New results for minimising variation of flow time in two-machine proportionate no-wait flow shops

Abstract

In this paper, the two-machine no-wait proportionate flow shop problem is analysed with the objective of minimising the total absolute deviation of job completion times. The optimality of V-shaped sequences is extended to problems with 12 jobs and it is shown that an optimal sequence may not be V-shaped with 13 jobs. For problems of larger size, the best V-shaped sequence is determined in linear time without resorting to dynamic programming. For larger size problems, it is shown that the number of non-dominated potentially optimal semi-V-shaped sequences increases rapidly. This indicates that derivation of optimal solutions in low order polynomial time is unlikely with a large number of jobs. Finally, the findings are extended to the corresponding problem with the objective of minimising the total absolute differences in waiting times.