Dynamic pricing and replenishment policy under price, time, and service level-dependent demand and preservation investment

Time, price, and servicing are three important factors which affect the demand for any product. In a multi-period inventory model, different pricing in different periods may have a positive impact on demand. Offering discounts to customers during a shortage period is an efficient way to reduce lost sales. To address all these issues, a multi-period inventory model is developed and analyzed in this paper to obtain optimal pricing and replenishment periods where the market demand depends on price, time and service level provided by the retailer. The time horizon is fixed; the replenishment cycles are of equal length, but the shortage period may vary in different cycles. The retailer is allowed to charge different prices in different periods and provide discounts if someone places demand during a shortage period. Learning effects in holding and ordering costs are considered. Under a dynamic pricing framework, this study examines service improvement through learning and price discounts during shortages as an incentive for customers. It demonstrates that discounting indeed helps to produce more revenue when the back-order rate is low, and the service level is critical in generating demand when the stock-out period is lengthy, revealing a critical relationship between shortage periods and service level. A numerical experiment is performed to investigate the optimal policy in different situations and obtain some managerial insights.