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

Abstract

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.

Contributions to new variants of the open shop scheduling problem: modeling and solution methods

“…Naderi et al (2010) implemented efficient heuristics based on redundant solution filters. Finally, Colak and Agarwal (2005) and Bai and Tang (2011) solved the classical problem using constructive greedy heuristics.…”

“…Colak and Agarwal (2005) proposed a heuristic as an amendment to DS/LTRP, creating the Dense Scheduling Longest Total Remaining Processing Time (DS/LTRPAM) rule. Finally, Bai and Tang (2011) proposed a rotation heuristic that achieves good approximate solutions for large problems, the Modified Rotation Scheduling (MRS) heuristic.…”

“…Guéret and Prins (1998) presented two constructive heuristics, the first based on dispatching rules and the second based on the construction of matchings in a bipartite graph. Bai and Tang (2011) proposed a modified rotation scheduling heuristic for the problem, with relevant theoretical contributions, such as proof of optimality when the number of jobs tends to infinity.…”