Pricing ELS with freight cost

Because of the economic globalization, products are manufactured in one place and sold all over the world. As freight cost accounts for a large part of the total costs for these products, it plays a more important role in the management of inventory. Recent years, phenomenal growth of successful deployments of innovative pricing strategies in a variety of industries makes scores of retail and manufacturing companies started exploring dynamic pricing to improve profit. We study multi-period review inventory and pricing problem under price-dependent deterministic demand with freight cost, in which the capacity of one vehicle is limited and the freight cost is proportional to the number of the vehicles used. In each period, we determine the sale price and ordering quantity simultaneously and the leadtime is zero. The unsold inventory incurs a holding cost and shortages are not permitted. The objective is to maximize the total profit. We first characterize the structure of the optimal policy. We show that the optimal ordering quantity is either zero or some multiple of the vehicle's capacity. Based on those properties, a way is developed to compute the optimal policy.