Problèmes fractionnaires : tour d'horizon sur les applications et méthodes de résolution

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1. 1. J. ABRHAM et S. LUTHRA, Comparison of duality models in fractional linear programming, Zeitschrift Oper. Res., 1977, 21, p. 125-130. Zbl0358.90063MR452692
2. 2. S. C. AGRAWAL et M. CHAND, A note on integer solutions to linear fractional interval programming problems by Branch and Bound technique, Naval Res. Logist. Quart., 1981, 28, n°4, p. 671-677. Zbl0534.90085MR664873
3. 3. Y. ANZAI, On integer fractional programming, J. Oper. Res. Soc. Japan, 1974, 17, n° l, p. 49-69. Zbl0278.90052MR416565
4. 4. H. ARSHAM et A. B. KHAN, A complete algorithm for linear fractional programs, Comput. Math. Appl., 1990, 20, n°7, p. 11-23. Zbl0712.90078MR1070846
5. 5. E. BALAS, An additive algorithm for solving linear programs with zero-one variables, Oper. Res., 1965, 13, n°4, p. 517-546. Zbl0133.42701MR183535
6. 6. C. R. BECTOR, Duality in nonlinear fractional programming, Zeitschrift Oper. Res., 1973, 17, p. 183-193. Zbl0267.90086MR416593
7. 7. B. BEREANU, Decision regions and minimum risk solutions in linear programming, in: A. Prekopa, Ed., Colloquium on applications of mathematics to economics, Budapest, 1963, Publ. house of the Hungarian academy of sciences, Budapest, 1965, p. 37-42. Zbl0142.16701
8. 8. G. R. BITRAN et T. L. MAGNANTI, Duality and sensitivity analysis for fractional programs, Oper. Res., 1976, 24, n°4, p. 675-699. Zbl0361.90073MR469280
9. 9. M. BLUM, R. W. FLOYD, V. PRATT, R. L. RIVEST et R. E. TARJAN, Time bounds for selection, J. Comput. Syst. Sci., 1973, 7, p. 448-461. Zbl0278.68033MR329916
10. 10. P. BOUCHER, A. NAGIH et G. PLATEAU, Méthodes heuristiques pour le problème hyperbolique en variables 0-1, Optimizations Days, Montréal, Canada, mai 1996. 
11. 11. S. CHANDRA et M. CHANDRAMOHAN, A Branch and Bound Method for Integer Nonlinear Fractional Programs, ZAMM, 1980, 60, p. 735-737. Zbl0462.90088MR614420
12. 12. S. CHANDRA et M. CHANDRAMOHAN, A note on integer linear fractional programming, Naval Res. Logist. Quart., 1980, 27, p, 171-174. Zbl0437.90091MR569150
13. 13. A. CHARNES et W. W. COOPER, Programming with linear fractional functionals, Naval Res. Logist. Quart., 1962, 9, p. 181-186. Zbl0127.36901MR152370
14. 14. B. D. CRAVEN, Fractional Programming, Helderman, Berlin, 1988. Zbl0638.90063MR949209
15. 15. C. DERMAN, On sequential decisions and Markov chains, Management Sci., 1962, 9, p. 16-24. Zbl0995.90621MR169685
16. 16. W. DINKELBACH, On nonlinear fractional programming, Management Sci., 1967, 13, p. 492-498. Zbl0152.18402MR242488
17. 17. M. FLORIAN et P. ROBILLARD, Programmation hyperbolique en variables bivalentes, Revue Française d'Informatique et de Recherche Opérationnelle, 1971, 5, n°1, p. 3-9. Zbl0232.90042MR312911
18. 18. A. M. GEOFFRION, An improved implicit enumeration approach for integer programming, Oper. Res., 1969, 17, p. 437-454. Zbl0174.20801
19. 19. A. M. GEOFFRION, The Lagrangean Relaxation for Integer Programming, Math.Programming, 1974, 2, p. 82-114. Zbl0395.90056MR439172
20. 20. F. GLOVER, Surrogate constraints, Oper. Res., 1968, 16, n°4, p. 741-749. Zbl0165.22602MR250670
21. 21. L. S. GOLD'STEIN, Dual problems of convex and fractionally-convex programming in functional spaces, Soviet Math. Dokl., 1967, 8, p. 212-216. Zbl0189.19701
22. 22. D. GRANOT et F. GRANOT, On solving fractional (0, 1) programs by implicit enumeration, INFOR, 1976, 14, p. 241-249. Zbl0344.90025MR426844
23. 23. D. GRANOT et F. GRANOT, On integer and mixed integer fractional programming problems, Ann. Discrete Math., 1977, I, p. 221-231. Zbl0358.90043MR496642
24. 24. M. GRUSPAN, Fractional programming: A survey, Technical Report 50, Department of Industrial and Systems Engineering, University of Florida, 1971. 
