FLOW SHOP SCHEDULING WITH RANDOM PROCESSING TIMES AS TRAPEZOIDAL FUZZY NUMBERS TO ATTAIN MINIMUM SUM OF WAITING TIME OF JOBS
By
Bharat Goyal1 and Deepak Gupta2
1General Shivdev Singh Diwan Gurbachan Singh Khalsa College, Patiala, Punjab, India-147001
2Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala, Haryana, India-133203
Email: bhartu89@gmail.com, bharat@khalsacollegepatiala.org, guptadeepak20003@gmail.com
(Received: February 09, 2023; In format: February 20, 2024; Revised October 13, 2024; Accepted: October 20, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54202
Abstract
In earlier times Flow shop scheduling (FSS) in fuzzy circumstantial has acknowledged slight attention. The paper presents the effect of the waiting time of jobs in a 2 machine k- job FSS in fuzzy environment. The processing time of jobs satisfies trapezoidal fuzzy membership function. The foremost goal of the study is to find a sequence of jobs which delivers a least total waiting time of jobs. A heuristic approach has been adopted to achieve the desired objective. The experiments has been conducted for more than 2000 problems of various sizes. The problems with special structures as well as with random times of processing has been considered in the computational experiments. The Weighted Mean Absolute error (WMAE) for the average of the total waiting time has been computed for each job size which reveals that the presented step by step procedure of the Heuristic significantly delivers close to optimal solutions.
2020 Mathematical Sciences Classification: 68M20, 90B35, 90B36, 03E75.
Keywords: Fuzzy, Special Structures, FSS, Waiting time, Processing Time, Heuristic