Exercises due March 24 - Exercises due March 24 1 Personnel...

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Exercises due March 24 1. Personnel Allocation problem: Projects A, B, and C require 18, 12 and 30 person months to complete. Hence consider 6-month periods. Persons 1,2,3, and 4 are available to work on these projects. Their monthly salaries are $3000, 3500, 3200 and 3900 respectively. All projects must be completed in 18 months, and each person can only be assigned one job each 6 months. Find the allocation of the four persons that minimizes the total cost of completing all the projects. Hint, consider X(i,j,k) a 0,1 variable, associated with person i, project j, period k. 2. Project scheduling Assume there are five tasks to complete a project. Their durations and sequence are defined in the table below. Task Duration Must follow A 14 - B 10 - C 8 A, B D 6 B E 9 C, D Define and solve a linear programming model to identify the start times of each task, and the minimum total project time. Also identify the critical path from the dual values associated with each constraint.
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