An inventory model for nonperishable items with warehouse mode selection and partial backlogging under trapezoidal-type demand

Considering a nonperishable product which may be stored either in an own warehouse or in both the own and the rented warehouse, this paper deals with the ordering decisions under a generalized trapezoidal-type demand rate in an inventory system. Shortages are allowed and the unsatisfied demand is assumed to be partially backlogged. Furthermore, the existence and uniqueness of the optimal solution to each warehouse mode is proved and used in an easy-to-use algorithm, and a decision-making theorem for measuring whether to adopt a rented warehouse is developed. Finally, numerical examples and a case study are presented to illustrate the feasibility and efficiency of the proposed model and algorithm. The results show that, the storage capacity of the own warehouse and the unit rental cost have remarkable impact on determining whether to use the rented warehouse. When both the unit rental cost and the unit opportunity cost are higher in the external market, the profitability of the inventory system mainly relies on the storage capacity of the own warehouse. Meanwhile, the optimal profit performance is sensitive to the selling price and the purchasing cost, and the optimal rented warehouse’s ordering quantity is sensitive to the order cycle length. But overall, the proposed model is basically robust.