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A guide to complexity theory in operations research

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  • Schirmer, Andreas

Abstract

It is a well-known fact that there exists an ever increasing number of problems for which, despite the efforts of many inventive and persistent researchers, it seems virtually impossible to find efficient algorithms. In this Situation, the theory of computational complexity may provide helpful insight into how probable the existence of such algorithms is at all. Unluckily, some of its concepts can still be found to be used erroneously, if at all. For instance, it is a common misunderstanding that any problem that generalizes an NP-complete problem is NP-complete or NP-hard itself; indeed any such generalization could as well be exponential in the worst case, i.e. solvable with effort exponentially increasing in the size of the instances attempted. In this work we develop the basic concepts of complexity theory. While doing so, we aim at presenting the material in a way that emphasizes the correspondences between the kind of problems considered in Operations research and the formal problem classes which are studied in complexity theory.

Suggested Citation

  • Schirmer, Andreas, 1995. "A guide to complexity theory in operations research," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 381, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    • Handle: RePEc:zbw:cauman:381
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    1. Schirmer, Andreas & Potzahr, Kathrin, 2001. "Lehrgangsplanung für die Ausbildung von Verkehrsflugzeugführern: Ergebnisse einer Studie bei Lufthansa Flight Training," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 538, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Salewski, Frank & Schirmer, Andreas & Drexl, Andreas, 1996. "Project Scheduling under Resource and Mode Identity Constraints. Part I: Model, Complexity Status, and Methods," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 387, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    3. Schirmer, Andreas & Drexl, Andreas, 1997. "Allocation of partially renewable resources: Concept, models and applications," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 455, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Constantine N. Goulimis, 2007. "ASP, The Art and Science of Practice: Appeal to NP-Completeness Considered Harmful: Does the Fact That a Problem Is NP-Complete Tell Us Anything?," Interfaces, INFORMS, vol. 37(6), pages 584-586, December.
    5. Salewski, Frank & Schirmer, Andreas & Drexl, Andreas, 1996. "Project Scheduling under Resource and Mode Identity Constraints. Part II: An Application to Audit-Staff Scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 388, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    6. Salewski, Frank & Schirmer, Andreas & Drexl, Andreas, 1997. "Project scheduling under resource and mode identity constraints: Model, complexity, methods, and application," European Journal of Operational Research, Elsevier, vol. 102(1), pages 88-110, October.
    7. Schirmer, Andreas, 1996. "New insights on the complexity of resource-constrained project scheduling: A case of single-mode scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 390, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    8. Schirmer, Andreas, 1996. "New insights on the complexity of resource-constrained project scheduling: Two cases of multi-mode scheduling," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 391, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.

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