On some lower bounds for the permutation flowshop problem

Letchford, Adam and Dang, Thu and Caceres Gelvez, Sebastian (2023) On some lower bounds for the permutation flowshop problem. Computers and Operations Research, 159. ISSN 0305-0548

Text (flowshop-bounds)
flowshop_bounds.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (396kB)


The permutation flowshop problem with makespan objective is a classic machine scheduling problem, known to be NP-hard in the strong sense. We analyse some of the existing lower bounds for the problem, including the “job-based” and “machine-based” bounds, a bound from linear programming (LP), and a recent bound of Kumar and co-authors. We show that the Kumar et al. bound dominates the machine-based bound, but the LP bound is stronger still. On the other hand, the LP bound does not, in general, dominate the jobbased bound. Based on this, we devise simple iterative procedures for strengthening the Kumar et al. and LP bounds. Computational results are encouraging. In particular, we are able to obtain improved lower bounds for the “hard, small” instances of Vallada, Ruiz and Framinan.

Item Type:
Journal Article
Journal or Publication Title:
Computers and Operations Research
Uncontrolled Keywords:
ID Code:
Deposited By:
Deposited On:
16 Jun 2023 08:20
Last Modified:
19 Sep 2023 03:02