TY - JOUR

T1 - Maximizing the weighted number of just-in-time jobs on a single machine with position-dependent processing times

AU - Mosheiov, Gur

AU - Shabtay, Dvir

N1 - Funding Information:
Acknowledgments This paper was supported in part by Charles Rosen Chair of Management and by the Recanati Fund of The School of Business Administration, The Hebrew University of Jerusalem.

PY - 2013/10/1

Y1 - 2013/10/1

N2 - We study the problem of maximizing the weighted number of just-in-time jobs on a single machine with position-dependent processing times. Unlike the vast majority of the literature, we do not restrict ourselves to a specific model of processing time function. Rather, we assume that the processing time function can be of any functional structure that is according to one of the following two cases. The first is the case where the job processing times are under a learning effect, i.e.; each job processing time is a non-increasing function of its position in the sequence. In the second case, an aging effect is assumed, i.e.; each job processing time is a non-decreasing function of its position in the sequence. We prove that the problem is strongly N P -hard under a learning effect, even if all the weights are identical. When there is an aging effect, we introduce a dynamic programming (DP) procedure that solves the problem with arbitrary weights in O (n 3) time (where n is the number of jobs). For identical weights, a faster optimization algorithm that runs in O (n log n) time is presented. We also extend the analysis to the case of scheduling on a set of m m parallel unrelated machines and provide a DP procedure that solves the problem in polynomial time, given that m m is fixed and that the jobs are under an aging effect.

AB - We study the problem of maximizing the weighted number of just-in-time jobs on a single machine with position-dependent processing times. Unlike the vast majority of the literature, we do not restrict ourselves to a specific model of processing time function. Rather, we assume that the processing time function can be of any functional structure that is according to one of the following two cases. The first is the case where the job processing times are under a learning effect, i.e.; each job processing time is a non-increasing function of its position in the sequence. In the second case, an aging effect is assumed, i.e.; each job processing time is a non-decreasing function of its position in the sequence. We prove that the problem is strongly N P -hard under a learning effect, even if all the weights are identical. When there is an aging effect, we introduce a dynamic programming (DP) procedure that solves the problem with arbitrary weights in O (n 3) time (where n is the number of jobs). For identical weights, a faster optimization algorithm that runs in O (n log n) time is presented. We also extend the analysis to the case of scheduling on a set of m m parallel unrelated machines and provide a DP procedure that solves the problem in polynomial time, given that m m is fixed and that the jobs are under an aging effect.

KW - Aging effect

KW - Just-in-time scheduling

KW - Learning effect

KW - Position-dependent processing times

UR - http://www.scopus.com/inward/record.url?scp=84884354261&partnerID=8YFLogxK

U2 - 10.1007/s10951-013-0327-z

DO - 10.1007/s10951-013-0327-z

M3 - Article

AN - SCOPUS:84884354261

VL - 16

SP - 519

EP - 527

JO - Journal of Scheduling

JF - Journal of Scheduling

SN - 1094-6136

IS - 5

ER -