Critical Path Method(CPM)
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The document discusses network analysis and the critical path method (CPM). It explains that CPM can be used to determine the minimum time required to complete a project if activity durations are known. CPM was developed in the 1950s by researchers at DuPont and Sperry Rand. It also discusses the Program Evaluation and Review Technique (PERT) which can estimate project completion probabilities when durations are uncertain. Both CPM and PERT helped reduce the Polaris missile development time. The document provides examples of CPM and PERT applications and rules for constructing a project network diagram.
Critical Path Method(CPM)
- 2. Network analysis Network models can be used as an aid in scheduling large complex projects that consist of many activities. If the duration of each activity is known with certainty, then the critical path method (CPM) can be used to determine the length of time required to complete a project. CPM also can be used to determine how long each activity in the project can be delayed without delaying the completion of the project. CPM was developed in the late 1950s by researchers at DuPont and Sperry Rand.
- 3. CPM and PERT If the duration of the activities is not known with certainty, the Program Evaluation and Review Technique (PERT) can be used to estimate the probability that the project will be completed by a given deadline. PERT was developed in the late 1950s by consultants working on the development of the Polaris missile. CPM and PERT were given a major share of the credit for the fact that the Polaris missile was operational two years ahead of schedule.
- 4. CPM and PERT applications CPM and PERT have been successfully used in many applications, including: Scheduling construction projects such as office buildings, highways, and swimming pools. Installing a new computer system Designing and marketing a new product Building a ship
- 5. CPM rules project network or project diagram) can be constructed by using the following rules: Node 1 represents the start of the project. An arc should lead from node 1 to represent each activity that has no predecessors. A node (called the finish node) representing the completion of the project should be included in the network.
- 6. CPM rules Number the nodes in the network so that the node representing the completion of an activity always has a larger number than the node representing the beginning of an activity. An activity should not be represented by more than one arc in the network. Two nodes can be connected by at most one arc.
- 7. Finding a critical path of a project Widgetco is about to introduce a new product (product 3). One unit of product 3 is produced by assembling 1 unit of product 1 and 1 unit of product 2. Before production begins on either product 1 or 2, raw materials must be purchased and workers must be trained. Before products 1 and 2 can be assembled into product 3, the finished product 2 must be inspected. A list of activities and their predecessors and of the duration of each activity is given in Table 12. Draw a project diagram for this project.
- 8. Finding a critical path of a project
- 9. Finding a critical path of a project
- 10. Finding a critical path of a project Computation of Early Event Time: The early event time for node i, represented by ET(i), is the earliest time at which the event corresponding to node i can occur.
- 11. Finding a critical path of a project Computation of Late Event Time:
- 12. Finding a critical path of a project Free Float:
- 13. Finding a critical path of a project Critical Path: Critical Path: 1–2–3–4–5–6
- 14. Finding a critical path of a project Free float:
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