Minimizing the Total Waiting Time for Fuzzy Two-Machine Flow Shop Scheduling Problem with Uncertain Processing Time

Abstract

Scheduling involves assigning resources to jobs within specified constraints over time. Traditionally, the processing time for each job was considered a constant value. However, in practical scenarios, job processing times can dynamically fluctuate based on prevailing circumstances. In this article, a novel approach is presented for the two-machine fuzzy Flow-Shop Scheduling Problem (FSSP) in a fuzzy environment, where job processing times are represented by trapezoidal fuzzy numbers. Additionally, a novel algorithm based on Goyal's approach for the two-machine FSSP with fuzzy processing times has been proposed and developed. Simultaneously, an existing algorithm has been enhanced to improve its performance in this specific context. The study aims to minimize the total waiting time for jobs. A defuzzification function is employed to rank fuzzy numbers, with the ultimate goal of minimizing the total waiting time. Furthermore, the article evaluates the performance of these methods in terms of solution quality, using test problems with 10, 20, 30, 40, 50, 60, 80, 90, 100, 120, 200, 250, 300, and 500 jobs, along with 2 machines. The mean total waiting time is compared to existing algorithms, including the NEH algorithm, Palmer's method, Johnson's method, B. Goyal and B. Kaur, and the proposed algorithm. Additionally, the obtained results, along with a well-structured ANOVA test, highlight the effectiveness of the proposed method in addressing the scheduling problem under investigation. The experimental results showcase that the proposed algorithm can effectively minimize the waiting time in fuzzy two-machine FSSP and achieve superior results when compared to various existing algorithms.