Selective capacitated location-routing problem with incentive-dependent returns in designing used products collection network

This paper addresses a generalization of the capacitated location-routing problem (CLRP) arising in the design of a collection network for a company engaged in collecting used products from customer zones. The company offers customers a financial incentive per unit of used products. This incentive determines the quantity of used products which are returned by customers. Moreover, it is not necessary for the company to visit all customer zones or to collect all returns in each visited customer zone. The objective is to simultaneously find the location of collection centers, the routes of vehicles, the value of incentive offered and the amount of used products collected from customer zones, so as to maximize the company's overall profit. We develop two mixed integer linear programming formulations of the problem and a heuristic algorithm based on iterated local search. Extensive computational experiments on this problem demonstrate the effectiveness of the proposed algorithm.