Performance analysis of rotation schedule and improved strategy for open shop problem to minimise makespan

This article addresses the open shop scheduling problem with the objective to minimise the maximum completion time, or makespan. Both asymptotical analysis and worst case analysis are conducted for the heuristic, rotation schedule (RS) algorithm. In the asymptotical analysis, we prove that the RS algorithm is asymptotically equal to the optimal solution when the problem size is large enough. In the worst case analysis, we show that the tight worst case performance ratio of RS algorithm is equal to the machine number m. To accelerate the convergence of the RS algorithm for medium size problems, the improved version of the heuristic, the modified RS (MRS) algorithm is presented. At the end of this article, the asymptotical optimality of the RS algorithm and the practical effectiveness of the MRS algorithm are shown by numerical simulations.