An integrated vendor-buyer inventory model with partial backordering

Purpose - The purpose of this paper is to analyze the effects of supply chain coordination on inventory management while the retailer inventory cycle consists of a shortage period and the backorder rate linearly decreases as a function of shortage duration. It is intended to consider how on-hand inventory and shortage durations are altered when the decisions are centralized. Design/methodology/approach - Mathematical modelling of inventory costs for the retailer and the vendor is used to formulate objective functions. The vendor sets his inventory period as an integer multiple (n) of the retailer inventory cycle in which the integer multiple is a decision variable. Solution spaces of models are analyzed to determine two other decision variables including, on-hand inventory duration and shortage length. Findings - The integrated model consists of a unique pseudo convex area when (n) is fixed and as a result, there is a unique minimum point. Based on numerical examples and sensitivity analysis, in most situations coordinated inventory management reduces total costs of the supply chain and cost reduction rate increase at larger production rates. Originality/value - This paper is a combination between production-inventory models in two-stage supply chains and partial backordering, which has appeared in single inventory models. To the best of the authors' knowledge, no mathematical model has yet been proposed. Moreover, the benefits of synchronization are analyzed through numerical examples.