A Constructive Heuristic “MDSA” Solving the Flexible Job Shop Scheduling Problem

Abstract

This paper considers a novel heuristic algorithm called “MDSA” (Minimal Deviation Strategy Algorithm) for solving Flexible Job Shop Scheduling Problems (FJSSP). In the optimization of the machine schedule, one objective function is considered - the “makespan”, i.e., the maximum completion time for all operations of all jobs is minimized. The algorithm is based on a strategy of minimizing machine idle times and scheduling the operations so that they are executed in an optimal time (Shortest Processing Time - SPT) or in a time with minimum deviation from the SPT. The aim is that the sum of the working time of a machine and its idle times is approximately equal to this sum for each of the other machines, i.e. the completion times of the machines should be approximately equal. The heuristic algorithm is constructive and generates a near-optimal solution in a time that depends polynomially on the number of operations and the number of machines. The performance of the algorithm on an illustrative example is considered. We compare the MDSA performance on 20 test instances taken from the literature with the performance results of a Genetic Algorithm (GA) on the same instances. The obtained results are encouraging and show that this type of heuristics can be used to quickly find approximately optimal solutions, which in turn can serve as initial solutions for exact methods and can save a large amount of computational effort and time, especially for problems of large size.