Solving the fuzzy earliness and tardiness in scheduling problems by using genetic algorithms

The scheduling problems with fuzzy processing times and fuzzy due dates are concerned in this paper. The fuzzy earliness and fuzzy tardiness are proposed based on the concepts of subtraction and maximum of any two fuzzy numbers, which are defined by using the well-known “Extension Principle” in fuzzy sets theory. The objective function is taken as the weighted sum of fuzzy earliness and fuzzy tardiness through the concept of addition among fuzzy numbers. In this case, the objective function turns into a fuzzy-valued function. The purpose of this paper is to obtain an optimal schedule that minimizes this fuzzy-valued objective function. The genetic algorithm will be invoked to solve this problem. Two numerical examples are also provided to clarify the discussions in this paper by using the commercial software MATLAB.