A stochastic inventory model for newsvendor-type products with two warehouses

Almost all the studies to date on the two-warehouse (one is an owned warehouse, denoted by OW, and the other is a rented warehouse, denoted by RW) inventory problem concentrated on the deterministic demand pattern. In practice, however, it is very common for a distributor that sells the seasonal goods with random demand to store excess inventory in rented warehouses when the storage capacity of the owned warehouse is not enough. Therefore, this paper develops a stochastic inventory model for newsvendor-type products with two warehouses and a mixture of backorders and lost sales. Unlike the exiting newsvendor models, it is assumed in the present paper that the inventory system has two ordering opportunities and is willing to place a second order to meet part of unfilled demand at the selling period only if the backordered demand exceeds a threshold quantity. The existence and the uniqueness of the solution to relevant systems are examined, and the sufficient and necessary condition of judging whether to rent RW and the solution procedure of the considered model are presented as well. At last, numerical example is implemented to illustrate the application of the model.