Optimal pricing policy with inventory related costs and reference effects

Abstract

This paper addresses the problem of a retailer who buys a certain amount of inventory at the start of a selling season. Holding inventory is costly and the demand is dependent on the current price and the reference price. The reference price is developed by customers and acts as a benchmark against the current price. The aim of the retailer is to maximize its discounted profit. The problem is modeled as an optimal control problem to determine the optimal pricing policy. For general demand models, the marginal cost due to an increase in the inventory and the marginal gain due to an increase in the reference price are provided analytically. For the linear demand models, the optimal pricing strategy is given explicitly and shown to be characterized by three stages: After a penetration or a skimming pricing strategy at the initial stage, the optimal price increases with time and the season ends with a discount. By introducing the reduced price which is the premium over the cost of the products, it is shown that the existence of procurement and holding cost is the driver for the increase in the price during the intermediary stage. The sensitivity of the optimal price to demand and cost parameters is also provided with a numerical study.