Total absolute deviation of job completion times on uniform and unrelated machines

Authors:
Baruch Mor;Gur Mosheiov
Affiliations:
School of Business Administration, The Hebrew University, Jerusalem 91905, Israel;School of Business Administration, The Hebrew University, Jerusalem 91905, Israel
Venue:
Computers and Operations Research
Year:
2011

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Abstract

Unlike other measures of variation of job completion times considered in scheduling literature, the measure of minimizing total absolute deviation of job completiontimes (TADC) was shown to have a polynomial time solution on a single machine. It was recently shown to remain polynomially solvable when position-dependent job processing times are assumed. In this paper we further extend these results, and show that minimizing TADC remains polynomial when position-dependent processing times are assumed (i) on uniform and unrelated machines and (ii) for a bicriteria objective consisting of a linear combination of total job completion times and TADC. These extensions are shown to be valid also for the measure of total absolute differences of job waiting times (TADW).