Special Classes of Fuzzy Integer Programming Models with All-different Constraints

Abstract

Abstract: In this paper, a fuzzy approach is applied to special classes of integer programming problems with all different constraints. In the first model, a fuzzy integer programming model is developed to represent the all-different constraints in mathematical programming. In order to solve the proposed model, a new branching scheme for the B&B algorithm is also presented. In the second model, a special class of large-scale multi-objective fuzzy integer programming problems with all-different constraints is introduced. A solution method for the proposed model is also developed by using the decomposition technique, weighting method and B&B algorithm. An illustrative numerical example is also given to clarify the theory and the method discussed in this paper.