TY - JOUR
T1 - Semi-V-shape property for two-machine no-wait proportionate flow shop problem with TADC criterion
AU - Kovalev, Sergey
AU - Kovalyov, Mikhail Y.
AU - Mosheiov, Gur
AU - Gerstl, Enrique
N1 - Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/1/17
Y1 - 2019/1/17
N2 - The problem of minimising total absolute deviation of job completion times in a two-machine no-wait proportionate flow shop has been recently studied. It was shown that the LPT (largest processing time first) job sequence is optimal if the number of jobs n does not exceed 7, and that the LPT sequence is not optimal for instances with n ≥ 8. We prove that there exists an optimal semi-V-shaped job sequence, in which the first job has the largest processing time, a certain number, greater than n / 2, of the following jobs appear in the LPT order, and jobs following job with the minimum processing time are sequenced in the SPT (shortest processing time first) order. We also present an O(n3) time dynamic programming algorithm to find the best V-shaped job sequence, in which the jobs on the left of the job with the minimum processing time are sequenced in the LPT order and those on the right of this job are sequenced in the SPT order.
AB - The problem of minimising total absolute deviation of job completion times in a two-machine no-wait proportionate flow shop has been recently studied. It was shown that the LPT (largest processing time first) job sequence is optimal if the number of jobs n does not exceed 7, and that the LPT sequence is not optimal for instances with n ≥ 8. We prove that there exists an optimal semi-V-shaped job sequence, in which the first job has the largest processing time, a certain number, greater than n / 2, of the following jobs appear in the LPT order, and jobs following job with the minimum processing time are sequenced in the SPT (shortest processing time first) order. We also present an O(n3) time dynamic programming algorithm to find the best V-shaped job sequence, in which the jobs on the left of the job with the minimum processing time are sequenced in the LPT order and those on the right of this job are sequenced in the SPT order.
KW - dynamic programming
KW - scheduling
KW - two-machine no-wait flow shop
KW - v-shape property
UR - http://www.scopus.com/inward/record.url?scp=85046891427&partnerID=8YFLogxK
U2 - 10.1080/00207543.2018.1468097
DO - 10.1080/00207543.2018.1468097
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AN - SCOPUS:85046891427
SN - 0020-7543
VL - 57
SP - 560
EP - 566
JO - International Journal of Production Research
JF - International Journal of Production Research
IS - 2
ER -