Multilocation Newsvendor Problem: Centralization and Inventory Pooling

We study a multilocation newsvendor model with a retailer owning multiple retail stores, each of which is operated by a manager who decides the order quantity for filling random customer demand of a product. Store managers and the retailer are all risk averse, but managers are more risk averse than the retailer. We adopt conditional value-at-risk (CVaR) as the performance measure and consider two alternative strategies to improve the system’s performance. First, the retailer centralizes the ordering decisions. Second, managers still decide the order quantity for their own store, whereas their inventories are pooled together. We analyze and compare the optimal order quantities and the resultant CVaR values of the systems and study their comparative statistics. For centralization, we find that each store has a higher inventory level in the centralized system than in the decentralized system, and centralization positively benefits the retailer as long as some store managers are strictly more risk averse than the retailer. When there is inventory pooling, the ordering decisions in the decentralized system depend on how the additional profit from pooling is allocated among the stores. We consider a weighted proportional allocation rule and characterize the Nash equilibrium of the resultant ordering game among the store managers. Our key finding is that as long as the store managers are sufficiently more risk averse than the retailer or the demands are very heavy tailed, inventory pooling is less beneficial than centralization. We further derive a lower bound on the value of centralization and two upper bounds on the value of inventory pooling. Finally, our analytical results are illustrated using a data set from an online retailer in China, and various comparative statics are further examined via extensive numerical experiments.