TY - JOUR

T1 - Multi-scenario scheduling to maximise the weighted number of just-in-time jobs

AU - Gilenson, Miri

AU - Shabtay, Dvir

N1 - Funding Information:
The authors are grateful to Professor V. N. Kokryakov for valuable scientific discussions. This work was partly supported by the Russian Foundation of Fundamental Research Grant 97-04-48888, the Russian Federation Program “Support of Scientific Schools” Grant 96-15-97742, Grant 1-286 of the Program “Frontiers in Genetics,” Grant 743 of the Federal Program “Integration,” MURST, and CNR. This study was carried out within the framework of the CNR–RAMS collaborative program “Copper Proteins and Copper Metabolism.”
Publisher Copyright:
© 2019 Operational Research Society.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - We study a multi-scenario scheduling problem on a single-machine and a two-machine flow-shop system. The criterion is to maximise the weighted number of just-in-time jobs. We first analyze the case where only processing times are scenario-dependent. For this case, we prove that the single-machine problem is solvable in polynomial time. We also prove that the unit weight two-machine flow-shop problem is solvable in polynomial time if processing times are scenario-dependent only on the second machine, and is ordinary (Formula presented.) -hard when processing times are scenario-dependent only on the first machine. This ordinary (Formula presented.) -hard result holds as long as the number of scenarios is fixed. Otherwise, the problem becomes strongly (Formula presented.) -hard. We then analyze the case where only weights are scenario-dependent. We adopt a multi-criteria approach and define several problem variations. We prove that one of them is polynomial solvable on a single machine and ordinary (Formula presented.) -hard in a two-machine flow-shop system. We also prove that all other problem variations are ordinary (Formula presented.) -hard even if there are only two scenarios, and are strongly (Formula presented.) -hard when the number of scenarios is arbitrary. Finally, we provide two pseudo-polynomial time algorithms for solving all the hard problems when the number of scenarios is fixed.

AB - We study a multi-scenario scheduling problem on a single-machine and a two-machine flow-shop system. The criterion is to maximise the weighted number of just-in-time jobs. We first analyze the case where only processing times are scenario-dependent. For this case, we prove that the single-machine problem is solvable in polynomial time. We also prove that the unit weight two-machine flow-shop problem is solvable in polynomial time if processing times are scenario-dependent only on the second machine, and is ordinary (Formula presented.) -hard when processing times are scenario-dependent only on the first machine. This ordinary (Formula presented.) -hard result holds as long as the number of scenarios is fixed. Otherwise, the problem becomes strongly (Formula presented.) -hard. We then analyze the case where only weights are scenario-dependent. We adopt a multi-criteria approach and define several problem variations. We prove that one of them is polynomial solvable on a single machine and ordinary (Formula presented.) -hard in a two-machine flow-shop system. We also prove that all other problem variations are ordinary (Formula presented.) -hard even if there are only two scenarios, and are strongly (Formula presented.) -hard when the number of scenarios is arbitrary. Finally, we provide two pseudo-polynomial time algorithms for solving all the hard problems when the number of scenarios is fixed.

KW - -hard

KW - Single-machine scheduling

KW - flow-shop scheduling

KW - just-in-time scheduling

KW - multi-scenario scheduling

UR - http://www.scopus.com/inward/record.url?scp=85064664533&partnerID=8YFLogxK

U2 - 10.1080/01605682.2019.1578628

DO - 10.1080/01605682.2019.1578628

M3 - Article

AN - SCOPUS:85064664533

VL - 72

SP - 1762

EP - 1779

JO - Journal of the Operational Research Society

JF - Journal of the Operational Research Society

SN - 0160-5682

IS - 8

ER -