An algebraic approach to assignment problems

  title={An algebraic approach to assignment problems},
  author={Rainer E. Burkard and Willi Hahn and Uwe T. Zimmermann},
  journal={Mathematical Programming},
For assignment problems a class of objective functions is studied by algebraic methods and characterized in terms of an axiomatic system. It says essentially that the coefficients of the objective function can be chosen from a totally ordered commutative semigroup, which obeys a divisibility axiom. Special cases of the general model are the linear assignment problem, the linear bottleneck problem, lexicographic multicriteria problems,p-norm assignment problems and others. Further a polynomial… 

Assignment Problems

This paper introduces the basic problems of assignment problems, which are a well studied topic in combinatorial optimization and describes some of the most successful algorithms used to solve these problems.

Weakly admissible transformations for solving algebraic assignment and transportation problems

Weakly admissible transformations are introduced for solving algebraic assignment and transportation problems, which cover so important classes as problems with sum objectives, bottleneck objectives,

Algebraic Linear Programming

The algebraic approach to network-flow problems discussed by Burkard and Zimmermann is generalized to linearly-constrained problems and a primal-dual method is given for solving these “algebraic” linear programs.

Admissible Transformations and Assignment Problems

We introduce the notion of admissible transformations which is related to the Hungarian method for solving assignment problems. Admissible transformations are stated for linear, quadratic and


This paper is a tutorial on these higher dimensional assignment models and their applications and is a synthesis of a vast literature scattered throughout a great variety of journal articles and other miscellaneous sources.

The Solution of Algebraic Assignment and Transportation Problems

The solution methods for the algebraic transportation problem (ATP) are based on (weakly) admissible transformations which can be determined by maximal flow resp.



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