A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Serial-batch scheduling – the special case of laser-cutting machines

The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

Algorithms for Scheduling Problems

This edited book presents new results in the area of algorithm development for different types of scheduling problems. In eleven chapters, algorithms for single machine problems, flow-shop and job-shop scheduling problems (including their hybrid (flexible) variants), the resource-constrained project scheduling problem, scheduling problems in complex manufacturing systems and supply chains, and workflow scheduling problems are given. The chapters address such subjects as insertion heuristics for energy-efficient scheduling, the re-scheduling of train traffic in real time, control algorithms for short-term scheduling in manufacturing systems, bi-objective optimization of tortilla production, scheduling problems with uncertain (interval) processing times, workflow scheduling for digital signal processor (DSP) clusters, and many more

Algorithms for Scheduling Problems and Integer Programming

The first part of this thesis gives approximation results to scheduling problems. The classical makespan minimization problem on identical parallel machines asks for a distribution of a set of jobs to a set of machines such that the latest job completion time is minimized. For this strongly NP-complete problem we give a new EPTAS algorithm. In fact, it admits a practical implementation which beats the currently best approximation ratio of the MULTIFIT algorithm. A well-studied extension of the problem is the partition of the jobs into classes which impose a class-specific setup time on a machine whenever the processing switches to a job of a different class. For these so-called scheduling problems with batch setup times we present a 1.5-approximation algorithm for each of the three major settings. We achieve similar results for the likewise natural variant of many shared resources scheduling (MSRS) where instead of imposing a setup time each class is identified by a resource which can be occupied by at most one of its jobs at a time. For MSRS we present a 1.5-approximation and two EPTAS results. The second part provides results for fixed-priority uniprocessor real-time scheduling and variants of block-structured integer programming. We give a new approach to compute worst-case response times which admits a polynomial-time algorithm for harmonic periods even in the presence of task release jitters. In more detail, we prove a duality between Response Time Computation (RTC) and the Mixing Set problem. Furthermore, both problems can be expressed as block-structured integer programs which are closely related to simultaneous congruences. However, the setting of the famous Chinese Remainder Theorem is that each congruence has to have a certain remainder. We relax this setting such that the remainder of each congruence may lie in a given interval. We show that the smallest solution to these congruences can be computed in polynomial time if the set of divisors is harmonic

Timing in Technischen Sicherheitsanforderungen für Systementwürfe mit heterogenen Kritikalitätsanforderungen

Traditionally, timing requirements as (technical) safety requirements have been avoided through clever functional designs. New vehicle automation concepts and other applications, however, make this harder or even impossible and challenge design automation for cyber-physical systems to provide a solution. This thesis takes upon this challenge by introducing cross-layer dependency analysis to relate timing dependencies in the bounded execution time (BET) model to the functional model of the artifact. In doing so, the analysis is able to reveal where timing dependencies may violate freedom from interference requirements on the functional layer and other intermediate model layers. For design automation this leaves the challenge how such dependencies are avoided or at least be bounded such that the design is feasible: The results are synthesis strategies for implementation requirements and a system-level placement strategy for run-time measures to avoid potentially catastrophic consequences of timing dependencies which are not eliminated from the design. Their applicability is shown in experiments and case studies. However, all the proposed run-time measures as well as very strict implementation requirements become ever more expensive in terms of design effort for contemporary embedded systems, due to the system's complexity. Hence, the second part of this thesis reflects on the design aspect rather than the analysis aspect of embedded systems and proposes a timing predictable design paradigm based on System-Level Logical Execution Time (SL-LET). Leveraging a timing-design model in SL-LET the proposed methods from the first part can now be applied to improve the quality of a design -- timing error handling can now be separated from the run-time methods and from the implementation requirements intended to guarantee them. The thesis therefore introduces timing diversity as a timing-predictable execution theme that handles timing errors without having to deal with them in the implemented application. An automotive 3D-perception case study demonstrates the applicability of timing diversity to ensure predictable end-to-end timing while masking certain types of timing errors.Traditionell wurden Timing-Anforderungen als (technische) Sicherheitsanforderungen durch geschickte funktionale Entwürfe vermieden. Neue Fahrzeugautomatisierungskonzepte und Anwendungen machen dies jedoch schwieriger oder gar unmöglich; Aufgrund der Problemkomplexität erfordert dies eine Entwurfsautomatisierung für cyber-physische Systeme heraus. Diese Arbeit nimmt sich dieser Herausforderung an, indem sie eine schichtenübergreifende Abhängigkeitsanalyse einführt, um zeitliche Abhängigkeiten im Modell der beschränkten Ausführungszeit (BET) mit dem funktionalen Modell des Artefakts in Beziehung zu setzen. Auf diese Weise ist die Analyse in der Lage, aufzuzeigen, wo Timing-Abhängigkeiten die Anforderungen an die Störungsfreiheit auf der funktionalen Schicht und anderen dazwischenliegenden Modellschichten verletzen können. Für die Entwurfsautomatisierung ergibt sich daraus die Herausforderung, wie solche Abhängigkeiten vermieden oder zumindest so eingegrenzt werden können, dass der Entwurf machbar ist: Das Ergebnis sind Synthesestrategien für Implementierungsanforderungen und eine Platzierungsstrategie auf Systemebene für Laufzeitmaßnahmen zur Vermeidung potentiell katastrophaler Folgen von Timing-Abhängigkeiten, die nicht aus dem Entwurf eliminiert werden. Ihre Anwendbarkeit wird in Experimenten und Fallstudien gezeigt. Allerdings werden alle vorgeschlagenen Laufzeitmaßnahmen sowie sehr strenge Implementierungsanforderungen für moderne eingebettete Systeme aufgrund der Komplexität des Systems immer teurer im Entwurfsaufwand. Daher befasst sich der zweite Teil dieser Arbeit eher mit dem Entwurfsaspekt als mit dem Analyseaspekt von eingebetteten Systemen und schlägt ein Entwurfsparadigma für vorhersagbares Timing vor, das auf der System-Level Logical Execution Time (SL-LET) basiert. Basierend auf einem Timing-Entwurfsmodell in SL-LET können die vorgeschlagenen Methoden aus dem ersten Teil nun angewandt werden, um die Qualität eines Entwurfs zu verbessern -- die Behandlung von Timing-Fehlern kann nun von den Laufzeitmethoden und von den Implementierungsanforderungen, die diese garantieren sollen, getrennt werden. In dieser Arbeit wird daher Timing Diversity als ein Thema der Timing-Vorhersage in der Ausführung eingeführt, das Timing-Fehler behandelt, ohne dass sie in der implementierten Anwendung behandelt werden müssen. Anhand einer Fallstudie aus dem Automobilbereich (3D-Umfeldwahrnehmung) wird die Anwendbarkeit von Timing-Diversität demonstriert, um ein vorhersagbares Ende-zu-Ende-Timing zu gewährleisten und gleichzeitig in der Lage zu sein, bestimmte Arten von Timing-Fehlern zu maskieren