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.

中文翻译：

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具有非瞬时恶化项目和部分积压的随机库存系统的动态定价和最优控制

在本文中，我们考虑了需求不确定的非瞬时恶化物品的动态定价和库存控制问题，其中需求对价格敏感并且受扩散过程控制。短缺和遗留是允许的，积压率是可变的，并取决于下一次补货的等待时间。为了最大化预期的总利润，动态定价和库存控制问题被描述为随机最优控制问题。基于动态规划原理，将随机控制模型转换为Hamilton-Jacobi-Bellman（HJB）方程。然后，通过求解HJB方程获得最优动态定价策略的精确表达式。此外，最佳的初始库存水平，最佳的销售价格，