Convex Optimization of Centralized Inventory Operations

Samuel Burer (samuel-bureruiowa.edu)
Moshe Dror (mdroreller.arizona.edu)

Abstract: Given a finite set of outlets with joint normally distributed demands and identical holding and penalty costs, inventory centralization induces a cooperative cost allocation game with nonempty core. It is well known that for this newsvendor inventory setting the expected cost of 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 variance of demand at each outlet corresponds to a semidefinite optimization problem. This paper establishes a closed-form optimal solution of the semidefinite program and a core allocation of the cost at optimality. The issue of cost (and benefit) allocation separate from the optimization is also studied and it is shown that an exponential-size linear program can be approximated by a polynomial-size second-order program.

Keywords:

Category 1: Applications -- OR and Management Sciences (Production and Logistics )

Category 2: Other Topics (Game Theory )

Category 3: Linear, Cone and Semidefinite Programming

Citation: Manuscript, Department of Management Sciences, University of Iowa, Iowa City, IA, USA, January 2005.

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Entry Submitted: 01/11/2005
Entry Accepted: 01/12/2005
Entry Last Modified: 01/11/2005

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