An efficient algorithm for finding minimal cycle time in cyclic job shop scheduling problem

We consider the cyclic production system providing on output the mixture of various products. Each product is produced by certain chain of operations, i. e. the unique sequence followed from the technological order. Each operations is performed on the dedicated machine. This sequence of operations is called the job. The aim is to find the cyclic schedule ensuring minimal cycle length. The problem belongs to deterministic scheduling theory, appears with the name cyclic job shop scheduling problem, is strongly NP-hard, and has been analyzed very rarely in the literature. Methodology of designing efficient optimization procedures for hard scheduling problem refers commonly to the component subproblem, namely the problem of finding cycle time or minimal cycle time for fixed job sequence. Numerical properties of this method have crucial influence on the quality of the final optimization algorithm. In this paper we propose several algorithms to solve the problem of finding cycle time for fixed job sequence. Then, we discuss and examine theoretical as well as numerical properties of these algorithms. Obtained results are illustrated by wide results of computational tests.