Improved approximation algorithms for two-stage flowshops scheduling problem

•This relationship between the multiple two-stage flowshops problem and the classical MAKESPAN problem is studied.•If the MAKESPAN problem has an α-approximation algorithm, then the problem has a 2α-approximation algorithm.•Two restricted cases of the problem, which are of practical importance, have an (α+1/2)-approximation algorithm.•The approximation ratios 2.6 for the problem and 11/6 for two restricted cases are improved to 2+ϵ and 1.5+ϵ respectively.