Optimal echelon stock policies for multi-stage supply chains in fuzzy environments

This paper investigates decision-making in multi-echelon serial supply chain management in the presence of imprecision or uncertainty arising from human reasoning, emphasising the computational resolution. The proposed analysis method is based on a combination of the extension principle and the alpha-representation in fuzzy theory and optimisation theory. The problem is first formulated as a fuzzy optimisation model with several fuzzy parameters. To conserve the fuzziness of the input information of the supply chain, such as forecast market demands and inventory costs, a pair of two-level mathematical programs is proposed to identify the lower and upper bounds of the fuzzy performance at different possibility levels, so that the complete membership function can be described. Four example scenarios are solved to demonstrate the validity of the proposed analysis method. The proposed methodology is widely applicable with different types of membership functions for fuzzy parameters, positive lead times or other more complicated cases. The managerial implications are also discussed for reference by decision-makers.