Optimizing constant pricing and inventory decisions for a periodic review system with batch ordering

Abstract

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.