An inventory model with discounts for omnichannel retailers of slow moving items

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.