Optimal partial backordering two-storage inventory model for deteriorating items with variable demand

The goal of this work is to develop an inventory model (deterministic) for single deteriorating items having two separate storage facilities (owned and rented warehouse) due to limited capacity of the existing storage (owned warehouse). The demand rate of the item is dependent on time, selling price of an item and frequency of advertisement in the popular electronic and print media, also through the sales representative. The stocks of rented warehouse are transported to the owned warehouse 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 warehouses are assumed to be limited (finite). According to the relative size of the storage capacities of warehouses, the different scenarios with sub-scenarios have been mentioned for the stock level at initial and reorder point of the proposed inventory system and solved with the help of generalised reduced gradient method. To illustrate the results, a numerical example is given. Finally, to study the effect of change of demand, deterioration and backlogging parameters on initial stock level, reorder point stock level, cycle length and frequency of advertisement along with the maximum profit of the system.