On (min,max, plus )-inequalities

In this paper we concentrate on processes consisting of events on which constraints are put on the order in which the individual events can take place. We ask ourselves the question whether the constraints allow the processes to happen at all, or contain intrinsic bottlenecks. Further, if the processes can take place and are supposed to repeat themselves, we investigate whether or not a periodic behavior is possible. We distinguish between a periodic behavior with one overall period, and the case in which the more general cycle time vector has to be considered. We will use a (min, max, +) formulation and present our results in graph theoretic terms. Also we will also discus some of the computational aspects of our approach.