Approximation algorithms for the multiprocessor open shop scheduling problem

We investigate the multiprocessor multi stage open shop scheduling problem In this variant of the open shop model there are s stages each consisting of a number of parallel identical machines Each job consists of s operations one for each stage that can be executed in any order The goal is to nd a non preemptive schedule that minimizes the makespan We derive two approximation results for this NP hard problem First we demonstrate the existence of a polynomial time approximation algorithm with worst case ratio for the case that the number s of stages is part of the input This algorithm is based on Racsm any s concept of dense schedules Secondly for the multiprocessor two stage open shop problem we derive a family of polynomial time approximation algorithms whose worst case ratios can be made arbitrarily close to