Throughput-Optimal Sequences for Cyclically Operated Plants

Mayer, Eckart; Haus, Utz-Uwe; Raisch, Jörg; Weismantel, Robert

doi:10.1007/s10626-008-0038-3

Cited by 12 publications

(6 citation statements)

References 20 publications

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“…This way of defining discrete time nodes was easy to implement in the scheduling model. Another study [27] was a continuation of previous work [26], and was also based upon Petri net concepts with the aim of determining a globally optimal schedule for HTS systems. In addition, these authors extended their model to include the hierarchical nesting of cycles.…”

Section: Related Work: Literature Reviewmentioning

confidence: 99%

Fast Algorithm for High-Throughput Screening Scheduling Based on the PERT/CPM Project Management Technique

Levner,

Kats,

Yan

et al. 2024

Algorithms

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High-throughput screening systems are robotic cells that automatically scan and analyze thousands of biochemical samples and reagents in real time. The problem under consideration is to find an optimal cyclic schedule of robot moves that ensures maximum cell performance. To address this issue, we proposed a new efficient version of the parametric PERT/CPM project management method that works in conjunction with a combinatorial subalgorithm capable of rejecting unfeasible schedules. The main result obtained is that the new fast PERT/CPM method finds optimal robust schedules for solving large size problems in strongly polynomial time, which cannot be achieved using existing algorithms.

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Section: Related Work: Literature Reviewmentioning

confidence: 99%

Fast Algorithm for High-Throughput Screening Scheduling Based on the PERT/CPM Project Management Technique

Levner,

Kats,

Yan

et al. 2024

Algorithms

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“…Such a scheduling problem optimization has already been investigated in (Mayer et al 2008) by deriving a mixed integer optimization problem. A comparison of the two methods would be an interesting outlook for future work.…”

Section: Remark 61mentioning

confidence: 99%

Networked conflicting timed event graphs representation in (Max,+) algebra

Addad¹,

Amari²,

Lesage³

2012

Discrete Event Dyn Syst

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Timed Event Graphs (TEGs) are a specific class of Petri nets that have been thoroughly studied given their useful linear state representation in (Max,+) algebra. Unfortunately, TEGs are generally not suitable for modeling systems displaying resources sharing (or conflicts). In this paper, we show that if a system with conflicts is modeled using a NCTEG (Networked Conflicting Timed Event Graphs), it is quite possible to obtain an equivalent (Max,+) representation. More precisely, we prove that the evolution of a NCTEG satisfies linear time-varying (Max,+) equations. In case of cyclic NCTEGs, which are a natural model of many repetitive systems, we provide a standard time-invariant (Max,+) representation. As an application of the proposed approach to exhibit its interest, we consider the case of Jobshops. We first propose a generic NCTEG-based model of these systems and subsequently apply the corresponding (Max,+) representation to evaluate some of their performances.

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“…Setzt man (11) und (12) in (4) ein und lässt redundante Bedingungen weg, ergeben sich nach Einführung entsprechender Abkürzungen die folgenden Ungleichungen in den neuen Variablen θ k :…”

Section: Zyklische Systemeunclassified

“…Für die Behandlung paralleler Ressourcen (multi-capacity resources) wird auf [12] verwiesen. Solche Ressourcen können (müssen aber nicht) durch mehrere Werkstücke gleichzeitig belegt werden.…”

Section: Zusammenfassungunclassified

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Optimale Ablaufplanung für zyklische Prozesse mit Pooling-Ressourcen (Optimal Scheduling of Cyclic Processes with Pooling-Resources)

Mayer

Wulff

Horst

et al. 2008

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Dieser Beitrag behandelt die zeitoptimale Ablaufplanung für zyklische Prozesse mit PoolingRessourcen. 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.

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Throughput-Optimal Sequences for Cyclically Operated Plants

Cited by 12 publications

References 20 publications

Fast Algorithm for High-Throughput Screening Scheduling Based on the PERT/CPM Project Management Technique

Fast Algorithm for High-Throughput Screening Scheduling Based on the PERT/CPM Project Management Technique

Networked conflicting timed event graphs representation in (Max,+) algebra

Optimale Ablaufplanung für zyklische Prozesse mit Pooling-Ressourcen (Optimal Scheduling of Cyclic Processes with Pooling-Resources)

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