Lot-sizing model with advance payment pricing and disruption in supply under planned partial backordering

Inventory management is a group of policies used to enhance company efficiencies in using the inventory and decrease its related costs. Inventory management policies operate efficiently only in the normal market environment. When the manager faces disruption, the common decisions do not lead to optimality. In this paper, a lot-sizing model for when the retailer may face disruption is developed. A portion of purchasing cost should be spent before delivery by several predetermined equal-sized advanced payments; shortage is permitted and will be partially back-ordered. The total cost function includes purchasing, holding, capital, backordering, and lost sale costs. The optimal decisions are obtained after proving the convexity of the expected total cost function. Finally, a solution algorithm is presented and several numerical examples and analysis are provided to show that the developed model and derived results can be applied to real-world problems.