solution

24. PSI believes it will need the amounts of generating capacity shown in Table 103 during the next five years. The company has a choice of building (and then operating) power plants with the specifications shown in Table 104. Formulate an IP to minimize the total costs of meeting the generating capacity requirements of the next five years. TABLE 103 Generating Capacity (Million kwh) Year 1 2 3 80 100 120 140 160 4 5 TABLE 104 Generating Capacity Construction Cost (\$ Millions) Annual Operating Cost (\$ Millions) Plant (Million kwh) 1 2 3 70 50 20 16 1.5 0.8 1.3 0.6 60 40 18 14 4 Suppose that at the beginning of year 1, power plants 1-4 have been constructed and are in operation. At the beginning of each year, PSI may shut down a plant that is operating or reopen a shut-down plant. The costs associated with reopening or shutting down a plant are shown in Table 105. Formulate an IP to minimize the total cost of meeting the demands of the next five years. (Hint: Let Mix = 1 if plant i is operated during year t YÃ¼ = 1 if plant i is shut down at end of year t Zit = 1 if plant i is reopened at beginning of year t You must ensure that if Xix = 1 and Xix+1=0, then Yu = 1. You must also ensure that if Xut-1 = 0 and Xia= 1, then Zit = 1.) TABLE 105 Reopening Cost Shutdown Cost (\$ Millions) Plant (\$ Million) 1 1.9 1.5 2 3 4 1.7 1.2 1.3 0.8 1.6 1.1

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