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

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 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. 1. Introduction Scheduling is a decision-making process which concerns with the optimal allocation or assignment of resources to a set of tasks or activities over time, so it plays an important role in most manufacturing and production systems (Kumar, Kumar, Tiwari, and Chan 2008) as well as in most information-processing environments (Chen, Huang, Zheng, and Xiang 2008). Since the 1960s, modern scheduling theory has grown sharply with the strong support from academic, industry and government. The advancement of manufacturing technology and the development of computer science, recently, promote the appearance of new scheduling environments (Chen, Wang, and He 2009) and novel scheduling algorithms (Lian, Gu, and Jiao 2008). In this article, a well-known scheduling problem, open shop makespan problem, is investigated. In an open shop model, there is a set of m machines, on which a set of n jobs, each consisting of m operations, has to be processed without pre-emption. Furthermore, each operation …