E 30 G Obtain financing E 24 H Hire contractor F,G 16 Draw a network for this project and determine the critical path. How long would it take to finish this project?

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