Geodesic
A procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem
Applications of Mathematics, Tome 19 (1974) no. 3, pp. 177-183
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A procedure is given which will give the necessary and sufficient conditions for the existence of a solution to the multi-index problem of any given dimensions. It is shown that the number of such conditions is finite, and that the conditions provide lower bounds to functions of the unknowns of the problem.
A procedure is given which will give the necessary and sufficient conditions for the existence of a solution to the multi-index problem of any given dimensions. It is shown that the number of such conditions is finite, and that the conditions provide lower bounds to functions of the unknowns of the problem.
DOI : 10.21136/AM.1974.103528
Classification : 90C05 
@article{10_21136_AM_1974_103528,
     author = {Smith, Graham},
     title = {A procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem},
     journal = {Applications of Mathematics},
     pages = {177--183},
     year = {1974},
     volume = {19},
     number = {3},
     doi = {10.21136/AM.1974.103528},
     mrnumber = {0349219},
     zbl = {0284.90056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1974.103528/}
}
TY  - JOUR
AU  - Smith, Graham
TI  - A procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem
JO  - Applications of Mathematics
PY  - 1974
SP  - 177
EP  - 183
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1974.103528/
DO  - 10.21136/AM.1974.103528
LA  - en
ID  - 10_21136_AM_1974_103528
ER  - 
%0 Journal Article
%A Smith, Graham
%T A procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem
%J Applications of Mathematics
%D 1974
%P 177-183
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1974.103528/
%R 10.21136/AM.1974.103528
%G en
%F 10_21136_AM_1974_103528
Smith, Graham. A procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem. Applications of Mathematics, Tome 19 (1974) no. 3, pp. 177-183. doi: 10.21136/AM.1974.103528

[1] M. L. Balinski: An Algorithm for Finding all Vertices of Convex Polyhedral Sets. J. Soc. Indust. Appl. Math. 9, 72-88 (1961). | DOI | MR | Zbl

[2] K. B. Haley: The Solid Transportation Problem. Opns. Res. 10, 448 - 463 (1962). | DOI | Zbl

[3] K. B. Haley: The Multi-Index Problem. Opns. Res. 11, 368 - 379 (1963). | DOI | Zbl

[4] K. B. Haley: The Existence of a Solution to the Multi-Index Problem. Opnal Res. Quat. 16, 471-474 (1965).

[5] K. B. Haley: Note on the Letter by Morávek and Vlach. Opns. Res. 15, 545-546 (1967). | DOI

[6] J. Morávek, M. Vlach: On the Necessary Conditions for the Existence of a Solution to the Multi-index Problem. Opns. Res. 15, 542-545 (1967). | DOI

[7] J. Morávek, M. Vlach: On Necessary Conditions for a Class of Systems of Linear Inequalities. Aplikace matematiky 13, 299-303 (1968). | MR

[8] G. Smith: The Construction by Computer of a University Departmental Timetable. M. Eng. Sc. Thesis, The University of New South Wales, 1968.

[9] G. Smith: Further Necessary Conditions for the Existence of a Solution to the Multi-Index Problem. Opns. Res. 21, 380-386 (1973). | DOI | MR | Zbl

[10] S. Vajda: Mathematical Programming. p 42. Addison-Wesley (1961). | MR | Zbl

[11] M. Vlach: Branch and Bound Method for Three-Index Assignment Problem. Ekonomicko-matematický obzor 3, 181 - 191 (1967). | MR

Cité par Sources :