Risk-Pooling Effects of Emergency Shippping in a Two-Echelon Distribution System

Abstract

This paper analyzes the optimal replenishment policy in a one warehouse N-retailer distribution system operating in a periodic-review mode where emergency shipping from a central warehouse or a retailer to an individual customer is allowed to satisfy retailer backorders at the end of the cycle. We show that, under the assumption that it costs the same whether emergency shipping is made by the warehouse or by a retailer, it is optimal that the warehouse carries no inventory. Under the same assumption, the form of the optimal system-replenishment policy is shown to be a base-stock policy, and the necessary and sufficient condition of optimality, which is analogous to that of the Newsboy problem, is presented. The further analysis shows that, with emergency shipping allowed, the warehouse orders less from its supplier.

This paper analyzes the optimal replenishment policy in a one warehouse N-retailer distribution system operating in a periodic-review mode where emergency shipping from a central warehouse or a retailer to an individual customer is allowed to satisfy retailer backorders at the end of the cycle. We show that, under the assumption that it costs the same whether emergency shipping is made by the warehouse or by a retailer, it is optimal that the warehouse carries no inventory. Under the same assumption, the form of the optimal system-replenishment policy is shown to be a base-stock policy, and the necessary and sufficient condition of optimality, which is analogous to that of the Newsboy problem, is presented. The further analysis shows that, with emergency shipping allowed, the warehouse orders less from its supplier.