**The critical path**

**The critical path**

Objectives: 309.3.2-01: Determine the critical path identified by a given PERT/CPM analysis. 309.3.2-02: Utilize PERT analysis to determine the probability that a given project will meet a specified deadline for completion. 309.3.2-03: Determine slack time for a given project activity. 309.3.2-04: Determine scheduled start time for a given project activity. 309.3.2-05: Determine scheduled completion time for a given project activity. 309.3.2-06: Use time-cost trade-offs to appropriately crash a project network. Introduction: This task requires candidates to prepare a program evaluation and review technique (PERT) chart and apply critical path method (CPM) techniques. Given: Company A is installing a Web-based customer-feedback system to meet customer needs for quick response when rolling out new products. A new product line is rolling out in 34 weeks and the customer-feedback system must be installed and running in time for the new product launch. Table 1.1 in the attached worksheet “QAT 4 Student Tables” shows three estimates of the time it will take Company A to complete each of the activities and project tasks in the customer-feedback system project (optimistic, probable, pessimistic). Company B is installing a similar feedback system to accompany a new product line and originally had the same time line as Company A. Company B just announced that its new product line is ahead of schedule and will be launched in 30 weeks instead of the initially projected 34 weeks. Because the Web-based customer feedback system must be installed and running in time for the revised date of the product launch, something must be done to shorten implementation time required for the customer-feedback system project. Refer to Table 1.2 in the attached worksheet “QAT 4 Student Tables” that lists the expected time it will take to complete the activities if shortened as much as possible (crash time), the cost to complete the activity using normal resources (normal cost), and the cost of completing the activity on an accelerated basis (crash cost). Task: A. Use the estimates for Company A in Table 1.1 to do each of the following: 1. Determine the expected completion time for each of the ten project activities, showing all your work. a. Determine the variance for each project activity, showing all your work. 2. Prepare a PERT chart (network diagram) to identify the critical path for project completion. Note: If you don’t have software to build a PERT chart, use text boxes with lines or arrows in a word processing program. 3. Determine each of the following, showing all of your work or reasoning: a. Expected duration of the entire project b. Slack for project task A c. Slack for project task H d. The week project task F is scheduled to start e. The week project task I is scheduled to finish 4. Determine the probability of completing this project in time for the product launch in 34 weeks, showing all your work. B. Assume that Company B has the same expected completion times for project activities as Company A. Use your results from part A1 and the data in Table 1.2 to determine the following, showing all your work: 1. Maximum reduction in time 2. Crash cost per week C. Identify the following by using your results from part B, showing all of your work or reasoning: 1. Activities to be crashed in order to complete the project within 30 weeks 2. Number of weeks each of these activities should be crashed to meet the deadline with the lowest possible increase in cost 3. Additional crashing cost of the activities identified in part C1. D. If you use sources, include all in-text citations and references in APA format