Approximation Algorithms for Scheduling Multiple Two-Stage Flowshops

This paper studies the problem that schedules n two-stage jobs on m multiple two-stage flowshops, with the objective of minimizing the makespan. The problem is NP-hard even when m is a fixed constant, and becomes strongly NP-hard when m is a part of input. A 17/6-approximation algorithm along with its analysis is presented for arbitrary m >= 2. This is the first approximation algorithm for multiple flowshops when the number m of flowshops is a part of input. The arbitrary m and the time complexity O(n log n + mn) of the algorithm demonstrate that the problem, which plays an important role in the current research in cloud computing and data centers, can be solved efficiently with a reasonable level of satisfaction.