Polynomial Time Approximation Schemes for the Multiprocessor Open and Flow Shop Scheduling Problem

We investigate the multiprocessor multi-stage open shop and flow shop scheduling problem. In both problems, there are s stages each consisting of a number m_i of parallel identical machines for 1 ≤ i ≤ s. Each job consists of s operations with one operation for each stage. The goal is to find a non-preemptive schedule that minimizes the makespan. We propose polynomial time approximation schemes for the multiprocessor open shop and flow shop scheduling problem when the number of stages s is constant and the numbers of machines m_i are non-constant.