Dynamic Pricing and Optimal Control for a Stochastic Inventory System with Non-Instantaneous Deteriorating Items and Partial Backlogging

Abstract

In this paper, we consider a problem of the dynamic pricing and inventory control for non-instantaneous deteriorating items with uncertain demand, in which the demand is price-sensitive and governed by a diffusion process. Shortages and remains are permitted, and the backlogging rate is variable and dependent on the waiting time for the next replenishment. In order to maximize the expected total profit, the problem of dynamic pricing and inventory control is described as a stochastic optimal control problem. Based on the dynamic programming principle, the stochastic control model is transformed into a Hamilton-Jacobi-Bellman (HJB) equation. Then, an exact expression for the optimal dynamic pricing strategy is obtained via solving the HJB equation. Moreover, the optimal initial inventory level, the optimal selling pricing, the optimal replenishment cycle and the optimal expected total profit are achieved when the replenishment cycle starts at time 0. Finally, some numerical simulations are presented to demonstrate the analytical results, and the sensitivities analysis on system parameters are carried out to provide some suggestions for managers.