Liu Jue, Pang Zhan, Qi Linggang
School of Management and Engineering, Nanjing University, Nanjing, China.
Krannert School of Management, Purdue University, United States.
Comput Oper Res. 2020 Dec;124:105078. doi: 10.1016/j.cor.2020.105078. Epub 2020 Aug 18.
We consider a retail firm selling a durable product in a volatile market where the demand is price-sensitive and random but its distribution is unknown. The firm dynamically replenishes inventory and adjusts prices over time and learns about the demand distribution. Assuming that the demand model is of the multiplicative form and unmet demand is partially backlogged, we take the empirical Bayesian approach to formulate the problem as a stochastic dynamic program. We first identify a set of regularity conditions on demand models and show that the state-dependent base-stock list-price policy is optimal. We next employ the dimensionality reduction approach to separate the scale factor that captures observed demand information from the optimal profit function, which yields a normalized dynamic program that is more tractable. We also analyze the effect of demand learning on the optimal policy using the system without Bayesian update as a benchmark. We further extend our analysis to the case with unobserved lost sales and the case with additive demand.
我们考虑一家零售公司，该公司在一个波动的市场中销售耐用产品，市场需求对价格敏感且具有随机性，但其分布未知。该公司会动态补充库存并随时间调整价格，同时了解需求分布。假设需求模型为乘法形式且未满足的需求部分积压，我们采用经验贝叶斯方法将该问题表述为一个随机动态规划。我们首先确定需求模型的一组正则条件，并表明状态依赖的基本库存标价政策是最优的。接下来，我们采用降维方法，从最优利润函数中分离出捕获观察到的需求信息的比例因子，从而得到一个更易于处理的归一化动态规划。我们还以不进行贝叶斯更新的系统为基准，分析需求学习对最优政策的影响。我们进一步将分析扩展到未观察到销售损失的情况以及加法需求的情况。
