Closed-Loop Supply Chain Network Design under Uncertainties Using Fuzzy Decision Making

The importance of considering forward and backward flows simultaneously in supply chain networks spurs an interest to develop closed-loop supply chain networks (CLSCN). Due to the expanded scope in the supply chain, designing CLSCN often faces significant uncertainties. This paper proposes a fuzzy multi-objective mixed-integer linear programming model to deal with uncertain parameters in CLSCN. The two objective functions are minimization of overall system costs and minimization of negative environmental impact. Negative environmental impacts are measured and quantified through CO₂ equivalent emission. Uncertainties include demand, return, scrap rate, manufacturing cost and negative environmental factors. The original formulation with uncertain parameters is firstly converted into a crisp model and then an aggregation function is applied to combine the objective functions. Numerical experiments have been carried out to demonstrate the effectiveness of the proposed model formulation and solution approach. Sensitivity analyses on degree of feasibility, the weighing of objective functions and coefficient of compensation have been conducted. This model can be applied to a variety of real-world situations, such as in the manufacturing production processes.