1. Introduction

Inventory systems are often subject to different kinds of uncertainties in the demand and replenishment processes. These uncertainties have often made inventory planning difficult in terms of determining the optimal replenishment policy and its corresponding parameters. This paper studies a single-item, periodic review inventory model with uncertainties in demand information. In this model, each customer purchasing a product should make a reservation one period ahead of time before the product can be delivered. Customers, however, may change their minds and

cancel the reservations during the demand leadtime period. Thus, the demand information available due to the reservation practice is not perfectly reliable. Our objective in this paper is to determine the optimal inventory policy for such a model.

Indeed demand reservation procedures are commonly practiced across industries. In a majority of the service industries such as airlines, hotels and car rental companies, reservation is a standard practice. In the distribution and retail industries, bookings are often required by the suppliers in order to facilitate their production or inventory plans. This is even more true for manufacturers who operate in a make-to-order manner. In addition, we have learned through our professional contacts with a computer manufacturer that, a period of demand reservation is useful for the company when certain time-consuming in-house paperwork or clearance of payment is handled prior to the actual shipment. In many of these businesses customers are allowed to cancel orders during the period of demand reservation. Obviously, this creates difficulties for planning purposes and can be viewed as a drawback of the reservation practice.

Although as admittedly common and important phenomena, demand reservation and cancellation have not been addressed until recently in the inventory literature. The presence of demand leadtime is known to be beneficial to inventory systems. Hariharan and Zipkin (1995) develop continuous review, single- and multi-stage inventory systems with demand leadtimes. In their model, base-stock policies are utilized as there is no fixed cost in ordering. They prove the important property that demand leadtime leads to the same kind of impact that a reduction of supply leadtime does. In Hariharan and Zipkin (1995), perfect demand information is assumed over the demand leadtime, i.e., every single unit of demand reserved will be realized, and there is no cancellation. Subsequently, Cheung and Zhang (1999) explicitly model the cancellation phenomenon and evaluate its impact on an inventory system. They develop a single-stage, periodic review system in which demands are Poisson. They show that if inventory is properly planned , the benefits from a demand leadtime often outweigh penalties from demand cancellation. Their paper, however, does not address the issue of the optimality of inventory policy; instead, they assume stationary order-up-to and (s, S) inventory policies for the cases with and without fixed setup costs and the fundamental issue of optimality remains unanswered.