Selection of Collection Centers for Reverse Logistic Networks

In this paper, we address the problem of locating collection centers for a company that collects used products from product holders. Each product holder has an inherent willingness to return the product, and makes the decision on the basis of financial incentive offered by the company. We present a mixed-integer nonlinear facility location-allocation model to find the optimal locations, the optimal incentive values for different product types and the optimal vehicle type. Because the problem is NP-complete, a heuristic method is proposed to solve medium and largesize instances. We experiment with location dependent transportation costs which reflect the road conditions and other geographical factors. We conclude that the location dependent transportation cost approach is inferior to fixed transportation cost approach resulting in a higher loss of profit when the variation of the cost with respect to location is relatively high. INTRODUCTION The alarming increase in the use of virgin resources to produce new products has threatened the environment. The governments and consumers are quite aware of this phenomenon which has led to several legislations and given birth to the concept of environment consciousness. The goal of environmentally conscious manufacturing is to produce goods with minimal (or zero) harm to the environment. The concept of environment consciousness, however, now extends beyond manufacturing and includes the responsibility to manage the end-of-life products by the manufacturer [3]. The process involved in collecting, transporting and managing the EOL products is known as reverse logistics. Reverse logistics and remanufacturing operations are more complex than forward logistics and traditional manufacturing operations. A lot of complexity stems from high degrees of uncertainties in the quality and quantity of products [2]. In reverse flow, the type of the recovery process is determined by the condition (quality) of returned products [1]. Just as the quality of returned products is unpredictable so is the quantity of returns as it may be dependent on the incentive offered to the last customer. The type of the product recovery is dependent on the condition of a returned product. The possibilities include repairing, refurbishing, remanufacturing, cannibalizing, and recycling [4]. Used product acquisition or collection is the first step of product recovery that triggers other activities of the recovery system. As was mentioned before, there are considerable uncertainties in quantity, timing, and quality of returned products. Manufacturers can influence the quantity of returns by using buy-back campaigns and incentives to product holders. Clearly, the amount of incentive offered by the company (also called unit acquisition price) influences the quality level of used product returns. Accepting all end-of-use products in the waste stream is not a viable strategy for most companies since a high percentage of these will have a poor quality, and hence will not be recoverable. As a result, a used product acquisition strategy, by offering an appropriate incentive, is crucial for a company engaged in product recovery [1]. In this paper, we present a model to find the optimal locations of a predetermined number of collection centers and the optimal incentive that should be offered by the company to product holders based on the quality condition of their used items. In this model we consider a pick-up scenario in which the company collects used products from the premises of the product holders and takes responsibility of all the collection-related costs. It is assumed that the willingness of the product holders to return is effected by the amount of the financial incentive offered. Thus, a higher incentive reduces the unit cost savings from a return, yet increases the product holders’ willingness to return their used products. MODEL Assumptions We assume that a pick-up strategy is in place according to which vehicles with limited capacity are dispatched from the collection centers to the locations of product holders to transport the returns. There are three vehicle alternatives (small, medium and large size) to be considered. There are no capacity constraints on collection centers. The cost per unit distance traveled between a customer zone and a candidate site is not fixed for all zone-site pairs. We also assume that the financial incentive offered by the company determines the willingness of product holders to return their used products. Nomenclature Parameters: m number of candidate sites, n number of customer zones, dij travel distance between customer zone j and, candidate site i, L number of vehicle alternatives, c1l operating cost of a vehicle of type l, c2ij cost per unit distance traveled between site i and zone j, ql capacity of a vehicle of type l, hj number of product holders living in zone j, K number product types, γjk proportion of product holders of type k in zone j, hjk number of product holders of type k living in zone j (hjk= γjkhj), sk unit cost savings from a used product of type k, ak the maximum incentive level of product holder of type k, ml travel cost coefficient for vehicles of type l, p number of collection centers to be opened. Variables: Π total profit, Xijk fraction of potential returns of type k collected in zone j and transported to the CC at site i, Vij number of vehicles required to transport returns from zone j to the CC at site i, Rk unit incentive offered (unit acquisition price) for a used product of type k,