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INDUSTRIAL ENGINEERING

12-6 A company must complete a job with seven tasks in 40 days. Some of the tasks can begin at any time, but others have predecessors that must be completed first. For instance, task 4 can start only if tasks 1 and 2 are completed. Table 1 below shows predecessor task numbers, the minimum and maximum times (in days) allowed for each task, and the cost that would be associated with accomplishing each task in its minimum and maximum times (more time reduces cost). The company wants to complete the job with minimum total cost. Suppose that the cost of each task is linearly interpolated for times between the minimum and maximum, e.g., the cost of 8-6 task 1 equals 1000 + 13-8 (1600 1000) = 1400, or 1600 - (1600 1000) = 1400, if 12-6 task 1 takes 8 days to complete. Please formulate an LP model to minimize the total cost and use GAMS to find the optimal solution and optimal value. Table 1. Task Information for a Job. Minimum Maximum Cost for Cost for Predecessor Task Time Time Minimum Time Maximum Time Tasks 1 6 12 1600 1000 None 2 8 16 2400 1800 None 3 16 24 2900 2000 2 4 14 20 1900 1300 1 and 2 5 4 16 3800 2000 3 6 12 16 2900 2200 3 7 2 12 1300 800 4