| Title:
|
A procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem (English) |
| Author:
|
Smith, Graham |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
3 |
| Year:
|
1974 |
| Pages:
|
177-183 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. () |
| MSC:
|
90C05 |
| idZBL:
|
Zbl 0284.90056 |
| idMR:
|
MR0349219 |
| DOI:
|
10.21136/AM.1974.103528 |
| . |
| Date available:
|
2008-05-20T17:58:48Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103528 |
| . |
| Reference:
|
[1] M. L. Balinski: An Algorithm for Finding all Vertices of Convex Polyhedral Sets.J. Soc. Indust. Appl. Math. 9, 72-88 (1961). Zbl 0108.33203, MR 0142057, 10.1137/0109008 |
| Reference:
|
[2] K. B. Haley: The Solid Transportation Problem.Opns. Res. 10, 448 - 463 (1962). Zbl 0109.13904, 10.1287/opre.10.4.448 |
| Reference:
|
[3] K. B. Haley: The Multi-Index Problem.Opns. Res. 11, 368 - 379 (1963). Zbl 0121.14604, 10.1287/opre.11.3.368 |
| Reference:
|
[4] K. B. Haley: The Existence of a Solution to the Multi-Index Problem.Opnal Res. Quat. 16, 471-474 (1965). |
| Reference:
|
[5] K. B. Haley: Note on the Letter by Morávek and Vlach.Opns. Res. 15, 545-546 (1967). 10.1287/opre.15.3.545 |
| Reference:
|
[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). 10.1287/opre.15.3.542 |
| Reference:
|
[7] J. Morávek, M. Vlach: On Necessary Conditions for a Class of Systems of Linear Inequalities.Aplikace matematiky 13, 299-303 (1968). MR 0240119 |
| Reference:
|
[8] G. Smith: The Construction by Computer of a University Departmental Timetable.M. Eng. Sc. Thesis, The University of New South Wales, 1968. |
| Reference:
|
[9] G. Smith: Further Necessary Conditions for the Existence of a Solution to the Multi-Index Problem.Opns. Res. 21, 380-386 (1973). Zbl 0259.90021, MR 0373592, 10.1287/opre.21.1.380 |
| Reference:
|
[10] S. Vajda: Mathematical Programming.p 42. Addison-Wesley (1961). Zbl 0102.36401, MR 0135621 |
| Reference:
|
[11] M. Vlach: Branch and Bound Method for Three-Index Assignment Problem.Ekonomicko-matematický obzor 3, 181 - 191 (1967). MR 0215609 |
| . |
