A two-warehouse inventory model with imperfect quality production processes

One of the weaknesses of some production-inventory models is the unrealistic assumption that all items produced are of good quality. But production of defective units is a natural phenomenon in a production process. Defective items should be treated as a result of imperfect quality production. On the other hand, the classical inventory models usually assume the available warehouse has unlimited capacity. In many practical situations, there exist many factors like temporary price discounts making retailers buy a capacity of goods exceeding their own warehouse. In this case, retailers may rent other warehouses for the need of business. A lot of researchers studied inventory models with two warehouses and inventory models with imperfect quality separately. Compared with previous models, based on Salameh and Jaber [Salameh, M. K., Jaber, M. Y. (2000). Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64, 59–64.], this paper tries to incorporate the above concepts to establish a new inventory model with two warehouses and imperfect quality simultaneously. The mathematical model by maximizing the annual total profit and the solution procedure are developed and numerical examples are provided to illustrate them.