MULTIDIMENSIONAL ASSIGNMENT PROBLEMS

Each of the many two-dimensional variations of the classical assignment problem has at least one counterpart in higher dimensions. This paper is a tutorial on these higher dimensional assignment models and their applications. It is a synthesis of a vast literature scattered throughout a great variety of journal articles and other miscellaneous sources. We have attempted to make the paper a complete bibliography with the emphasis on topics important to practitioners of decision sciences. These topics include original results by the authors, most notably, a polynomial solution approach for a class of multidimensional assignment problems which often arise in scheduling applications.

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[4]  Marshall L. Fisher,et al.  A generalized assignment heuristic for vehicle routing , 1981, Networks.

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[10]  William P. Pierskalla,et al.  Letter to the Editor - The Multidimensional Assignment Problem , 1968, Oper. Res..

[11]  K. B. Haley,et al.  Letter to the Editor - Note on the Letter by Morávek and Vlach , 1967, Oper. Res..

[12]  Milan Vlach,et al.  Conditions for the existence of solutions of the three-dimensional planar transportation problem , 1986, Discret. Appl. Math..

[13]  Michel Balinski,et al.  Signature Methods for the Assignment Problem , 1985, Oper. Res..

[14]  Robert S. Garfinkel,et al.  Technical Note - An Improved Algorithm for the Bottleneck Assignment Problem , 1971, Oper. Res..

[15]  James R. Evans.  The Factored Transportation Problem , 1984 .

[16]  Alan M. Frieze,et al.  A bilinear programming formulation of the 3-dimensional assignment problem , 1974, Math. Program..

[17]  Victor Klee,et al.  Combinatorial Optimization: What is the State of the Art , 1980, Math. Oper. Res..

[18]  H. Ryser,et al.  Extremal configurations and decomposition theorems. I , 1968 .

[19]  Michel Balinski,et al.  A competitive (dual) simplex method for the assignment problem , 1986, Math. Program..

[20]  Alan Frieze,et al.  An Algorithm for Solving 3-Dimensional Assignment Problems with Application to Scheduling a Teaching Practice , 1981 .

[21]  G. Ross,et al.  Modeling Facility Location Problems as Generalized Assignment Problems , 1977 .

[22]  Alan M. Frieze,et al.  On the quadratic assignment problem , 1983, Discret. Appl. Math..

[23]  Luc Devroye,et al.  An analysis of a decomposition heuristic for the assignment problem , 1985 .

[24]  Richard M. Soland,et al.  A branch and bound algorithm for the generalized assignment problem , 1975, Math. Program..

[25]  P. Hall.  On Representatives of Subsets , 1935 .

[26]  J Csima,et al.  Multidimensional stochastic matrices and patterns , 1970 .

[27]  Ruth Margaret Bisgrove Hofstra.  Multidimensional assignment and scheduling with application to a tourism convention scheduling problem , 1983 .

[28]  R. Gomory,et al.  A Primal Method for the Assignment and Transportation Problems , 1964 .

[29]  M. Fisher,et al.  A multiplier adjustment method for the generalized assignment problem , 1986 .

[30]  Leon F. McGinnis,et al.  Implementation and Testing of a Primal-Dual Algorithm for the Assignment Problem , 1983, Oper. Res..

[31]  Rainer E. Burkard,et al.  An algebraic approach to assignment problems , 1977, Math. Program..