Question: Three distribution centers (DCs) each face normally distributed demands, with D1 N(22,82), D2 N(19,42) and D3 N(17,32). All three DCs behave like newsvendors and have

Three distribution centers (DCs) each face normally distributed demands, with D1 N(22,82), D2 N(19,42) and D3 N(17,32). All three DCs behave like newsvendors and have a holding cost of h = $1 and shortage cost of p = $15 per unit per period, 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. Calculate the expected cost of the centralized system.

c) Suppose 12 = 13 = 23 = 0.75. Calculate the expected cost of the centralized system.

d) Suppose 12 = 0.75 and 13 = 23 = 0.75. Calculate the expected cost of the centralized system.

Everything with formula and calculation

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