The three-machine proportionate flow shop problem with unequal machine speeds

Sixiang Hou; Han Hoogeveen

doi:10.1016/S0167-6377(02)00232-8

The three-machine proportionate flow shop problem with unequal machine speeds

Sixiang Hou
, Han Hoogeveen^*

^*Corresponding author for this work

CAS - Institute of Policy and Management

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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.

Original language	English
Pages (from-to)	225-231
Number of pages	7
Journal	Operations Research Letters
Volume	31
Issue number	3
DOIs	https://doi.org/10.1016/S0167-6377(02)00232-8
Publication status	Published - May 2003

Bibliographical note

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).

Funding

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).

Keywords

Dynamic programming
Machine speeds
Makespan
Ordered processing times
Proportionate flow shop
script N sign ℘-hardness
V-shaped

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Cite this

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title = "The three-machine proportionate flow shop problem with unequal machine speeds",

abstract = "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.",

keywords = "Dynamic programming, Machine speeds, Makespan, Ordered processing times, Proportionate flow shop, script N sign ℘-hardness, V-shaped",

author = "Sixiang Hou and Han Hoogeveen",

note = "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).",

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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.

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KW - Ordered processing times

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KW - script N sign ℘-hardness

KW - V-shaped

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ER -

The three-machine proportionate flow shop problem with unequal machine speeds

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