Value of Inventory Pooling with Limited Demand Information and Risk Aversion*

Abstract

ABSTRACTIn this article, we study the value of inventory pooling for a risk‐averse firm who manages locations, when the demand information is limited in the sense that only the mean and the variance of the demand distribution are known. We employ the distributionally robust optimization framework and derive the optimal worst‐case inventory policies when the firm's utility is measured by Conditional Value‐at‐Risk (CVaR). We analyze the value of inventory pooling in terms of CVaR, total inventory, and utility loss due to demand uncertainty and safety stock, and study the effect of system parameters, i.e., risk‐averse level, correlation coefficient, and location number, on the value of inventory pooling. We first study the case when the selling prices are given. We show that inventory pooling always benefits the firm in terms of CVaR but such benefits are bounded above. However, inventory pooling does not always reduce total inventory, especially when the firm's risk‐averse level is high. In terms of utility loss due to demand uncertainty and safety stock, we show that when demands are independent, the relative benefits of inventory pooling are of order . Then, we analyze the case when the selling prices are endogenously determined. We find that similar results can be obtained, except that inventory pooling will always reduce total inventory in this case. Our results enrich the existing literature on the benefits from inventory pooling by incorporating risk‐averse attitude, limited demand information, and pricing decisions.