A fuzzy goal programming model to strategic planning problem of a lead/acid battery closed-loop supply chain

Economical, environmental and governmental considerations have forced the lead/acid battery manufacturers to build-up an effective and efficient spent battery collection and recovery systems. The design and implementation of such a collection and recycling system is affected by the distribution, collection and recycling facilities' location decisions which are strategic and important. A fuzzy multi-objective, multi-echelon and multi-product mixed integer linear programming model with different importance and priorities are developed in this paper. In contrast to the existing multi-objective closed-loop supply chain network design models which are generally cost or profit oriented, a new objective namely “maximization of the collection of returned batteries covered by the opened facilities” is also taken into account. Since the lack of flexibility issues in most of the supply chain planning models, new flexibility objectives such as total recycling and collection volume flexibility are also introduced due to the nature of reverse flows. Fuzzy goal programming model with different importance and priorities is used to solve the developed model. Furthermore, a novel approach for obtaining the desirable achievement degree of each fuzzy goal is proposed based on “weighted geometric mean” for group decision making procedure in which the importance/weights and the index of optimism of each group member are different. The proposed model is applied to an illustrative example based on inspiration from the lead/acid industry in Turkey. Solution of the proposed model is achieved by using ILOG OPL Studio version 6.3. Sensitivity analysis of the proposed model is also presented by considering different scenarios.