TY - JOUR

T1 - Minmax scheduling with acceptable lead-times

T2 - Extensions to position-dependent processing times, due-window and job rejection

AU - Gerstl, Enrique

AU - Mor, Baruch

AU - Mosheiov, Gur

N1 - Publisher Copyright:
© 2017 Elsevier Ltd

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We focus on a due-date assignment model where due-dates are determined by penalties for jobs exceeding pre-specified (job-dependent, different) deadlines. The underlying assumption of this model, denoted by DIF, is that there are "lead times that customers consider to be reasonable and expected". In a minmax DIF model, the value of the objective function is that of the largest job/due-date cost. The goal is to find both the job sequence and the due-dates, such that this value is minimized. In this paper we study several extensions of the minmax DIF model. First, we consider general position-dependent job processing times. Then we extend the model to a setting of a due-window for acceptable lead-times. Here, the assumption is that a time interval exists, such that due-dates assigned to be within this interval are not penalized. The last extension of the DIF model is to a setting allowing job-rejection. This option reflects many real-life situations, where the scheduler may decide to process only a subset of the jobs, and the rejected jobs are penalized. The first two extensions are shown to be polynomially solvable: we introduce solution algorithms requiring O(n3) and O(n4) time, respectively, where n is the number of jobs. The last extension (assuming job-rejection) is proved to be NP-hard in the ordinary sense, and an efficient pseudo-polynomial dynamic programming algorithm is introduced.

AB - We focus on a due-date assignment model where due-dates are determined by penalties for jobs exceeding pre-specified (job-dependent, different) deadlines. The underlying assumption of this model, denoted by DIF, is that there are "lead times that customers consider to be reasonable and expected". In a minmax DIF model, the value of the objective function is that of the largest job/due-date cost. The goal is to find both the job sequence and the due-dates, such that this value is minimized. In this paper we study several extensions of the minmax DIF model. First, we consider general position-dependent job processing times. Then we extend the model to a setting of a due-window for acceptable lead-times. Here, the assumption is that a time interval exists, such that due-dates assigned to be within this interval are not penalized. The last extension of the DIF model is to a setting allowing job-rejection. This option reflects many real-life situations, where the scheduler may decide to process only a subset of the jobs, and the rejected jobs are penalized. The first two extensions are shown to be polynomially solvable: we introduce solution algorithms requiring O(n3) and O(n4) time, respectively, where n is the number of jobs. The last extension (assuming job-rejection) is proved to be NP-hard in the ordinary sense, and an efficient pseudo-polynomial dynamic programming algorithm is introduced.

KW - Due-date assignment

KW - Job-rejection

KW - Minmax

KW - Position-dependent processing times

KW - Scheduling

KW - Single machine

UR - http://www.scopus.com/inward/record.url?scp=85013849367&partnerID=8YFLogxK

U2 - 10.1016/j.cor.2017.02.010

DO - 10.1016/j.cor.2017.02.010

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AN - SCOPUS:85013849367

SN - 0305-0548

VL - 83

SP - 150

EP - 156

JO - Computers and Operations Research

JF - Computers and Operations Research

ER -