25. 25. M. GRUNSPAN et M. E. THOMAS, Hyperbolic integer programming, Naval Res. Logist. Quart., 1973, 20, n°2, p. 341-356. Zbl0263.90019MR317764
26. 26. M. GUIGNARD et S. KIM, Lagrangean decomposition for integer programming: A model yielding stronger Lagrangean bounds, Math. Programming, 1987, 32, p. 215-228. Zbl0638.90074MR916006
27. 27. E. GUTENBURG, Einfuhrung in die Betriebswirtschaftlehre, Gabler Wiesbaden, 1975. 
28. 28. P. L. HAMMER et S. RUDEANU, Boolean methods in operations research and related areas, Springer, Berlin - New York, 1968. Zbl0155.28001MR235830
29. 29. P. HANSEN, M. MINOUX et M. LABBÉ, Extension de la programmation linéaire généralisée au cas des programmes mixtes, C. R. Acad. Sci. Paris Sér. I Math., 1987, 305, p. 569-572. Zbl0626.90062MR917570
30. 30. P. HANSEN, M. V. POGGI DE ARAGAO et C. C RIBEIRO, Hyperbolic 0-1 programming and query information retrieval, Math. Programming, 1991, 52, p. 255-263. Zbl0737.90044MR1126171
31. 31. S. HASHIZUME, M. FUKUSHIMA, N. KATOH et T. IBARAKI, Approximation Algorithms for combinatorial fractional programming problem, Math. Programming, 1991, 37, p. 255-267. Zbl0616.90078MR891125
32. 32. M. H. HEINE, Distance between sets as an objective measure of retrieval effectiveness, Information Storage and Retrieval, 1973, 9, p. 181-198. Zbl0247.68050
33. 33. E. HEINEN, Grundlagen betriebswirtschaftlicher Entscheidungen, Das Zielsystem der Unternehmung Gabler Wiesbaden, 1971. 
34. 34. T. IBARAKI, Parametric approaches to fractional programs, Math. Programming, 1983, 26, p. 345-362. Zbl0506.90078MR707067
35. 35. O. H IBARRA et C. E. KIM, Fast approximation algorithms for the knapsack and sum of subsets problems, J. Assoc. Comput. Machinery, 1975, 22, n°4, p. 463-468. Zbl0345.90049MR378463
36. 36. J. R. ISBELL et W. H MARLOW, Attribution games, Naval Res. Logist. Quart., 1956, 3, p. 71-94. Zbl0122.15405MR83408
37. 37. H ISHII, T. IBARAKI et H. MINE, A primal cutting plane algorithm for integer fractional programming problems, J. Oper. Res. Soc. Japan, 1976, 19, p. 228-244. Zbl0405.90074MR416572
38. 38. H. ISHII, T. IBARAKI et H. MINE, Fractional Knapsack problems, Math. Programming, 1977, 13, p. 255-271. Zbl0378.90071MR462582
39. 39. J. G. KALLBERG et W. T. ZIEMBA, Generalized Concave Functions in Stochastic Programming and Portfolio Theory. in: S. Schaible and W. T. Ziemba, eds., Generalized Concavity in Optimization and Economics, Academic Press, New York 1981, p. 719-767. Zbl0534.90006
40. 40. M. KLEIN, Inspection-maintenance-replacement schedule under Markovian deterioration, Management Sci., 1963, 9, p. 25-32. 
41. 41. L. S. LASDON, Optimization Theory for Large Systems, Collier-MacMillan, 1970. Zbl0224.90038MR337317
42. 42. S. MARTELLO et P. TOTH, Knapsack Problems, J. Wiley & Sons, 1990. Zbl0708.68002MR1086874
43. 43. B. MARTOS, Hyperbolic programming, Naval Res. Logist. Quart., 1964, 11, p. 135-155. Zbl0131.18504MR182456
44. 44. B. MARTOS, The Direct Power of Adjacent Vertex Programming Methods, Management Sci., 1965, 12, n°3, p. 241-252. Zbl0142.17002MR189824
45. 45. B. MARTOS, Nonlinear programming: Theory and methods, North-Holland, Amsterdam, 1975. Zbl0357.90027MR496692
46. 46. N. MEGGIDO, Combinatorial optimization with rational objective functions, Math. Oper. Res., 1979, 4, n°4, p. 414-424. Zbl0425.90076MR549127
47. 47. P. MICHELON et N. MACULAN, An algorithm for the mixed or integer fractional programming, Research Report ES-161-88, University of Rio de Janeiro, 1988. 
48. 48. P. MICHELON et N. MACULAN, Lagrangean methods for 0-1 quadratic problems, Discrete Applied Mathematics, 1993, 42, p. 257-269. Zbl0780.90068MR1217100
49. 49. K. M. MJELDE, Allocation of resources according to a fractional objective, EuropeanJ. Oper. Res., 1978, 2, p. 116-124. Zbl0371.90084MR472057
50. 50. K. M. MJELDE, Methods of the Allocation of Limited ressources, J. Wiley and Sons, Chichester, 1983. Zbl0511.90076
51. 51. A. NAGIH, Sur la résolution des programmes fractionnaires en variables 0-1, Thèse de Doctorat, Université Paris 13, France, juin 1996. 
