A two warehouse inventory model for deteriorating items with time dependent partial backlogging and variable demand dependent on marketing strategy and time

Abstract

This paper deals with a deterministic inventory model for single deteriorating items with two separate storage facilities (own and rented warehouses) due to limited capacity of the existing storage i.e., own warehouse. The demand rate of this item is dependent on continuous time, selling price of the item and the frequency of advertisement in the popular electronic and print media and also through the sales representatives. The replenishment rate is infinite. The stock is transferred from the rented warehouse to own warehouse in continuous release pattern and the associated transportation cost is taken into account. Shortages, if any, are allowed and partially backlogged with a rate dependent on the duration of waiting time up to the arrival of next lot. The corresponding problem has been formulated as a constrained non-linear mixed integer problem. Finally, the model has been illustrated with a numerical example and to study the effect of changes of different system parameters on initial stock level, maximum shortage level, cycle length, frequency of advertisement along with the maximum profit of the system, sensitivity analyses have been carried out by changing one parameter at a time and keeping the other parameters at their original values.