Solutions to the Constrained Flowshop Sequencing Problem

Abstract

If the flowshop sequencing problem is constrained so that job profiles are maintained independently of other work on the shop, then a range of new problem solutions are possible. Using geometrical relationships between the cumulative process times, a slope matching method has been devised which generally provides better results than Palmer's method and Gupta's algorithm. Secondly, it has been possible to reformulate the flowshop sequencing problem in terms of the travelling salesman problem. This has enabled the performance of the slope matching, Palmer and Gupta methods to be compared against a non-heuristic solution. Finally, provided that expressing a job in terms of the slopes of the cumulative start and end times is satisfactory, this enables in n-job, M-machine flowshop to be converted into an equivalent n-job 2 machine flowshop to which the use of Johnson's method will provide optimal sequences.

^*Now with Arthur Young, McClelland, Moores & Co.

^*Now with Arthur Young, McClelland, Moores & Co.