Abstract
We investigate the computational complexity of scheduling problems, where the operations consume certain amounts of renewable resources which are available in time-dependent quantities. In particular, we consider unit-time open shop problems and unit-time scheduling problems with identical parallel processors. For the case where the number of machines, the number of resources and the demand for every resource are all bounded by a constant, we derive polynomial time results for several objective functions. Furthermore, we establish a borderline between hard and easy variants of such problems by proving NP-hardness of most remaining cases.
Zusammenfassung
Wir untersuchen die Komplexität einiger Reihenfolgeprobleme, in denen die Abarbeitung der Operationen das Vorhandensein von gewissen Mengen erneuerbarer Ressourcen verlangt, die in zeitabhängigen Mengen verfügbar sind. Wir betrachten Open-Shop Systeme und Systeme mit parallelen Prozessoren mit Einheits-Zeit Operationen. Für den Fall, daß die Anzahl der Maschinen, die Anzahl der Ressourcen und der Ressourcenbedarf jeder Operation durch eine Konstante nach oben beschränkt sind, leiten wir polynomiale Algorithmen für einige Zielfunktionen her. Außerdem ziehen wir eine Grenzlinie zwischen einfachen und schwierigen Varianten, indem wir die NP-vollständigkeit der meisten übrigen Problemvarianten beweisen.
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Blazewicz, J., Cellary, W., Slowinski, R., Weglarz, J.: Scheduling under resource constraints — deterministic models. Ann. Oper. Res.7 (1996).
Blazewicz, J., Ecker, K.: A linear time algorithm for restricted bin packing and scheduling problems. OR Lett.2, 80–83 (1983).
Bräsel, H.: Lateinische Rechtecke und Maschinenbelegung. Dissertation B, TU Magdeburg, 1991.
Gabow, H., Nishizeki, T., Kariv, O., Leven, D., Terada, O.: Algorithms for edge-colouring graphs. Technical Report 41, University of Colorado at Boulder, 1985.
Garey, M. R., Johnson, D. S.: Computers and intractability. San Francisco: W.H. Freeman, 1979.
Graham, R. E., Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Disc. Math.5, 287–326 (1979).
Jurisch, B., Kubiak, W.: Open shops with renewable resources. Working paper, Memorial University of Newfoundland, 1994.
Lenstra, H. W.: Integer programming with a fixed number of variables. Math. Oper. Res.8, 538–548 (1983).
Schaefer, T. J.: The complexity of satisfiability problems. Proc. 10th Ann. ACM Symp. on Theory of Computing, Association for Computing Machinery, New York, pp. 216–226 (1978).
Smetaniuk, B.: A new construction on latin squares I. A proof of the Evans conjecture. Ars Combin.11, 155–172 (1981).
Tautenhahn, T., Woeginger, G. J.: Minimizing the total completion time in a unit time open shop with release times. Technical Report 291, TU Graz, 1994.
de Werra, D., Blazewicz, J., Kubiak, W.: A preemptive open shop scheduling problem with one resource. Oper. Res. Lett.10, 9–15 (1991).
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On leave from Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Universitätsplatz 1, D-39016 Magdeburg, supported by Deutscher Akademischer Austauschdienst.
Supported by the Spezialforschungsbereich F 003 ‘Optimierung und Kontrolle’, Projektbereich Diskrete Optimierung.
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Tautenhahn, T., Woeginger, G.J. Unit-time scheduling problems with time dependent resources. Computing 58, 97–111 (1997). https://doi.org/10.1007/BF02684434
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DOI: https://doi.org/10.1007/BF02684434