A two storage inventory model for deteriorating items with variable demand and partial backlogging

The goal of this article is to develop a deterministic inventory model for single deteriorating items with two separate storage facilities (owned and rented warehouse, RW) due to limited capacity of the existing storage (owned warehouse, OW). The demand rate of the item is dependent on time, selling price of an item, and the frequency of advertisement in the popular electronic and print media and also through the sales representatives. The stocks of RW are transported to OW in continuous release pattern. Shortages, if any, are allowed and partially backlogged with a variable rate dependent on the duration of waiting time up to the arrival of next lot. The storage capacities of the warehouses are assumed to be limited (finite). According to the relative size of the storage capacities of warehouses, the different scenarios with sub-scenario have been mentioned for the stock level at initial and reorder points of the proposed inventory system. For each sub-scenario, the corresponding problem has been formulated as mixed integer nonlinear constrained optimization problem. For solving this problem, we have used GRG method. To illustrate the proposed model, a numerical example has been considered and solved. Finally, to perform the sensitivity analyses, the effects of changes of demand, deterioration, and backlogging parameters on the initial stock level, reorder point, cycle length, and frequency of advertisement along with the maximum profit of the system have been studied.