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

Authors:
Sixiang Hou;Han Hoogeveen
Affiliations:
Institute of Policy and Management, Chinese Academy of Sciences, P.O. Box 8712, Beijing 100080, China;Department of Computer Science, Utrecht University, P.O. Box 80089, 3508 TB Utrecht, The Netherlands
Venue:
Operations Research Letters
Year:
2003

Citing 0
Cited 3

Proportionate flexible flow shop scheduling via a hybrid constructive genetic algorithm

Expert Systems with Applications: An International Journal
A note on makespan minimization in proportionate flow shops

Information Processing Letters
Minimizing makespan in an ordered flow shop with machine-dependent processing times

Journal of Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

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 NP-hardness in the ordinary sense.