Statement of Contributions Stochastic Multi-product Inventory Models with Limited Storage

An inventory manager is typically concerned with a number of diierent products. His decision-making task is made complicated by such factors as interdependent uncertain product demands and competition for limited storage space. The stochastic inventory problem involving these complexities cannot in general be decomposed into a number of distinct single product problems. In the paper \Stochastic Multiproduct Inventory Models with Limited Storage", Dirk Beyer, Suresh Sethi, and Ramaswamy Sridhar address a multiproduct inventory problem with proportional ordering costs, convex surplus costs, and a warehousing constraint. Optimality of a modiied base-stock policy is established for stationary and nonstationary discounted-cost problems. In the stationary case with separable cost functions, independent demand, and limited storage space, the optimality of an easy-to-compute myopic policy is established. These structural results about optimal ordering policies provide valuable insights into how to manage complex multiproduct inventory situations that may arise in practice. Abstract This paper studies multi-product inventory models with stochastic demands and a ware-housing constraint. Finite horizon as well as stationary and nonstationary discounted cost innnite horizon problems are addressed. Existence of optimal feedback policies is established under fairly general assumptions. Furthermore, the structure of optimal policies is analyzed when ordering cost is linear and inventory/backlog cost is convex. The optimal policies generalize the base-stock policies in the single-product case. Finally, in the stationary innnite horizon case, a myopic policy is proved to be optimal if the product demands are independent and cost functions are separable. The paper has beneeted from the comments of the participants in the OM seminar at University of Toronto, where an earlier version of the paper was presented.