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Coherent Risk Measures in Inventory Problems

Shabbir Ahmed (sahmed***at***isye.gatech.edu)
Ulas Cakmak (ucakmak***at***isye.gatech.edu)
Alexander Shapiro (ashapiro***at***isye.gatech.edu)

Abstract: We analyze an extension of the classical multi-period, single-item, linear cost inventory problem where the objective function is a coherent risk measure. Properties of coherent risk measures allow us to offer a unifying treatment of risk averse and min-max type formulations. For the single period newsvendor problem, we show that the structure of the optimal solution of the risk averse model is similar to that of the classical expected value problem. For a finite horizon dynamic inventory model, we show that, again, the optimal policy has a similar structure as that of the expected value problem. This result carries over even to the case when there is a fixed ordering cost. We also analyze monotonicity properties of the optimal order quantity with respect to the degree of risk aversion for certain risk measures.

Keywords: inventory models, newsvendor problem, coherent risk measures, mean-absolute deviation, conditional-value-at-risk,

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

Category 2: Stochastic Programming

Citation: Technical Report, School of Industrial and Systems Engineering, Georgia Institute of Technology.

Download: [PDF]

Entry Submitted: 12/19/2005
Entry Accepted: 12/19/2005
Entry Last Modified: 12/19/2005

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