A mathematical programming approach to supply chain models with fuzzy parameters

Supply chain (SC) models play an important role in supply chain management (SCM) for reducing costs and finding better ways to create and deliver value to customers. An approach to deriving the membership function of the fuzzy minimum total cost of the multi-product, multi-echelon, and multi-period SC model with fuzzy parameters is proposed in this article. On the basis of alpha-cut representation and the extension principle, a pair of mathematical programs are formulated to calculate the lower and upper bounds of the fuzzy minimum total cost at possibility level alpha. The membership function of the fuzzy minimum total cost is constructed by enumerating different values of alpha. To demonstrate the validity of the proposed procedure, a four-echelon five-period SC model with fuzzy parameters is solved successfully. Since the objective value is expressed by membership functions rather than by crisp values, they completely conserve the fuzziness of input information when some of the SC data are ambiguous. Thus the proposed approach can represent SCs with fuzzy parameters more accurately, and more information is provided for designing SCs in real-world applications.