A stochastic bi-objective location model for strategic reverse logistics

In this paper we propose a comprehensive model for reverse logistics planning where many real-world features are considered such as the existence of several facility echelons, multiple commodities, choice of technology and stochasticity associated with transportation costs and waste generation. Moreover, we adopt a bi-objective model for the problem. First, the cost for building and operating the network is to be minimized. Second, the obnoxious effect caused by the reverse network facilities is also to be minimized. A two-stage stochastic bi-objective mixed-integer programming formulation is proposed, in which the strategic decisions are considered in the first stage and the tactical/operational decisions in the second one. A set of different scenarios is considered, and the extensive form of the deterministic equivalent problem is presented. This model is tested with a case study based on some data from the Spanish province of Cordoba. Nondominated solutions are obtained by combining the two different objectives and by using a general solver.