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Risk Aversion in Inventory Management

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
Singapore-MIT Alliance and NUS Business School, National University of Singapore, Singapore
Department of Civil and Environmental Engineering and Engineering System Division, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Fuqua School of Business, Duke University, Durham, North Carolina 27708
xinchen{at}uiuc.edu
dscsimm{at}nus.edu.sg
dslevi{at}mit.edu
psun{at}duke.edu

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multiperiod inventory models as well as multiperiod models that coordinate inventory and pricing strategies. We show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. These structural results are extended to models in which the decision maker has access to a (partially) complete financial market and can hedge its operational risk through trading financial securities. Computational results demonstrate that the optimal policy is relatively insensitive to small changes in the decision-maker's level of risk aversion.

Subject classifications: inventory/production; policies; uncertainty; decision analysis; risk.
History: Received March 2004; revision received August 2006; accepted August 2006.