Joint Pricing And Inventory Control With A Price-dependent Shortage Cost

In recent years, research on joint pricing and inventory management is gradually obtaining the attention of the enterprise managers and academic researchers. Through reasonable joint pricing and inventory management strategy, enterprises can reduce the inventory holding cost and shortage cost to maximize their benefits. In the market with demand uncertainty, shortage can result in the loss of good will for potential consumers, where the loss is related to the selling price. Because price measures the value of this product for consumers who attempt to purchase, a higher selling price can cause more loss of will to customers. Besides, higher price usually means higher product quality or higher brand value, at the same time corresponding to higher storage cost. Therefore, we assume that the inventory holding cost is associated with the selling price as well.Based on this, we first address the joint pricing and inventory replenishment strategies with a price-dependent shortage penalty cost under the assumptions that the unit shortage cost is a linear increasing function or a power increasing function of price respectively. We characterize the structure of the optimal combined pricing and inventory strategies that maximizing the expected profit, prove the monotonicity of the optimal price in term of the marginal effect of the shortage in price and provide a sufficient condition of the monotonicity of optimal order quantity under the linear increasing setting. Secondly, we conduct a preliminary study on the joint pricing and inventory management under the situation that the holding cost is also related to the selling price. In this case, we discuss the structure of the optimal combined pricing and inventory strategies again. We testify the monotone decreasing of the optimal price with the sensitive coefficient of shortage cost in price and put forward a conjecture that the optimal price is also decreasing in the price sensitive coefficient of the holding cost. In addition, under the data analysis, we verify the conclusion of theoretical analysis and discuss the varying pattern of the optimal decision and expected profit with the price sensitive coefficient and other parameters. Through the comparison with the previous results, we explain the inconsistent variation of the optimal decision and the expected revenue in different cases. Finally, large numerical experiments indicate that the expected profit decreases gradually with the price sensitive coefficient, fixed shortage cost or holding cost.