TY - JOUR

T1 - Minimizing the total tardiness and job rejection cost in a proportionate flow shop with generalized due dates

AU - Mor, Baruch

AU - Mosheiov, Gur

AU - Shabtay, Dvir

N1 - Funding Information:
The second author was supported by the Israel Science Foundation (grant No.2505/19), by the Recanati Fund of The School of Business Administration, and by Charles I. Rosen Chair of Management, The Hebrew University of Jerusalem, Israel.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - We study a scheduling problem involving both partitioning and scheduling decisions. A solution for our problem is defined by (i) partitioning the set of jobs into a set of accepted and a set of rejected jobs and (ii) scheduling the set of accepted jobs in a proportionate flow shop scheduling system. For a given solution, the jth largest due date is assigned to the job with the jth largest completion time. The quality of a solution is measured by two criteria, one for each set of jobs. The first is the total tardiness of the set of accepted jobs, and the second is the total rejection cost. We study two problems. The goal in the first is to find a solution minimizing the sum of the total tardiness and the rejection cost, while the goal in the second is to find a solution minimizing the total rejection cost, given a bound on the total tardiness. As both problems are NP-hard, we focus on the design of both exact algorithms and approximation schemes.

AB - We study a scheduling problem involving both partitioning and scheduling decisions. A solution for our problem is defined by (i) partitioning the set of jobs into a set of accepted and a set of rejected jobs and (ii) scheduling the set of accepted jobs in a proportionate flow shop scheduling system. For a given solution, the jth largest due date is assigned to the job with the jth largest completion time. The quality of a solution is measured by two criteria, one for each set of jobs. The first is the total tardiness of the set of accepted jobs, and the second is the total rejection cost. We study two problems. The goal in the first is to find a solution minimizing the sum of the total tardiness and the rejection cost, while the goal in the second is to find a solution minimizing the total rejection cost, given a bound on the total tardiness. As both problems are NP-hard, we focus on the design of both exact algorithms and approximation schemes.

UR - http://www.scopus.com/inward/record.url?scp=85111692123&partnerID=8YFLogxK

U2 - 10.1007/s10951-021-00697-4

DO - 10.1007/s10951-021-00697-4

M3 - Article

AN - SCOPUS:85111692123

SN - 1094-6136

VL - 24

SP - 553

EP - 567

JO - Journal of Scheduling

JF - Journal of Scheduling

IS - 6

ER -