A heuristic approach to minimizing the waiting time of jobs in two-stage flow shop scheduling

The paper presents the influence of the waiting time of jobs in a 2 machine k-job Flow Shop Scheduling (FSS) problem. The main intention of the study is to find a sequence of jobs that delivers the least sum of the time of waiting for jobs. A heuristic approach has been adopted to achieve the desired objective. The experiments are conducted for more than 2000 problems of various sizes for the problems with special structures and problems with random times of processing. The weighted mean absolute error (WMAE) for the average of the sum of the waiting times of jobs is computed for both kind of problems after comparing with the optimal solutions. WMAE has been obtained less than 0.0075 for problems with special structures and less than 0.087 for problems with random times of processing. The WMAE is also reducing significantly with the increase in job size. The results demonstrate that the presented step-by-step procedure of the heuristic delivers significantly close to optimal solutions.

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Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).