TY - JOUR

T1 - Low-complexity algorithms for sequencing jobs with a fixed number of job-classes

AU - Van Der Veen, Jack A.A.

AU - Zhang, Shuzhong

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1996/11

Y1 - 1996/11

N2 - In this paper we consider the problem of scheduling n jobs such that makespan is minimized. It is assumed that the jobs can be divided into K job-classes and that the change-over time between two consecutive jobs depends on the job-classes to which the two jobs belong. In this setting, we discuss the one machine scheduling problem with arbitrary processing times and the parallel machines scheduling problem with identical processing times. In both cases it is assumed that the number of job-classes K is fixed. By using an appropriate integer programming formulation with a fixed number of variables and constraints, it is shown that these two problems are solvable in polynomial time. For the one machine scheduling case it is shown that the complexity of our algorithm is linear in the number of jobs n. Moreover, if the problem is encoded according to the high multiplicity model of Hochbaum and Shamir, the time complexity of the algorithm is shown to be a polynomial in log n. In the parallel machine scheduling case, it is shown that if the number of machines is fixed the same results hold.

AB - In this paper we consider the problem of scheduling n jobs such that makespan is minimized. It is assumed that the jobs can be divided into K job-classes and that the change-over time between two consecutive jobs depends on the job-classes to which the two jobs belong. In this setting, we discuss the one machine scheduling problem with arbitrary processing times and the parallel machines scheduling problem with identical processing times. In both cases it is assumed that the number of job-classes K is fixed. By using an appropriate integer programming formulation with a fixed number of variables and constraints, it is shown that these two problems are solvable in polynomial time. For the one machine scheduling case it is shown that the complexity of our algorithm is linear in the number of jobs n. Moreover, if the problem is encoded according to the high multiplicity model of Hochbaum and Shamir, the time complexity of the algorithm is shown to be a polynomial in log n. In the parallel machine scheduling case, it is shown that if the number of machines is fixed the same results hold.

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U2 - 10.1016/0305-0548(96)00016-0

DO - 10.1016/0305-0548(96)00016-0

M3 - Article

AN - SCOPUS:0030290532

VL - 23

SP - 1059

EP - 1067

JO - Computers and Operations Research

JF - Computers and Operations Research

SN - 0305-0548

IS - 11

ER -