Used products collected for value recovery are characterized by higher uncertainty regarding their quality condition compared to raw materials used in forward supply chains. Because of the need for timely information regarding their quality, a common business practice is to establish procedures for the classification of used products (returns), which is not always error-free. The existence of a multitude of sites where used products can be collected, further increases the complexity of reverse supply chain design and management. In this paper we formulate the objective function for a reverse supply chain with multiple collection sites and the possibility of returns sorting, assuming general distributions of demand and returns quality in a single-period context. We derive conditions for the determination of the optimal acquisition and remanufacturing lot-sizing decisions under alternative locations of the unreliable classification/sorting operation. We provide closed-form expressions for the selection of the optimal sorting location in the special case of identical collection sites and guidelines for tackling the decision-making problem in the general case. Furthermore, we examine analytically the effect of the cost and accuracy of the classification procedure on the profitability of the alternative supply chain configurations. Our analysis, which is accompanied by a brief numerical investigation, offers insights regarding the impact of yield variability, number of collection sites, and location and characteristics of the returns classification operation both on the acquisition decisions and on the profitability of the reverse supply chain. 
Reverse supply chains: Effects of collection network and returns classification on profitability