Optimal ordering and pricing policy for an inventory system with order cancellations

This paper investigates the problem of ordering and pricing over a finite time planning horizon for an inventory system with advance sales and spot sales. It is assumed that the planning horizon is divided into several sales cycles each of which is divided into an advance sales period and a spot sales period. During the advance sales period, all customers are required to make reservations for their orders and will receive them at the arrival time of the replenishment orders. In the case of the spot sales periods, all customers receive their orders at the time of the purchase. In actual practice, since customers with reservations may cancel their orders before receiving them, this paper considers this phenomenon and develops a continuous time inventory model to deal with the proposed problem. This paper maximizes the total profit over a finite time planning horizon by determining the optimal advance sales price, spot sales price, order size, and replenishment frequency. Analysis of results shows that a simple algorithm can be developed to arrive at an optimal decision.