8.5.1

7.1 (Risk-Pooling Example) Three distribution centers (DCs) each face normally dis- tributed demands, with Di N(22, 82), D2 N(19,42), and D3 N(17,32). A11 three DCs have a holding cost of h = 1 and p 15, and all three follow a periodic-review base-stock policy using their optimal base-stock levels. a) Calculate the expected cost of the decentralized system. b) Suppose demands are uncorrelated among the three DCs: P12 EP13 P23 0. Calculate the expected cost of the centralized system. c) Suppose P12 = P13 = P23 = 0.75. Calculate the expected cost of the centralized system. d) Suppose P12 0.75, P13 = P23 = -0.75. Calculate the expected cost of the centralized system. = = 7.1 (Risk-Pooling Example) Three distribution centers (DCs) each face normally dis- tributed demands, with Di N(22, 82), D2 N(19,42), and D3 N(17,32). A11 three DCs have a holding cost of h = 1 and p 15, and all three follow a periodic-review base-stock policy using their optimal base-stock levels. a) Calculate the expected cost of the decentralized system. b) Suppose demands are uncorrelated among the three DCs: P12 EP13 P23 0. Calculate the expected cost of the centralized system. c) Suppose P12 = P13 = P23 = 0.75. Calculate the expected cost of the centralized system. d) Suppose P12 0.75, P13 = P23 = -0.75. Calculate the expected cost of the centralized system. = =