Optimizing product assortment, joint replenishments, and storage capacity allocation in a deteriorating inventory system

In this paper, we consider a single retailer who sells multiple products subject to decay, and that implements coordinated inventory replenishments among them. The overall available surface at the retailer is limited and is partitioned into two areas: the backroom facility and the display area. The demand rate of each product is a function of displayed quantity and location, and it also depends on the cross-elasticity among items. The objective is to find the product assortment, the replenishment policy of each product, the quantity to be displayed, and the surfaces assigned to the backroom and display areas that maximize the total profit per time unit. We develop the mathematical model and formulate the optimization problem. Finally, we investigate the model response by means of numerical experiments considering several problem instances.