A membership function approach for aggregate production planning problems in fuzzy environments

This paper proposes a novel approach for the aggregate production planning (APP) problem with fuzzy parameters. Different from the results of previous studies, in this paper the membership function of the fuzzy minimal total cost is constructed based on Zadeh's extension principle and fuzzy solutions are provided. A pair of mathematical programs parameterised by possibility level α is formulated to calculate the lower and upper bounds of the fuzzy total cost at α. By enumerating different values of α, the membership function of the fuzzy total cost is constructed. To illustrate the validity of the proposed approach, the example studied by Lai and Hwang (1992 Lai, YJ and Hwang, CL. 1992. Fuzzy mathematical programming: methods and applications, Berlin: Springer.  Google Scholar]) using Chanas's approach is investigated. Since the objective value is expressed by a membership function rather than by a crisp value, the proposed approach can represent APP systems more accurately, thus obtained solutions which contain more information can offer more chance to achieve the feasible disaggregate plan, and it is beneficial to the decision-maker in practical applications. The proposed approach can also be applied to APP problems with other characteristics.