A modeling framework for model predictive scheduling using switching max-plus linear models

Abstract

In this paper we discuss a modeling framework for model predictive scheduling of a class of semi-cyclic discrete event systems that can be described by switching max-plus linear models. We study the structure of the system matrices and derive how routing, ordering, and synchronization can be manipulated by a set of control variables. In addition, we show that this leads to a system matrix that is linear in the control variables. We define the model predictive scheduling design problem to optimize the schedule, and we show that the problem can be recast as a mixed integer linear programming (MILP) problem.

Model predictive scheduling of semi-cyclic discrete-event systems using switching max-plus linear models and dynamic graphs

“…This paper extends the results of van den Boom et al (2013): We introduce the dynamic graph for representing the switching behavior of an SMPL system. We highlight the importance of the dynamic graph concept by discussing controllability and maximum average path weight in terms of dynamic graphs and elaborate on the relation between the makespan of a schedule and the maximum average path weight of the SMPL system.…”

“…There are advantages in using SMPL systems as a basic model for scheduling. First of all there are many system-theoretical results for (S)MPL systems in literature (Baccelli et al 1992;van den Boom et al 2013). We can use them for finding bottlenecks in the scheduling process as well as good initial scheduling values by using system properties, based on the max-plus eigenvalue and eigenvectors (Kersbergen et al 2011).…”

Model Predictive Scheduling for Container Terminals

“…(4-13) to (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) to (4-25) and (4-27)…”

“…In [21] it is shown how the number of binary variables in MPS problems for SMPL systems can be reduced significantly. This is done by parameterizing the possible solutions using a different set of binary variables, such that each combination of binary variables represent a valid solution.…”

“…(4-13) to (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) and For vehicles with a carrying capacity larger than one, this leads to the following optimization problem:…”