Table 5

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3. Now suppose the realized demand for generators is D and the total quantity of generators purchased is Q. Estimates indicate that electricity will be out for three days in the event of a major hurricane and lost profit at stores unable to open is projected to be $5,000. Generators cost $1,000. Complete the following steps to analyze the generator procurement problem using an alternative objective, namely to minimize the maximum regret experienced. a. Express the realized cost of a decision to purchase Q generators, including procurement cost for generators and the cost of lost sales, in terms of Q and D. b. If a planner knew a priori what the total demand for generators would be, what is the optimal cost the planner would incur? Express this cost in terms of Q and D. c. Regret is defined as the difference between the realized cost of a procurement decision and the cost of an optimal decision that would have been made with a priori knowledge of the demand for generators. Express the regret incurred as a result of a decision to purchase Q generators when D are actually needed in terms of these two variables. d. Using the expressions you developed, complete Table 5, which summarizes the realized costs and the regret of procurement decisions. In this scenario, assume that the maximum number of generators that could possibly be needed in a season is 16. Table 5: Realized Costs and Maximum Regret Electricity Out 3 Days $5,000 lost profit/day Generator Cost = $1,000 Realized Cost if D=0 Realized Cost if D=16 Max Regret Q 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Table 1: Cumulative Distribution Function for Number of Major US Landfalling Hurricanes (from NOAA) Y Pr{y