Approximation Algorithms on Multiple Two-Stage Flowshops

This paper considers the problem of scheduling multiple two-stage flowshops that minimizes the makespan, where the number of flowshops is part of the input. We study the relationship between the problem and the classical MAKESPAN problem. We prove that if there exists an a-approximation algorithm for the MAKESPAN problem, then for the multiple two-stage flowshop scheduling problem, we can construct a 2 alpha-approximation algorithm for the general case, and (alpha+1/2)-approximation algorithms for two restricted cases. As a result, we get a (2+epsilon)-approximation algorithm for the general case and a (1.5 + epsilon)-approximation algorithm for the two restricted cases, which significantly improve the previous approximation ratios 2.6 and 11/6, respectively.