Title: Bounding strategies for obtaining a lower bound for N-job and M-machine flowshop scheduling problem with objective of minimising the total flowtime of jobs

Authors: S. Saravana Kumar; C. Rajendran; Rainer Leisten

Addresses: Department of Management Studies, Indian Institute of Technology Madras, Chennai-600036, Tamil Nadu, India ' Department of Management Studies, Indian Institute of Technology Madras, Chennai-600036, Tamil Nadu, India ' Business Administration and Operations Management, Faculty of Engineering, University of Duisburg-Essen, Bismarckstrasse 90, 47057 Duisburg, Germany

Abstract: In this paper, bounding strategies for determining a lower bound on the completion time of a job sequenced in each position in the permutation sequence on each machine in permutation flowshop scheduling problem with minimisation of total flowtime of jobs as objective are discussed. Basically, the bounding strategies are machine-based bounding strategies used for determining the lower bound on total flowtime of jobs for all the small-sized and large-sized benchmark flowshop scheduling problem instances proposed by Vallada et al. (2015). The lower bound matrix can be pruned as tightening constraints into the mixed integer linear programming (MILP) model with objective of minimisation of total flowtime of jobs. Since the flowshop scheduling problem with total flowtime objective is difficult, two kinds of linear programming (LP) relaxation methods are used for determining an LP-based lower bound on total flowtime of jobs for some benchmark problem instances proposed by Vallada et al. (2015).

Keywords: scheduling; flowshop; total flowtime of jobs; lower bound.

DOI: 10.1504/IJOR.2021.115634

International Journal of Operational Research, 2021 Vol.41 No.2, pp.244 - 269

Received: 29 May 2018
Accepted: 14 Jul 2018
Published online: 15 Jun 2021 *

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