In this paper, we study an inventory model for an omnichannel retailer, that is, a retailer that sells items both via brick-and-mortar stores and online. Online items are delivered from a warehouse, which also replenishes the stores. When the inventory in a store drops below a certain level, the retailer offers customers a discount for purchasing online. In this way, the retailer can save items for customers who need the item immediately and thus avoid lost sales. For this model, we propose an approximation method for calculating the average inventory costs for one store and one warehouse and an optimization procedure for the case of more stores. Using extensive numerical experiments, we show that the approximations are very close to the performance measured via simulation. Finally, we show that by adopting the discounts policy proposed in this paper, the retailer can reduce its total cost, on average, by 8.5% compared to the no-discounts policy.

在本文中，我们研究了全渠道零售商的库存模型，即通过实体店和在线销售商品的零售商。在线商品从仓库交付，仓库也为商店补货。当商店中的库存下降到一定水平以下时，零售商会为客户提供在线购买折扣。通过这种方式，零售商可以为需要该物品的客户立即保存物品，从而避免销售损失。对于这个模型，我们提出了一种近似方法来计算一个商店和一个仓库的平均库存成本，以及一个针对更多商店情况的优化程序。通过广泛的数值实验，我们表明近似值非常接近通过模拟测量的性能。最后，