Single item periodic review inventory control with sales dependent stochastic return flows

Retailers have to deal with increasing levels of product returns as the shares of e-commerce sales soars. With this increase, it is no longer feasible to dispatch returned products to outlets or landfills, hence retailers must re-evaluate them both to maximize profit and to minimize their environmental impact. Our objective is to study a retailer’s optimal inventory control policy under product returns to maximize expected profit which is the sales revenue minus the procurement, backorder, holding, and salvage costs incurred in a finite horizon. We model a period’s returns to be stochastically dependent on the previous period’s sales quantity. Using dynamic programming formulation, we solve for the optimal periodic review inventory policy and provide structural results on the optimal policy of the final period. Through numerical studies, we show that incorporating detailed sales-dependent returns could increase a retailer’s expected profit by 23%. Ignoring this dependency in determining the optimal inventory policy results with increased order frequency, higher levels of backorders and more leftovers which could eventually end up in a landfill, but above all could lead to a significant overestimation of the resulting profit.