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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
Balas E, Landweer P (1983) Traffic Assignment in Communication Satelites. Oper Res Lett 2:141–147
Balas E, Qi L (1993) Linear-time separation algorithms for three-index assignment polytope. Discr Appl Math 43:1–12
Balas E, Saltzman MJ (1989) Facets of the three-index assignment polytope. Discr Appl Math 23:201–229
Balas E, Saltzman MJ (1991) An algorithm for three-index assignment problem. Oper Res 39:150–161
Bandelt HJ, Crama Y, Spieksma FCR (1994) Approximation algorithms for multidimensional assignment problems with decomposable costs. Discr Appl Math 49:25–50
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
Burkard RE, Klinz B, Rudolf R (1996) Perspectives of Monge properties in optimization. Discr Appl Math 70:95–161
Burkard RE, Rudolf R, Woeginger GJ (1996) Three‐dimensional axial problem with decomposable cost coefficients. Discr Appl Math 65:123–169
Crama Y, Spieksma FCR (1992) Approximation algorithms for three‐dimensional assignment problems with triangle inequalities. Eur J Oper Res 60:273–279
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
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
Euler R (1987) Odd cycles and a class of facets of the axial 3-index assignment polytope. Applicationes mathimaticae (Zastowania Matematyki) 19:375–386
Euler R, Burkard RE, Grommes R (1986) On Latin squares and facial structure of related polytopes. Discr Math 62:155–181
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
Garey MR, Johnson DS (1979) Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Francisco
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
Grundel D, Pardalos P (2005) Test Problem Generator for the Multidimensional Assignment Problem. Comput Optim Appl 30(2):133–146
Haley KB (1963) The Multi-index Problem. Oper Res 11:368–379
Hansen P, Kaufman L (1973) A primal-dual algorithm for three‐dimensional assignment problem. Cahiers du CERO 15:327–336
Hilton A (1980) The reconstruction of Latin Squares with Applications to School Timetabling and to Experimental Desin
Lidstrom N, Pardalos P, Pitsoulis L, Toraldo G (1996) An approximation algorithm for the three-index assignment problem, Technical Report
Magos D (1996) Tabu search for the planar three‐dimensional assignment problem. J Global Optim 8:35–48
Magos D, Miliotis P (1994) An algorithm for the planar three-index assignment problem. Eur J Oper Res 77:141–153
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
Pierskalla WP (1967) The tri-substitution method for the three-multidimensional assignment problem. CORS J 5:71–81
Pierskalla WP (1968) The multidimensional assignment problem. Oper Res 16:422–431
Poore AB (1994) Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking. Comput Optim Appl 3:27–54
Poore AB, Robertson AJ (1997) A New Lagrangian Relaxation Based Algorithm for a Class of Multidimensional Assignment Problems. Comput Optim Appl 8:129–150
Pierskalla WP (1967) The tri-substitution method for the three‐dimensional assignment problem. J Canadian Oper Res Soc 5:71–81
Pusztaszeri JF, Rensing PE, Liebling TM (1996) Tracking Elementary Particles Near Their Primary Vertex: A Combinatorial Approach. J Global Optim 9(1):41–64
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
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
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
Vlach M (1967) Branch and bound method for the three-index assignment problem. Economicko-Matematicky Obzor 3:181–191
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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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DOI: https://doi.org/10.1007/978-0-387-74759-0_411
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