Abstract

Consider a finite set of outlets with joint normally distributed demands and identical holding and penalty costs. It is well known that for a newsvendor inventory setting the expected cost of inventory centralization can be expressed as a constant multiple of the standard deviation of the joint distribution. The lowering of the centralized cost without changing the mean and standard deviation of demand at each outlet corresponds to a semidefinite optimization problem. This talk presents a closedform optimal solution of the semidefinite program and a fair allocation of the cost at optimality. The issue of cost allocation separate from the optimization is also studied where it is shown that an exponential-size linear program can be approximated by a polynomial-size second-order program.