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.Keywords: interruption; advance payment; price; partial backordering; lot sizing
Literature reviewInventory management is a group of policies used to enhance company efficiencies in using the inventory and decrease its related costs. The main goal of each inventory control system is improving the total profits of firms without decreasing the customers' satisfaction and also service levels. This area has attracted significant investigation since 1913 when the first mathematical model was developed by Harris, although most of these studies were performed under a deterministic environment (Cárdenas-Barrón et al., 2014). On the other hand, usually the cost of an order is spent at delivery time, while prepayment for some special products is commonly requested from the supplier ensuring that the purchaser never cancels the order.Nowadays, a new aspect of real-world problems named "disruption" has attracted both researchers' and practitioners' attention. Recently, the rate at which mathematical models are C 2016 The Authors.