TY - JOUR
T1 - The three-machine proportionate flow shop problem with unequal machine speeds
AU - Hou, Sixiang
AU - Hoogeveen, Han
N1 - Funding Information:
The authors thank an anonymous referee for his/her comments. Part of this research was conducted when the first author visited Eindhoven University of Technology, which visit was made possible by a grant from Nuffic. The second author was partially supported by EC Contract IST-1999-14186 (Project ALCOM-FT).
PY - 2003/5
Y1 - 2003/5
N2 - In flow shop scheduling it is usually assumed that the processing times of the operations belonging to the same job are unrelated. But when a job corresponds to producing a certain quantity of some good, then it is likely that the processing times are related to this quantity, and hence are constant except for some factor that depends on the speed of the machine. In this paper, we consider this special case of the flow shop problem, which we call the proportionate flow shop problem with unequal machine speeds. This is a special case of the flow shop problem with ordered processing times that has been studied by Smith, Panwalkar, and Dudek. Their results imply that makespan minimization is easy if the first or last machine is slowest; if the second machine is slowest, then there exists an optimum schedule that is V-shaped. We provide an algorithm that solves this problem (and the more general problem with ordered processing times) to optimality in pseudopolynomial time, and we show that this is best possible by establishing script N sign ℘-hardness in the ordinary sense.
AB - In flow shop scheduling it is usually assumed that the processing times of the operations belonging to the same job are unrelated. But when a job corresponds to producing a certain quantity of some good, then it is likely that the processing times are related to this quantity, and hence are constant except for some factor that depends on the speed of the machine. In this paper, we consider this special case of the flow shop problem, which we call the proportionate flow shop problem with unequal machine speeds. This is a special case of the flow shop problem with ordered processing times that has been studied by Smith, Panwalkar, and Dudek. Their results imply that makespan minimization is easy if the first or last machine is slowest; if the second machine is slowest, then there exists an optimum schedule that is V-shaped. We provide an algorithm that solves this problem (and the more general problem with ordered processing times) to optimality in pseudopolynomial time, and we show that this is best possible by establishing script N sign ℘-hardness in the ordinary sense.
KW - Dynamic programming
KW - Machine speeds
KW - Makespan
KW - Ordered processing times
KW - Proportionate flow shop
KW - script N sign ℘-hardness
KW - V-shaped
UR - http://www.scopus.com/inward/record.url?scp=0037402799&partnerID=8YFLogxK
U2 - 10.1016/S0167-6377(02)00232-8
DO - 10.1016/S0167-6377(02)00232-8
M3 - Article
AN - SCOPUS:0037402799
SN - 0167-6377
VL - 31
SP - 225
EP - 231
JO - Operations Research Letters
JF - Operations Research Letters
IS - 3
ER -