In business practice the misalignment between frequent inventory adjustments and a sticky price is common. Motivated by Pipi Milk, a diary manufacturer who commits its customer at a fixed price for a whole year meanwhile weekly replenishes its cheese product stock at a specific batch size, this paper develops an integrated constant pricing and inventory control model in a periodic-review system with batch order consideration. For such a system, our focus is on an ( nQ , r )- p policy: the price p is determined and committed at the beginning of the planning horizon; inventories are managed based on an ( nQ , r ) policy with reorder level r and order quantities at non-negative integer multiples of batch size Q . With a fixed ordering cost included, we develop an efficient algorithm to compute the optimal policy parameters with the purpose to maximize the expected long-run average profit. We also numerically investigate the policy performance and verify its advantages by comparing to a sequential optimization of price and inventory decisions. Finally, managerial insights are generated.

中文翻译：

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优化具有批量订购的定期审查系统的恒定定价和库存决策

在商业实践中，频繁的库存调整和粘性价格之间的错位很常见。受 Pipi Milk 的启发，一家日记制造商以固定价格向客户承诺一整年，同时每周以特定批量补充其奶酪产品库存，本文在定期审查系统中开发了一个集成的恒定定价和库存控制模型考虑批量订单。对于这样的系统，我们的重点是 (nQ , r )-p 策略：价格 p 在规划期开始时确定并承诺；库存基于 (nQ, r) 策略进行管理，重新订购级别为 r，订购数量为批量大小 Q 的非负整数倍。包括固定的订购成本，我们开发了一种有效的算法来计算最优策略参数，目的是最大化预期的长期平均利润。我们还通过与价格和库存决策的顺序优化进行比较来数值研究政策表现并验证其优势。最后，产生管理洞察力。