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We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting.
S. N. N. Pandit, “A new matrix calculus,” J. SIAM
1961
Earlier work this paper cites.
R. A. Cuninghame-Green, “Describing industrial processes with interference and approximating their steady-state behaviour,” Oper. Res. Quart
1962
Earlier work this paper cites.
B. Giffler, “Scheduling general production systems using schedule algebra,” Naval Res. Logist. Quart
1963
Earlier work this paper cites.
N. N. Vorob’ev, “The extremal matrix algebra,” Soviet Math. Dokl
1963
Earlier work this paper cites.
I. V. Romanovskiĭ, “Asymptotic behavior of dynamic programming processes with a continuous set of states,” Soviet Math. Dokl
1964
Earlier work this paper cites.
B. A. Carré, “An algebra for network routing problems,” IMA J. Appl. Math
1971
Earlier work this paper cites.
J. Elzinga and D. W. Hearn, “Geometrical solutions for some minimax location problems,” Transport. Sci
1972
Earlier work this paper cites.
Oxford Applied Mathematics and Computing Science Series. Clarendon Press, Oxford, 1979
B. Carré, Graphs and Networks · 1979
Earlier work this paper cites.
Springer, Berlin, 1979
R. Cuninghame-Green, Minimax Algebra · 1979
Earlier work this paper cites.
P. Hansen, D. Peeters, and J.-F. Thisse, “Location of public services: a selective method-oriented survey,” Annals of Public and Cooperative Economics
1980
Earlier work this paper cites.
Elsevier, Amsterdam, 1981
U. Zimmermann, Linear and Combinatorial Optimization in Ordered Algebraic Structures · 1981
Earlier work this paper cites.
North-Holland, 1981
P. Hansen, D. Peeters, and J.-F. Thisse, “Constrained location and the Weber-Rawls problem,” in Annals of Discrete Mathematics (11) Studies on Graphs and Discrete Programming · 1981
Earlier work this paper cites.
R. A. Cuninghame-Green, “Minimax algebra and applications,” Fuzzy Sets and Systems
1991
Cited alongside, same era.
K. Zimmermann, “Optimization problems with unimodal functions in max-separable constraints,” Optimization
1992
Cited alongside, same era.
Wiley Series in Probability and Statistics. Wiley, Chichester, 1993
F. L. Baccelli, G. Cohen, G. J. Olsder, and J.-P. Quadrat, Synchronization and Linearity: An Algebra for Discrete Event Systems · 1993
Cited alongside, same era.
O. Hudec and K. Zimmermann, “A service points location problem with min-max distance optimality criterion,” Acta Univ. Carolin. Math. Phys
1993
Cited alongside, same era.
Academic Press, San Diego, CA, 1994
R. A. Cuninghame-Green, “Minimax algebra and applications,” in Advances in Imaging and Electron Physics, Vol. 90 · 1994
Cited alongside, same era.
Kluwer Academic Publishers, Dordrecht, 1997
Springer, New York, 2008
M. Gondran and M. Minoux, Graphs, Dioids and Semirings: New Models and Algorithms , vol. 41 of Operations Research/Computer Science Interfaces · 2008
Later among the works it cites.
Physica-Verlag, 2009
E. Moradi and M. Bidkhori, “Single facility location problem,” in Facility location · 2009
Later among the works it cites.
N. K. Krivulin, “On solution of a class of linear vector equations in idempotent algebra,” Vestnik St. Petersburg University. Ser. 10. Applied Mathematics, Informatics, Control Processes
2009
Later among the works it cites.
Saint Petersburg University Press, St. Petersburg, 2009
N. K. Krivulin, Methods of Idempotent Algebra for Problems in Modeling and Analysis of Complex Systems · 2009
Later among the works it cites.
Springer Monographs in Mathematics. Springer, London, 2010
P. Butkovič, Max-linear Systems: Theory and Algorithms · 2010
Later among the works it cites.
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V. N. Kolokoltsov and V. P. Maslov, Idempotent Analysis and Its Applications · 1997
Cited alongside, same era.
O. Hudec and K. Zimmermann, “Biobjective center – balance graph location model,” Optimization
1999
Cited alongside, same era.
Marcel Dekker Ltd, New York, 2001
D. R. Sule, Logistics of facility location and allocation · 2001
Cited alongside, same era.
Springer, New York, 2003
J. S. Golan, Semirings and Affine Equations Over Them: Theory and Applications · 2003
Cited alongside, same era.
Princeton Series in Applied Mathematics. Princeton University Press, Princeton, 2006
B. Heidergott, G. J. Olsder, and J. van der Woude, Max-plus at Work: Modeling and Analysis of Synchronized Systems · 2006
Cited alongside, same era.
N. K. Krivulin, “Solution of generalized linear vector equations in idempotent algebra,” Vestnik St. Petersburg Univ. Math
2006
Cited alongside, same era.
Taylor and Francis, Boca Raton, FL, 2007
M. Akian, R. Bapat, and S. Gaubert, “Max-plus algebra,” in Handbook of Linear Algebra · 2007
Cited alongside, same era.
A. Tharwat and K. Zimmermann, “One class of separable optimization problems: solution method, application,” Optimization
2010
Later among the works it cites.
2011
Later among the works it cites.
Springer, New York, 2011
Z. Drezner, “Continuous center problems,” in Foundations of Location Analysis · 2011
Later among the works it cites.
2012
Later among the works it cites.
N. Krivulin and K. Zimmermann, “Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints,” in Mathematical Methods and Optimization Techniques in Engineering · 2013
Closest in time.
2013
Closest in time.
American Mathematical Society, Providence, RI, 2014
N. Krivulin, “A constrained tropical optimization problem: complete solution and application example,” in Tropical and Idempotent Mathematics and Applications · 2014
Closest in time.