Abstract
In this paper we discuss scheduling of semi-cyclic discrete-event systems, for which the set of operations may vary over a limited set of possible sequences of operations. We introduce a unified modeling framework in which different types of semi-cyclic discrete-event systems can be described by switching max-plus linear (SMPL) models. We use a dynamic graph to visualize the evolution of an SMPL system over a certain period in a graphical way and to describe the order relations of the system events. We show that the dynamic graph can be used to analyse the structural properties of the system. In general the model predictive scheduling design problem for SMPL systems can be recast as a mixed integer linear programming (MILP) problem. In order to reduce the number of optimization parameters we introduce a novel reparametrization of the MILP problem. This may lead to a decrease in computational complexity.
Highlights
Scheduling is the process of deciding how to allocate a set of jobs to limited resources over time in such a way that one or more objectives are optimized (Leung 2004; Pinedo 2001)
The contribution this paper is that by considering switching max-plus linear (SMPL) systems the performance of the scheduling procedure can be improved by using the properties of SMPL models and dynamic graphs, such as detecting bottlenecks and using reparametrization of the mixed integer linear programming (MILP) problem based on max-plus expressions to reduce the number of optimization parameters
In this paper we have shown that various semi-cyclic discrete-event systems can be modeled as switching max-plus linear (SMPL) systems and that dynamic graphs are a useful tool in the modeling and analysis process
Summary
Scheduling is the process of deciding how to allocate a set of jobs to limited resources over time in such a way that one or more objectives are optimized (Leung 2004; Pinedo 2001). Many flow shop scheduling problems can be solved very well by considering a class of cyclic discrete event systems (DES), namely the class of max-plus linear systems (Baccelli et al 1992; Heidergott et al 2006), which is capable of representing job and resource unavailability. The contribution this paper is that by considering SMPL systems the performance of the scheduling procedure can be improved by using the properties of SMPL models and dynamic graphs, such as detecting bottlenecks and using reparametrization of the MILP problem based on max-plus expressions to reduce the number of optimization parameters.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
