Cost Evaluation of a (Q, r, K) Inventory Model with Two Demand Classes of Lost Sales and Backorders.

This paper considers an omnichannel retailer where a single product is sold to customers through both online and offline channels. The demand for the product in each channel is described by a Poisson process, and the two demand processes are independent. The retailer uses a (Q, r) policy to replenish the product from its supplier with a fixed ordering cost for each replenishment order. The replenishment lead time is constant. An inventory rationing policy known as critical level policy is employed, which allocates inventory to customer orders on a first-come, first-served basis if the on-hand inventory is above a threshold K. However, if the on-hand inventory falls below K, the retailer reserves the inventory for offline customers and online orders are backordered, but backorder costs are incurred only when there are online orders not delivered to customers before or at their required delivery time. Whenever the product is out of stock, offline orders are lost, incurring lost sales costs. The expected total cost of the inventory model composed of holding costs, backorder costs, lost sales costs, and ordering costs is evaluated analytically and compared with simulation results. Our findings indicate that the analytical results exhibit a high degree of precision, with the maximum deviation from the simulation results being within 0.5 percent. Furthermore, the computational time required for the numerical illustration of the analytical results was considerably less, amounting to over 98% reduction in comparison to the computational time for numerical simulation.