Zusammenfassung
Es wird ein Algorithmus zur Lösung des bekannten Set-Partitioning-Problems mit Randbedingungen dargestellt. Der Algorithmus ist vom Typ der Impliziten Enumeration und benutzt Subgradientenoptimierung zur Kostentransformation. Eine Heuristik zur Zerlegung der Menge der Variablen in Blöcke sowie ein Fixierungs-Test basierend auf den Randbedingungen werden entwickelt. Abschließend sind einige Details der Computer-Implementation und numerische Testergebnisse aufgeführt.
Summary
An algorithm for solving the well-known Set-Partitioning-Problem with Side Constraints will be presented. The algorithm is of the Implicit Enumeration type and uses Subgradient Optimization for cost-transformation. A heuristic for partitioning the variables into blocks and a Fixing-Test based upon the Side Contraints are developed. Finally some details of Computer-Implementation and numerical test results are given.
This is a preview of subscription content, log in via an institution to check access.
Literatur
Albers, S.: Einsatzplanung von Flugzeugbesatzungen. Dissertation, Hamburg (1977)
Arabeyre, J. P., Fearnley, J., Steiger, F., Teather, W.: The airline crew scheduling problem: a survey. Transportation Sci.3, 140–163 (1969)
Balas, E., Padberg, M. W.: On the set-covering problem II: an algorithm for set partitioning. Oper. Res.23, 74–90 (1975)
Balas, E., Padberg, M. W.: Set partitioning: a survey. Siam Rev.18, 710–760 (1976)
Balas, E., Samuelson, H.: A symmetric subgradient cutting plane method for set-partitioning. W. P. 5-74-75 Carnegie-Mellon University (1974)
Dantzig, G. B., Ramser, J. H.: The truck dispatching problem. Manage. Sci.6, 80–91 (1959)
Délorme, J.: Contribution à la résolution du probléme de recouvrement: méthodes de trancature. Thése de Docteur Ingénieur. Université Paris VI (1974)
Garfinkel, R. S., Nemhauser, G. L.: The set partitioning problem: set covering with equality constraints. Oper. Res.17, 848–856 (1969)
Garfinkel, R. S., Nemhauser, G. L.: Optimal political districting by implicit enumeration techniques. Manage. Sience16, B495-B508 (1970)
Garfinkel, R. S., Nemhauser, G. L.: Integer programming. New York: John Wiley 1972
Geoffrion, A. M.: Lagrangean relaxation for integer programming. Math. Programming. Study2, 82–114 (1974)
Gillet, B. E., Miller, L. R.: A heuristic algorithm for the vehicle-dispatch problem. Oper. Res.22, 340–349 (1974)
Held, M., Wolfe, Ph., Crowder, H. D.: Validation of subgradient optimization. Math. Programming6, 62–88 (1974)
Lasdon, L. S.: Optimization theory for large systems. New York, London: Macmillan 1970
Marsten, R. E.: An algorithm for large set partitioning problems. Manage. Sci.20, 779–787 (1974)
Martin, G. T.: An accelerated euclidean algorithm for integer linear programming. In: Advances in mathematical programming. Graves, R. L., Wolfe, Ph. (eds.). London, New York: John Wiley 1963
Pierce, J. F.: Application of combinatorial programming to a class of all-zero-one integer programming problems. Manage. Sci.15, 191–209 (1968)
Pierce, J. F., Lasky, J. S.: Improved combinatorial programming to a class of all-zero-one integer programming problems. Manage. Sci.19, 528–543 (1973)
Rohde, M.: Das Set-Partitioning Problem — Wirtschaftliche Anwendungen und Algorithmen. Dissertation, FU Berlin (1978)
Salkin, H. M., Koncal, R. D.: Set covering by an all integer algorithm: computational experience. J. Assoc. Comput. Math.20, 189–193 (1973)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rohde, M. Set Partitioning mit linearen Randbedingungen. OR Spektrum 1, 75–87 (1979). https://doi.org/10.1007/BF01719072
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01719072