The set covering problem : a group theoretic approach

 Access to full text

 Full (PDF)

1. [1] J. P. ARABEYRE, J. FEARNLEY, F. STEIGER and W. TEATHER, «The airline crew scheduling problem : a survey», Transportation Science, 3, n° 2, May 1969. 
2. [2] P. BERTHIER, PHONG TRUAN NGHIEM et B. ROY, «Programmes linéaires en nombres entiers et procédures S.E.P.», METRA, vol. 4, n° 3, 1965. 
3. [3] E. BALAS, « An additive algorithm for solving linear programs with 0-1 variables »,Operations Research, 13, n° 4, 1965. Zbl0133.42701MR183535
4. [4] R. S. GARFINKEL and G. L. NEMHAUSER, «The set partitioning problem : set covering with equality constraints», Operations Research, 17, pp. 848-856, 1969. Zbl0184.23101
5. [5] A. M. GEOFFRION, An Improved Implicit Enumeration Approach for Integer Programming, The Rand Corporation, RM-5644-PR, June 1968. Zbl0174.20801
6. [6] F. GLOVER. A Multiplan Dual Algorithm for the 0-1 Integer Programming Problem. Case Institute of Technology, Management Science Report n° 25, 1965. 
7. [7] R. E. GOMORY, « On the relation between integer and noninteger solutions to linear programs », Proc. Nat. Acad. Sci., 53, pp. 260-295, 1965. Zbl0132.13702MR182454
8. [8] R. E. GOMORY, « An Algorithm for Integer Solutions to Linear Programs », pp. 269-302 in Recent Advances in Mathematical Programming, Graves, R. L., and Wolfe, P., (Eds.), McGraw-Hill, 1963. Zbl0235.90038MR174390
9. [9] W. C. HEALY Jr., « Multiple choice programming », Operations Research, 12, pp. 122-138, 1964. Zbl0123.37205MR163765
10. [10] R. W. HOUSE, L. D. NELSON and T. RADO, « Computer Studies of a Certain Class of Linear Integer Problems », Recent Advances in Optimization Techniques, Lavi, A., and Vogl, T., (Eds.), Wiley, 1966. Zbl0146.41007
11. [11] A. H. LAND and A. G. DOIG, « An automatic method of solving discrete linear programming problems », Econometrica, 28, pp. 497-520, 1960. Zbl0101.37004MR115825
12. [12] E. L. LAWLER and M. D. BELL, « A method for solving discrete optimization problems », Operations Research, 14, n° 6, 1966. 
13. [13] G. D. MOSTOW, J. H. SAMPSON and J. P. MEYER, Fundamental Structures of Algebra, McGraw-Hill, 1963. Zbl0107.01103MR154830
14. [14] J. F. PIERCE, « Application of combinatorial programming to a class of all-zero-one integer programming problems », Management Science, 15, pp. 191-209, 1968. MR241111
15. [15] R. ROTH, « Computer solutions to minimum cover problems », Operations Research, 17, pp. 455-466, 1969. Zbl0174.20706
16. [16] B. ROY et R. BENAYOUN, « Programmes linéaires en variables bivalentes et continues sur un graphe (Programme Poligami) », METRA, vol. 6, n° 4, 1967. 
17. [17] B. ROY, Algèbre Moderne et Théorie des Graphes, Dunod éd., 1970. MR260413
18. [18] B. ROY, An Algorithm for a General Constrained Set Covering Problem, Computing and Graph Theory (To be published), Academic Press, New York. Zbl0255.05006MR340061
19. [19] J. F. SHAPIRO, « Dynamic programming algorithms for the integer programming problem-I : the integer programming problem viewed as a knapsack type problem »,Operations Research, 16, 1968. Zbl0159.48803MR232596
20. [20] J. F. SHAPIRO, « Group theoretic algorithms for the integer programming problem-II : extension to a general algorithm », Operations Research, 16, n° 5, 1968. Zbl0169.22401MR237177
21. [21] H. M. THIRIEZ, Implicit Enumeration Applied to the Crew Scheduling Problem, Dept. of Aeronautics, M.I.T., 1968. 
22. [22] H. M. THIRIEZ, Airline Crew Scheduling : a Group Theoretic Approach, Ph. D. Thesis, M.I.T. FTL-R69-1, 1969.