Managing perishable inventory systems with positive lead times and finite ordering capacities is important but notoriously difficult in both theory and computation. The optimal control policy is extremely complicated, and no effective heuristic policy has been proposed in the literature. In this paper, we develop an easy-to-compute approximation algorithm for this class of problems and prove that it admits a theoretical worst-case performance guarantee under independent and many commonly used positively correlated demand processes. Our worst-case analysis departs significantly from those in the previous studies, requiring several novel ideas. In particular, we introduce a transient unit-matching rule to dynamically match the supply and demand units, and the notion of associated demand processes that provides the right future demand information to establish the desired results. Our numerical study demonstrates the effectiveness of the proposed algorithm. This paper was accepted by Yinyu Ye, optimization.
We study a continuous-review, infinite-horizon inventory system with compound Poisson demand and dual sourcing/delivery modes. Ordering from either source/mode incurs a fixed cost and the expedited mode provides a shorter lead time than the regular mode. As the optimal ordering policy is unknown, while expected to be very complicated, we propose a class of simple policies called single-index (R, nQ) policies—when ordering from each mode, based on the inventory position, the system follows an (R, nQ)-type of policy. We provide an exact procedure to compute the expected long-run average cost. Specifically, we first analyze the steady-state distribution of the inventory position, which is found to be no longer uniform in general as in the classic (R, nQ) inventory system where only one delivery mode is available. We then develop a recursive procedure, which overcomes the order-crossing effect, to determine the steady-state distribution of the inventory level. Two simple heuristics for computing near-optimal policy parameters are provided. For a special case where ordering from the regular mode incurs no fixed cost and follows a base-stock policy, we derive closed-form solution bounds by applying normal approximation. To assess the performance of the single-index (R, nQ) policy, we further study a more complicated class of policies called dual-index (R, nQ) policies and numerically illustrate that the simpler single-index policy performs close to the dual-index policy. Finally, the performance of the single-index policy is also shown comparable to the policy computed via dynamic programming.
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. This paper was accepted by Charles Corbett, operations management.
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