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Multidimensional Assignment Problem

MAP

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Encyclopedia of Optimization

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Keywords and Phrases

Introduction

Formulation

Cases

Methods

Applications

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References

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References

  1. Aiex RM, Resende MGC, Pardalos PM, Toraldo G (2005) GRASP with path relinking for the three-index assignment. INFORMS J Comput 17(2):224–247

    Article  MathSciNet  Google Scholar 

  2. Balas E, Landweer P (1983) Traffic Assignment in Communication Satelites. Oper Res Lett 2:141–147

    Article  MATH  Google Scholar 

  3. Balas E, Qi L (1993) Linear-time separation algorithms for three-index assignment polytope. Discr Appl Math 43:1–12

    Article  MathSciNet  MATH  Google Scholar 

  4. Balas E, Saltzman MJ (1989) Facets of the three-index assignment polytope. Discr Appl Math 23:201–229

    Article  MathSciNet  MATH  Google Scholar 

  5. Balas E, Saltzman MJ (1991) An algorithm for three-index assignment problem. Oper Res 39:150–161

    Article  MathSciNet  MATH  Google Scholar 

  6. Bandelt HJ, Crama Y, Spieksma FCR (1994) Approximation algorithms for multidimensional assignment problems with decomposable costs. Discr Appl Math 49:25–50

    Article  MathSciNet  MATH  Google Scholar 

  7. Burkard RE, Çela E (1999) Linear Assignment Problems and Extensions. In: Pardalos P, Du D-Z (eds) The Handbook of Combinatorial Optimization. Kluwer, Dordrecht, pp 75–149

    Google Scholar 

  8. Burkard RE, Klinz B, Rudolf R (1996) Perspectives of Monge properties in optimization. Discr Appl Math 70:95–161

    Article  MathSciNet  MATH  Google Scholar 

  9. Burkard RE, Rudolf R, Woeginger GJ (1996) Three‐dimensional axial problem with decomposable cost coefficients. Discr Appl Math 65:123–169

    Article  MathSciNet  MATH  Google Scholar 

  10. Crama Y, Spieksma FCR (1992) Approximation algorithms for three‐dimensional assignment problems with triangle inequalities. Eur J Oper Res 60:273–279

    Article  MATH  Google Scholar 

  11. Clemons W, Grundel D, Jeffcoat D (2004) Applying simulated annealing to the multidimensional assignment problem. In: Grundel DA, Pardalos PM, Murphey R (eds) Theory and Algorithms for Cooperative Systems. World Scientific, Singapore

    Google Scholar 

  12. Deb S, Pattipatti KR, Bar-Shalom Y (1992), A s‑dimensional assignment algorithm for track initiation. Proceedings of the IEEE International Systems Conference, Kobe, Japan, September 127–130

    Google Scholar 

  13. Euler R (1987) Odd cycles and a class of facets of the axial 3-index assignment polytope. Applicationes mathimaticae (Zastowania Matematyki) 19:375–386

    Google Scholar 

  14. Euler R, Burkard RE, Grommes R (1986) On Latin squares and facial structure of related polytopes. Discr Math 62:155–181

    Article  MathSciNet  MATH  Google Scholar 

  15. Frieze AM, Yadegar J (1981) An algorithm for solving 3‑dimensional assignment problems with application to scheduling a teaching practice. J Oper Res Soc 32:969–995

    Google Scholar 

  16. Garey MR, Johnson DS (1979) Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Francisco

    MATH  Google Scholar 

  17. Grundel D, Krokhmal P, Oliveira C, Pardalos P (2007) On the number of local minima for the multidimensional assignment problem. J Comb Optim 13(1):1–18

    Article  MathSciNet  MATH  Google Scholar 

  18. Grundel D, Pardalos P (2005) Test Problem Generator for the Multidimensional Assignment Problem. Comput Optim Appl 30(2):133–146

    Article  MathSciNet  MATH  Google Scholar 

  19. Haley KB (1963) The Multi-index Problem. Oper Res 11:368–379

    Article  MATH  Google Scholar 

  20. Hansen P, Kaufman L (1973) A primal-dual algorithm for three‐dimensional assignment problem. Cahiers du CERO 15:327–336

    MathSciNet  MATH  Google Scholar 

  21. Hilton A (1980) The reconstruction of Latin Squares with Applications to School Timetabling and to Experimental Desin

    Google Scholar 

  22. Lidstrom N, Pardalos P, Pitsoulis L, Toraldo G (1996) An approximation algorithm for the three-index assignment problem, Technical Report

    Google Scholar 

  23. Magos D (1996) Tabu search for the planar three‐dimensional assignment problem. J Global Optim 8:35–48

    Article  MathSciNet  MATH  Google Scholar 

  24. Magos D, Miliotis P (1994) An algorithm for the planar three-index assignment problem. Eur J Oper Res 77:141–153

    Article  MATH  Google Scholar 

  25. Murphey R, Pardalos P, Pitsoulis L (1998) A greedy randomized adaptive search procedure for the multitarget multisensor tracking problem. DIMACS Ser Am Math Soc 40:277–302

    MathSciNet  Google Scholar 

  26. Pierskalla WP (1967) The tri-substitution method for the three-multidimensional assignment problem. CORS J 5:71–81

    Google Scholar 

  27. Pierskalla WP (1968) The multidimensional assignment problem. Oper Res 16:422–431

    Article  MATH  Google Scholar 

  28. Poore AB (1994) Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking. Comput Optim Appl 3:27–54

    Article  MathSciNet  MATH  Google Scholar 

  29. Poore AB, Robertson AJ (1997) A New Lagrangian Relaxation Based Algorithm for a Class of Multidimensional Assignment Problems. Comput Optim Appl 8:129–150

    Article  MathSciNet  MATH  Google Scholar 

  30. Pierskalla WP (1967) The tri-substitution method for the three‐dimensional assignment problem. J Canadian Oper Res Soc 5:71–81

    Google Scholar 

  31. Pusztaszeri JF, Rensing PE, Liebling TM (1996) Tracking Elementary Particles Near Their Primary Vertex: A Combinatorial Approach. J Global Optim 9(1):41–64

    Article  MathSciNet  MATH  Google Scholar 

  32. Qi L, Balas E, Gwan G (1994) A new facet class and a polyhedral method for three-index assignment problem. In: Du D-Z (ed) Advances in Optimization. Kluwer, Dordrecht, pp 256–274

    Google Scholar 

  33. Schell E (1955) Distribution of a Product by Several Properties, Proc. Second Symposium in Linear Programming, Washington, D.C., January 27-29, vol 1–2, pp 615–642

    Google Scholar 

  34. Spieksma FCR (2000) Multi index assignment problems: complexity, approximation, applications. In: Pitsoulis L, Pardalos P (eds) Nonlinear Assignment Problems, Algorithms and Applications. Kluwer, Dordrecht, pp 1–12

    Google Scholar 

  35. Vlach M (1967) Branch and bound method for the three-index assignment problem. Economicko-Matematicky Obzor 3:181–191

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

    Alla R. Kammerdiner

Authors
  1. Alla R. Kammerdiner
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Kammerdiner, A.R. (2008). Multidimensional Assignment Problem . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_411

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