Numerical Studies of Single Machine Scheduling Problem (SMSP) using Fuzzy Logic & Genetic Algorithm

Abstract

Single Machine Scheduling Problems arise in the literature of scheduling problems where n number of jobs is to be scheduled on a single machine with minimization of Tardiness. Most of the earlier literature dealt with solving the SMSP using dispatch rules such as FCFS, SPT, LPT, EST, EDD, MPT, MCT and CR. Genetic Algorithms are class of evolutionary algorithms, where the solution set is determined by Genetic Operators such as Crossover & Mutation. Most of the researchers in the area of combinatorial optimization are using fuzzy logic to solve the SMSP. Fuzzy logic is basically a multi valued logic that allows intermediate values to be defined between conventional evaluations like yes or No, True or false & black or white. Hence in the following paper a SMSP is solved using GA and Fuzzy logic. A comparative study with numerical example is presented for Moving average, average High Ranking, triangular membership function, Trapezoidal membership function and Gaussian membership functions. The obtained results are compared with solutions of GA. The penalty cost for earliness and tardiness are also presented. Genetic Algorithm with fuzzy parameterization in Mutation Function is discussed as future scope of work.