Optimal pricing and deteriorating inventory control when inventory stimulates stochastic demand with reference price effect

We study the joint dynamic pricing and deteriorating inventory management problem in the presence of reference price and stock display effects. In a random potential market setting with convex replenishment/ordering and holding/shortage cost functions, the retailer replenishes/orders and sells a single deteriorating product over a continuous-time infinite horizon to maximize its profit. The demand rate depends negatively on the sales price and positively on the consumers' reference price and displayed stock quantity. The inventories deteriorate physically at a constant fraction of the on-hand stocks. A stochastic optimal control model is established to characterize the optimal policy in a linear feedback form of the state variables when the observed inventory level is either positive or negative. We also investigate the asymptotic behavior of the system and provide sufficient conditions for the stability and monotone convergence of the expected long-run behavior. Finally, we perform numerical examples to illustrate the theoretical results and sensitivity analysis to derive insights into deteriorating inventory management under reference price and stock display effects. The findings suggest that current reference price level has a positive effect while inventory level has a negative on the optimal replenishment rate and price. We characterize the sample paths of optimal strategies and find that the initial consumer reference price has an important impact on the firm's optimal operations management. On the expected long-run behavior, it is beneficial for the firm to reduce demand uncertainty and deteriorating rate. We also observe that a large factor of displayed stock effect brings a positive effect on the total expected profit. Additionally, the firm needs to reduce (increase) the price and increase (reduce) the replenishment rate with high reference price effect intensity (memory factor).