Eckart Mayer

Time-optimal scheduling for high throughput screening processes using cyclic discrete event models

A method for solving the scheduling problem for a class of cyclic systems with respect to throughput maximization is presented. A strictly cyclic mode of operation is considered, where the time offset between the start of consecutive jobs is always constant. All jobs have to follow an identical time scheme. The time scheme may be restricted by due dates or time window constraints. There are no buffers between the resources of the system. Based on discrete events systems (DES) modeling, this job shop scheduling problem can be formulated as a mixed integer linear optimization problem. Throughput is maximized by minimization of the cycle time. The method is applied to high throughput screening (HTS) problems and illustrated by means of a small example.

Throughput-Optimal Sequences for Cyclically Operated Plants

In this paper, we present a method to determine globally optimal schedules for cyclically operated plants where activities have to be scheduled on limited resources. In cyclic operation, a large number of entities is processed in an identical time scheme. For strictly cyclic operation, where the time offset between entities is also identical for all entities, the objective of maximizing throughput is equivalent to the minimization of the cycle time. The resulting scheduling problem is solved by deriving a mixed integer optimization problem from a discrete event model. The model includes timing constraints as well as open sequence decisions for the activities on the resources. In an extension, hierarchical nesting of cycles is considered, which often allows for schedules with improved throughput. The method is motivated by the application to high throughput screening plants, where a specific combination of requirements has to be obeyed (e.g. revisited resources, absence of buffers, or time window constraints).

Optimal hybrid control for switched affine systems under safety and liveness constraints

In this contribution, we propose a two-level hierarchical control strategy to solve the problem of minimising a cost function for a switched affine system under safety and liveness constraints. The constraints are handled on the lower level by a discrete supervisory controller designed using l-complete approximation. Its action can be represented as state invariants added to the plant model. In a bottom-up strategy, we can then synthesis a high-level controller, which computes a set of switching tables using the remaining degrees of freedom to optimise a quadratic performance index

A NEW HIERARCHICAL CONTROL SCHEME FOR A CLASS OF CYCLICALLY REPEATED DISCRETE-EVENT SYSTEMS

We extend the hierarchical control method in (Li et al., 2004) to a more generic setting which involves cyclically repeated processes. A hierarchical architecture is presented to facilitate control synthesis. Specifically, a conservative max-plus model for cyclically repeated processes is introduced on the upper level which provides an optimal online plan list. An enhanced min-plus algebra based scheme on the lower level not only handles unexpected events but, more importantly, addresses cooperation issues between sub-plants and different cycles. A rail traffic example is given to demonstrate the effectiveness of the proposed approach.

A novel hierarchical control architecture for a class of discrete-event systems

Abstract This paper proposes a novel hierarchical control architecture for a class of discrete-event systems. Under the proposed control scheme, a max-plus algebra model is introduced on the upper level to provide an optimal online plan. On the lower (implementation) level, min-plus algebra is used to solve cooperation problems between sub-plants as well as problems caused by unexpected events. A simple rail traffic example is given to show the effectiveness of the idea.

Modeling and Optimization for High-Throughput-Screening Systems

Abstract The problem of cyclic scheduling under the requirement of throughput maximization is considered for a special class of cyclically repeated batch processes. All batches have to follow an identical time scheme. The same resource may be visited more than ouce by the same batch and time window constraints may be stated by the user. It is shown that the cyclic scheduling problem can be transformed into a mixed integer linear optimization problem. The methodsapplication to High-Throughput-Screening processes is demonstrated.

Modelling and performance evaluation for DES: A Max-Plus Algebra toolbox for Matlab

This paper discusses the usefulness of (max, +) algebra as a mathematical modelling framework for discrete event systems (DESs). A Max-Plus Algebra Toolbox developed at Lehrstuhl für Systemtheorie technischer Prozesse is presented. This software package is a set of functions to take advantage of the (max, +) algebra in the Matlab environment for rapid prototyping, design, and analysis of DESs. An overview of the modelling and analysis concepts of the (max, +) algebra approach for DES is given. Application examples are provided in the final part of the paper to illustrate the potential of this approach and the toolbox.

Optimal Scheduling of Cyclic Processes with Pooling-Resources

Dieser Beitrag behandelt die zeitoptimale Ablaufplanung für zyklische Prozesse mit Pooling-Ressourcen. Wir stellen einen Ansatz vor, mit dem eine große Klasse zyklischer Ablaufplanungsprobleme modelliert werden kann. Wir zeigen, wie das resultierende Modell durch Reduktion der Freiheitsgrade und Reparametrierung vereinfacht werden kann, ohne die optimale Lösung auszuschließen. Durch eine geeignete Transformation wird das reduzierte Problem auf ein lineares gemischt-ganzzahliges Optimierungsproblem abgebildet, das mit etablierten Verfahren effizient gelöst werden kann. Pooling-Ressourcen, d. h. Ressourcen, die bei jeder Aktivierung eine vorgegebene Anzahl von Werkstücken/Proben verarbeiten müssen, lassen sich ebenfalls in den vorgestellten Ansatz integrieren. The topic of this contribution is the time-optimal scheduling of cyclic processes with pooling resources. We present a modelling framework that captures a large class of cyclic scheduling problems. We show how the resulting model can be considerably simplified without cutting the optimal solution. This involves a reduction and a reparametrisation of the degrees of freedom. The reduced model can be transformed into a linear mixed-integer program (MILP), for which a globally optimal solution can be efficiently computed using standard algorithms and tools. We also show how pooling resources can be treated in our framework. Pooling resources have a capacity greater than one and must, at each activation, be loaded to capacity.