A decision support system for mean-variance analysis in multi-period inventory control

a r t i c l e i n f o Keywords: Stochastic dynamic programming Risk-reward heuristic Mean–variance analysis Efficient frontier analysis Inventory management Traditionally inventory management models have focused on risk-neutral decision making with the objective of maximizing the expected rewards or minimizing costs over a specified time horizon. However, for items marked by high demand volatility such as fashion goods and technology products, this objective needs to be balanced against the risk associated with the decision. Depending on how the product performs vis-à-vis the seller's original forecast, the seller could end up with losses due to either short or surplus supply. Unfortunately, traditional models do not address this issue. Stochastic dynamic programming models have been extensively used for sequential decision making in the context of multi-period inventory management, but in the traditional way where one either minimizes costs or maximizes profits. Risk is implicitly considered by accounting for stock-out costs. Considering risk and reward simultaneously and explicitly in a stochastic dynamic setting is a cumbersome task and often difficult to implement for practical purposes, since dynamic programming is designed to optimize on one variable, not two. In this paper we develop an algorithm, Variance-Retentive Stochastic Dynamic Programming that tracks variance as well as expected reward in a stochastic dynamic programming model for inventory control. We use the mean–variance solutions in a heuristic, RiskTrackr, to construct efficient frontiers which could be an ideal decision support tool for risk-reward analysis. Inventory control plays a critical role in day-today business operations and is often a crucial differentiator in determining the success or failure of firms. Traditionally inventory control models have focused on risk-neutral decision making where the usual optimization criteria have been either maximizing the sum of discounted rewards or minimizing the sum of accumulated costs over a specified time horizon. Starting from as early as the 1950's operations researchers have studied inventory control models under various economic and market conditions. Arrow et al. [5] and Dvoretzky [20] were the first to analyze a single-period inventory control model under stochastic demand which became popularly known as the newsvendor model. We refer the reader to Khouja [32] for a comprehensive review of the classical newsvendor model and its many extensions. Subsequently the single period stochastic inventory model was extended to multiple periods. The well-known (s,S) policy was proposed where an order is placed to bring the inventory level to S whenever the …