Title: Multi-objective fuzzy job shop scheduling

Authors: Manjeet Singh; Gürsel A. Süer; Feyzan Arikan

Addresses: Industrial and Systems Engineering, Ohio University, Athens, OH, 45701, USA ' Industrial and Systems Engineering, Ohio University, Athens, OH, 45701, USA ' Industrial Engineering Department, Gazi University, Celal Bayar Boulevard, 06570 Maltepe-Ankara, Turkey

Abstract: The job shop scheduling problem (JSSP) deals with determining schedule for each resource/machine under job and machine flow restrictions such that the selected objective function is satisfied. Multi-objective scheduling is widely used to obtain desirable results in the existence of more than one performance measure in scheduling problems. The paper focuses on multi-objective scheduling in a job shop environment. One of the useful methods in multi-objective environment is the use of fuzzy operators in modelling the system. Fuzzy operators provide the model with characteristics where user can input desired bounds for all of the performance measures with suitable membership functions. In this study, three mathematical models are presented and combined as a multiple objective scheduling model where the considered three objectives are minimising number of tardy jobs, total tardiness and maximum tardiness, respectively. For the solution of the model, fuzzy programming is utilised by using min operator and augmented max-min operator. The model with augmented max min operator found only non-dominated solutions. Then mathematical model optimising two performance measure is also discussed. The quality between solutions obtained from math model optimising two performance measures model versus three performance measures is also discussed.

Keywords: job shop scheduling; fuzzy theory; non-dominated solutions; multi-objective scheduling; fuzzy scheduling; fuzzy logic; mathematical modelling; performance measures.

DOI: 10.1504/IJFCM.2014.064225

International Journal of Fuzzy Computation and Modelling, 2014 Vol.1 No.1, pp.15 - 36

Received: 18 May 2013
Accepted: 14 Jun 2013

Published online: 08 Aug 2014 *

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