Inventory systems with random arrival of shipments

Abstract

In single-period inventory models, neither excess demand nor excess inventory can be carried forward to the next period. In stochastic multi-period models, an order is placed at some point in time during the cycle, and lead-time is considered to be either constant or random. Lead-time demand, however, is assumed to be probabilistic. At the time an order is placed, the amount of inventory which will be on hand when replenishment arrives is unknown. In this paper, we propose a variation of these models to determine the optimal economic order quantity. Shipments arrive according to a Poisson process. The status of the inventory becomes known at the time of the arrival of the shipment, and the selection of order quantity is made at that time. However, the arrival time of future shipments is uncertain. It is also demonstrated that traditional single- and multi-period inventory models can be obtained as special cases of the proposed model.