Abstract We investigate a manufacturer’s joint dynamic production and pricing problem under stochastic reference price effect over an infinite horizon in a continuous-time framework. The demand for products, which depends on their price and a memory-based reference price, is uncertain and characterized by a stochastic process. The reference price effect varies across consumers and subjects to some randomness characterized by a stochastic process. A joint dynamic production and pricing problem to maximize the total expected profit is modeled as a stochastic optimal control problem. We give the sufficient conditions of the existence of the optimal solutions and characterize the solutions for the general convex cost structure. In addition, we show that the strategies in a linear feedback form of the state variables (i.e., inventory and reference price) are optimal for a strictly convex cost structure, and provide sufficient conditions of stability and monotone convergence properties for the expected steady-state inventory and reference price. Numerical examples and sensitivity analysis are performed to provide several important managerial insights. We find that the optimal production rate and sales price are each negatively related to the inventory stock while positively to the reference price level. In expected steady-state, demand uncertainty has no influence on optimal strategies while a higher reference price uncertainty would result in a lower production rate as well as shortage level but a higher (reference) price. Moreover, the manufacturer is worse off when demand uncertainty is increased, whereas he can generate more profit by taking advantage of the randomness of the reference price. Finally, we show that the expected steady-state production rate decreases, but price increases as the reference effect factor or customers’ memory parameter increases.

中文翻译：

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随机参考价格效应下的联合生产定价库存系统

摘要 我们在连续时间框架中研究了在无限范围内随机参考价格效应下制造商的联合动态生产和定价问题。对产品的需求取决于其价格和基于内存的参考价格，是不确定的，并具有随机过程的特点。参考价格效应因消费者而异，并受一些以随机过程为特征的随机性的影响。使总预期利润最大化的联合动态生产和定价问题被建模为随机最优控制问题。我们给出了最优解存在的充分条件，并刻画了一般凸成本结构的解。此外，我们展示了状态变量的线性反馈形式的策略（即，库存和参考价格）对于严格凸成本结构是最优的，并且为预期稳态库存和参考价格提供稳定性和单调收敛性的充分条件。执行数值示例和敏感性分析以提供几个重要的管理见解。我们发现最优生产率和销售价格均与库存存量呈负相关，而与参考价格水平呈正相关。在预期稳态下，需求不确定性对最优策略没有影响，而较高的参考价格不确定性会导致较低的生产率和短缺水平，但会导致较高的（参考）价格。此外，当需求不确定性增加时，制造商的处境更糟，而他可以利用参考价格的随机性产生更多的利润。最后，我们表明预期稳态生产率下降，但价格随着参考效应因子或客户记忆参数的增加而增加。