Location and selective routing problem with pricing for the collection of used products

One of the key concerns of the companies involved in product recovery is used product (core) acquisition. In this paper, we consider a firm that aims to locate facilities which serve as collection centers (CCs) for the cores to be collected from the dealers. The dealer addresses as well as the amount of cores piled up at each dealer are known. Also, each dealer has a reservation price for the cores, and if the offered acquisition price by the firm is less than this reservation price, the dealer will not return its cores. The collection operation is performed by vehicles that must start and end their routes at the same CC without visiting another one in the route. The objective of the firm is to maximize its profit by determining the locations of the CCs, the acquisition price offered for each core, the number of vehicles allocated to each opened CC and the route of each vehicle. The source of the revenue is the cost savings that results from using the components of the cores in remanufacturing as-good-as-new products. For the solution of this problem, we develop a mixed-integer linear programming formulation, which is an extension of the classical location-routing problem where (i) there is a profit associated with each dealer visited and not all dealers have to be visited, and (ii) an acquisition price has to be paid to the dealers for each core. Since this problem is NP-hard, we develop a tabu search heuristic for solving large instances.