52. 52. A. NAGIH et G. PLATEAU, A Lagrangian Decomposition for 0-1 Hyperbolic Programming Problems, Int. J. Math. Algorithms, to appear. Zbl0997.90084
53. 53. A. NAGIH et G. PLATEAU, Méthodes lagrangiennes pour les problèmes hyperboliques en variables 0-1, FRANCORO: Rencontres Francophones de Recherche Opérationnelle, Mons, Belgique, juin 1995. Zbl1092.90031
54. 54. A. NAGIH et G. PLATEAU, An exact Method for the 0-1 Fractional Knapsack Problem, INFORMS, New Orleans, USA, 29 octobre - 1er novembre 1995. 
55. 55. A. NAGIH et G. PLATEAU, Sur la résolution des programmes fractionnaires en variables 0-1, CIRO : Conférence Internationale en Recherche Opérationnelle, Marrakech, Maroc, juin 1996. Zbl0967.90090
56. 56. A. NAGIH et G. PLATEAU, Dualité lagrangiennne en programmation fractionnaire concave-convexe en variables entières, Rapport de Recherche, LIPN 96, Université Paris 13, 1996. 
57. 57. A. NAGIH et G. PLATEAU, A Partition Algorithm for 0-1 unconstrained hyperbolic programs, Investigación Oper., 1999, 8, n° 1. Zbl0997.90084
58. 58. C. H. PAPADMITRIOU et K. STEIGLITZ, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, NJ, 1982. Zbl0503.90060MR663728
59. 59. J. PONSTEIN, Seven Kinds of convexity, SIAM Review, 1967, 9, n°1. Zbl0164.06501MR213961
60. 60. T. RADZIK, Newton's method for fractional combinatorial optimization, Report STAN-CS-92-1406, Stanford university, California, 1992. Zbl0977.68546
61. 61. P. ROBILLARD, 0-1 hyperbolic programming, Naval Res. Logist. Quart., 1971, 18, p. 47-58. Zbl0231.90033MR303959
62. 62. A. L. SAIPE, Solving a (0, 1) hyperbolic program by branch and bound, Naval Res.Logist. Quart., 1975, 22, p. 397-416. Zbl0335.90042
63. 63. S. SCHAIBLE, Duality in fractional programming: a unified approach, Oper. Res., 1976, 24, n°3, p. 452-461. Zbl0348.90120MR411644
64. 64. S. SCHAIBLE, Fractional programming: Applications and algorithms, European J. Oper. Res., 1981, 17, p. 111-120. Zbl0452.90079MR618913
65. 65. S. SCHAIBLE et T. IBARAKI, Fractional programming, European J. Oper. Res., 1983, 12, p. 325-338. Zbl0529.90088MR703439
66. 66. I. C. SHARMA et K. SWARUP, On duality in linear fractional functionals programming, Zeitschrift für Operations Research, 1972, 16, p. 91-100. Zbl0243.90045MR309556
67. 67. I. M. STANCU-MINASIAN, Applications of the fractional programming, Econom. Comput. Econom. Cybernet. Stud. Res., 1980, 14, p. 69-86. Zbl0435.90101MR574672
68. 68. C. J. VAN RIJSBERGEN, Function of evaluation, The Journal of Documentation, 1974, 30, n°4, p. 365-373. 
69. 69. V. VERMA, Constrainted Integer Linear Fractional Programming Problem, Optimization, 1990, 21, n°5, p. 749-757. Zbl0717.90073MR1072476
70. 70. V. VERMA, H. C. BAKHSHI et M. C. PURI, Ranking in integer linear fractional programming problems, Methods and ModeIs of Operations Research, 1990, 34, p. 325-334. Zbl0721.90072MR1074568
71. 71. H. M. WAGNER et J. S. C. YUAN, Algorithmic equivalence in linear fractional programming, Management Sci., 1968, 14, p. 301-306. Zbl0153.49101MR243821
72. 72. T. WEIR et B. MOND, Duality for Frational Programming without Constraint QualificationUtilitas Mathe., 1990, 38, p. 193-197. Zbl0723.90076MR1093890
73. 73. H. P. WILLIAMS, Experiments in the formulation of integer programming problems, Math. Programming Studi, 1974, 2, p. 180-197. Zbl0353.90062MR855888
74. 74. H. WOLF, Parametric Analysis in linear fractional programming, Oper. Res., 1986, 34, n°6, p. 930-937. Zbl0627.90085MR886660
75. 75. W. T. ZIEMBA, C. PARKAN et R. BROOKS-HILL, Calculation of investment portfolios with risk free borrowing and lending, Management Sci., 1974, 21, p. 209-222. Zbl0294.90004