Open shop cyclic scheduling

Abstract

The paper deals with cyclic scheduling problem in the production system working according to the so called open shop policy. The considered case is more general than standard open-shop and job-shop scheduling problems discussed so far in operations research literature. The proposed approach is a nontrivial extension of the permutation-and-graph modelling technology introduced earlier by us for job-shop scheduling. In this paper we provide a mathematical model of the problem and a few graph models. Using these graphs, we formulate several properties employed in the time-efficient method of finding minimal cycle time for the given processing orders. Then, we prove graph properties useful for the elimination of a priori unfeasible or inferior solutions without direct calculation of cycle time. Based on the established theoretical properties, we propose an approximation algorithm of tabu search type. Empirical tests confirm high efficiency of the algorithm.