Title: Bicriteria scheduling on parallel machines: total tardiness and weighted flowtime in fuzzy environment

Authors: Sameer Sharma; Deepak Gupta; Seema Sharma

Addresses: Department of Mathematics, D.A.V. College, Jalandhar City, 144008 Punjab, India ' Department of Mathematics, M.M. University, Mullana, Ambala 133207 Haryana, India ' Department of Mathematics, D.A.V. College, Jalandhar City, 144008 Punjab, India

Abstract: This paper pertains to a bicriteria scheduling problem on parallel machines which minimises the weighted flowtime (WFT) with the condition that primary criteria of T_max remains optimised. The processing times of jobs are in fuzzy environment and are represented by triangular fuzzy numbers. The membership function of fuzzy processing times denotes the grades of satisfaction with respect to completion times of jobs. The objective of this paper is to schedule jobs on parallel, identical machines so as to minimise the secondary criteria of WFT without violating the primary criteria of maximum tardiness (T_max). Following the theoretical treatment, we provide numerical example(s) to demonstrate that the proposed algorithm has potential as a valuable analytical tool for researchers.

Keywords: fuzzy processing time; average high ranking; AHR; maximum tardiness; weighted flowtime; WFT; due dates; membership function; weighted jobs; parallel machine scheduling.

DOI: 10.1504/IJMOR.2013.054733

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.4, pp.492 - 507

Received: 09 Jun 2012
Accepted: 13 Jul 2012
Published online: 31 Mar 2014 *

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