Scheduling on Multiple Two-Stage Flowshops with a Deadline.

Motivated by applications in cloud computing, we study approximation algorithms for scheduling two-stage jobs on multiple two-stage flowshops with a deadline, aiming at maximizing the profit. For the case where the number of flowshops is part of the input, we present a fast approximation algorithm with a constant ratio. The ratio is improved via a study of the relationship between the problem and the multiple knapsack problem, combined with a recently developed approximation algorithm for the multiple knapsack problem. By integrating techniques in the study of the classical Knapsack problem and the Makespan problem on multiple processors, plus additional new techniques, a polynomial-time approximation algorithm with a further improved ratio is developed for the case where the number of flowshops is a fixed constant.