Scheduling choice method for flexible job shop problems using a fuzzy decision maker

Abstract

The Flexible Job Shop Scheduling Problem (FJSP) emerges as a challenging extension of the classic Job Shop, presenting NP-Hard characteristics. In the FJSP, a set of jobs, comprising multiple operations, must be allocated to a predefined set of machines, each with its respective execution times. The distribution of operations across machines significantly impacts scheduling efficiency, which can be evaluated and optimized based on various performance criteria and objectives. To address this complex problem, a multi-objective optimization algorithm is employed, focusing on three main performance criteria: completion time of all operations (Makespan), load assigned to the most heavily utilized machine, and the sum of loads across all machines. An FJSP algorithm based on the Artificial Bee Colony (ABC) metaheuristic (FJSP. ABC) generates a Pareto set comprising non-dominated and dominated solutions. These solutions represent optimal or near-optimal production schedules and offer diverse representations, such as Gantt charts. However, the decision-making process for selecting the best production schedule from the Pareto set demands additional considerations. To this end, we propose adopting a decision-making (DM) algorithm based on Fuzzy TOPSIS (Technique for Order of Preference by Similarity to the Ideal Solution in a Fuzzy environment). The DM Fuzzy TOPSIS algorithm accommodates the inclusion of variables not covered by the FJSP algorithm and aids decision-makers in identifying the most suitable production schedule based on the specific requirements of the production system. These additional variables may include maximizing or minimizing machine idleness, balancing the load of operations on machines, etc. Experimental results demonstrate that the application of the proposed algorithm yields values close to the expected outcomes for the analyzed variables proposed. The DM Fuzzy TOPSIS algorithm proves to be a valuable tool for supporting decision-making in production systems, assisting in the selection of the best production schedule among the optimal or near-optimal solutions obtained from the Pareto set. By integrating multi-objective optimization and decision-making techniques, this research contributes to more efficient and informed production scheduling practices, ultimately enhancing overall system performance.