A fuzzy multi-objective model for determining optimal warehouse location in a green multiproduct, multi-period distribution network

Facility decisions play an important role in supply chains because they impact the total logistics cost and customer services directly. Due to climate change, most companies attempt to make facility decisions that result in less greenhouse gas emissions. To incorporate an environmental aspect to the facility decisions, this article involves determining an optimal location, among candidate locations, of a new distribution center, its capacity, as well as optimal network flows for an existing supply chain network, while considering the environmental impacts on the supply chain. In addition, uncertainties in transportation costs and warehouse operation costs are considered. A fuzzy bi-objective mixed integer linear programming model is formulated for the problem. Effectiveness of the proposed model is demonstrated using an industrial case study. The problem instance is a four-echelon distribution network, containing 22 products in 20 periods of planning horizon. The model is solved by the min-max approach and augmented ε-constraint method using CPLEX solver. Analysis of the results indicates that the solutions from the augmented ε-constraint method yield Pareto optimal solutions, which is on the frontier of the trade-off between the total logistics cost and gas emission.