EOQ model with batch demand and planned backorders

The existing literature about the backorder EOQ problem usually focuses on B2C (Business-to-Customer) and neglects the impact of batch demands to the backlogging behavior in B2B (Business-to-Business) environment. This paper contributes by formulating the inventory problem for a wholesaler facing batch demands and using backorder to control her inventory. The wholesaler's non-differentiable average cost function encompasses a curtain-like pattern. Based on its structural properties, we disclose the optimality conditions for the backlogging and ordering quantities. By using these conditions, efficient algorithms can be built to search for the optimal policy. Our discussion about the algorithm design is separated into two parts, i.e., with and w/o an integer requirement to the ordering quantity. In practice, it is more convenient to control the inventory if a wholesaler's ordering quantity is exactly an integer multiple of her customer's demanding size. As the integer requirement exists, a closed-form solution is provided to answer the optimal ordering quantity.