Block approach to the cyclic flow shop scheduling

Keywords: Scheduling Cyclic flow shop problem Block properties a b s t r a c t The cyclic flow show problem with machine setups is considered in this paper. It relies in producing of a set of certain elements in fixed intervals of time (cycle time). Process optimization is reduced to minimization of cycle time, i.e., the time after which the next batch of the same elements may be produced. Since the problem is strongly NP-hard, in order to solve it an approximate algorithm was used. There is presented a graph model of a problem and the so called block eliminating properties capable of reducing, in a significant way, neighborhood used in the tabu search algorithm. Conducted computational experiments confirm high efficiency of the proposed technique. For many years, one could observe an increasing market demand for diversity (multiassortment) of production. This may be provided, among many other issues, by means of cyclic production. In fixed intervals of time (cycle time) a certain 'batch' of assortment (a mix of kit, a set) is produced. Process optimization is typically reduced to minimization of cycle time. Proper selection of mix and cycle time enables not only to meet demand, but also to improve efficacy and effectiveness of machinery use. Thus, recently, one can observe a significant increase of interest in the problems of cyclic tasks scheduling theory. For they are usually important and difficult, (mostly NP-hard) problems, from the standpoint of not only theory, but also practice. A comprehensive overview of the state of knowledge concerning the cyclic task scheduling problem can be found in the work of Levner, Kats, Lopez, and Cheng (2010) analyzing the issues of computational complexity of algorithms for solving various types of cycle scheduling problem. Here, in particular NP-difficult problems of various cyclic types including a variety of criterion functions and additional constraints (no wait, no buffer, etc.) are considered. In the scientific work by Panwalkar, Dudek, and Smith (1973) on task scheduling it was found that 75% of problems occurring in practice requires at least one setup dependent on the order of tasks execution. However, in 15% of the problems a setup of all tasks should be taken into consideration. Nevertheless, in the vast majority of works, in the field of scheduling setups are not taken into account at all. This applies both to single and multi-machine problems and to different goal functions. Cyclic problems belong …