Zusammenfassung
Es wird eine Bibliographie zur Quotientenprogrammierung veröffentlicht, die 551 Titel enthält. Es wurde versucht, alle Beiträge zu diesem Gebiet der nichtlinearen Programmierung zu berücksichtigen, das nun seit mehr als 45 Jahren erforscht wird.
Abstract
A bibliography in fractional programming is provided which contains 551 references. It was attempted to include all publications in this area of nonlinear programming as they have appeared in more than 45 years now.
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References
Abadie, J.M., and A.C. Williams: Dual and Parametric Methods in Decomposition. In: Graves, R., and P. Wolfe (eds.),Recent Advances in Mathematical Programming, McGraw-Hill, New York, 1963, 149–158.
Abrham, J., and R.N. Buie: Duality in Continuous Fractional Programming.Utilitas Mathematica 17, 1980, 35–44.
Abrham, J., and S. Luthra: Comparison of Duality Models in Fractional Linear Programming.ZOR — Zeitschrift für Operations Research 21, 1977, 125–130.
Aggarwal, S.P.: Stability of the Solution to a Linear Fractional Functional Programming Problem.Zeitschrift für Angewandte Mathematik und Mechanik 46, 1966, 343–349.
—: A Note on Quasiconvex Programming.Metrika 12, 1968, 97–105.
—: Parametric Linear Fractional Functional Programming.Metrika 12, 1968, 106–114.
—: Standard Error Fractional Functional Programming.Instanbul Üniversitesi Fen Fakültesi Mecmuasi, A Serisi 30, 1968, 45–51.
—: Analyses of the Solution to a Linear Fractional Functional Programming.Metrika 16, 1970, 9–26.
—: Quadratic Fractional Functional Programming with Non-Linear Constraints (Italian).Ricerca Operativa 2, 1972, 51–53.
—: Indefinite Quadratic Fractional Programming.Ekonomicko-Matematicky Obzor 8, 1972, 191–199.
—: Variation in Parameters of Quadratic Fractional Functional Programming.Revue Belge de Statistique d'Informatique et de Recherche Opérationelle 11 (4), 1972, 3–12.
—: Transportation Technique for Quadratic Fractional Programming.Revue Belge de Statistique d'Informatique et de Recherche Opérationelle 12 (2), 1972, 3–7.
—: Upper Bounds and Quadratic Fractional Functional Programming.Revue Belge de Statistique d'Informatique et de Recherche Opérationelle 12 (4), 1973, 17–21.
—: Indefinite Quadratic Fractional Programming with a Quadratic Constraint.Cahiers du Centre d'Etudes de Recherche Opérationelle 15, 1973, 405–410.
—: Quadratic Fractional Functional Programming.Cahiers du Centre d'Etudes de Recherche Opérationelle 15, 1973, 157–165.
Aggarwal, S.P., and S. Arora: A Special Class of Non-Linear Fractional Functional Programming Problems.SCIMA, Journal of Management Science and Applied Cybernetics 3, 1974, 30–39.
Aggarwal, S.P., and O. Parkash: Duality in General Linear Fractional Functional Programming.Cahiers du Centre d'Etudes de Recherche Opérationelle 20, 1978, 75–81.
Aggarwal, S.P., and P.C. Saxena: Duality Theorems for Fractional Functional Programming with Quadratic Constraint.Ekonomicko Matematicky Obzor. 10, 1974, 86–92.
—: Duality Theorems for Non-Linear Fractional Programs.Zeitschrift für Angewandte Mathematik und Mechanik 55, 1975, 523–525.
—: The Decomposition Method for Linear Programming Problems with Linear and Fractional Target Functions.Przeglad Statyst 23, 1976, 211–219.
—: A Class of Fractional Functional Programming Problems.New Zealand Operational Research 7, 1979, 79–90.
Aggarwal, S.P., and I.C. Sharma: Maximization of the Transmission Rate of a Discrete Constant Channel.Unternehmensforschung 14, 1970, 152–155.
Aggarwal, S.P., and K. Swarup: Fractional Functional Programming with a Quadratic Constraint.Operations Research 14, 1966, 950–956.
Aggarwal, V., S. Chandra, and K.P. Nair: Discounted Stochastic Ratio Games.Journal of Optimization Theory and Applications 27, 1977, 27–37.
Agrawal, S.C.: On Integer Solutions to Linear Fractional Functional Programming Problems.Acta Ciencia Indica 1, 1975, 203–208.
—: On Integer Solutions to Linear Fractional Functional by a Branch and Bound Technique.Acta Ciencia Indica 2, 1976, 75–78.
—: An Alternative Method on Integer Solutions to Linear Fractional Functionals by a Branch and Bound Technique.Zeitschrift für Angewandte Mathematik und Mechanik 57, 1977, 52–53.
Agrawal, S.C., and M. Chand: On Integer Solutions to Complementary Programming Problems with Linear Fractional Objective Function by a Branch and Bound Technique.Acta Ciencia Indica 4, 1978, 283–289.
—: On Intersection Cuts in Fractional Interval Integer Programming.Acta Ciencia Indica 5, 1979, 140–142.
—: A Note on the Sum of Linear and Fractional Interval Programming.Revista de Informatica e Investigacion Operativa 20, 1980, 33–36.
Agrawal, S.C., and R.K. Verma: p-Variables Replacement in Linear Fractional Functional Programming.Acta Ciencia Indica 6, 1980, 95–103.
Almogy, Y., and O. Levin: Parametric Analysis of a Multi-stage Stochastic Shipping Problem. In: Lawrence, J. (Ed.),Operational Research '69, Tavistock Publications, London, 1970, 359–370.
—: A Class of Fractional Programming Problems.Operations Research 19, 1971, 57–67.
—: The Fractional Fixed-Charge Problems.Naval Research Logistics Quarterly 18, 1971, 307–315.
Anand, P.: Dual and Parametric Methods in Decomposition for Linear Fractional Programs.Studia Scientarium Mathematicarum Hungarica 6, 1971, 267–275.
—: Decomposition Procedure for Linear Fractional Programs with Upper Bounds.Zeitschrift für Angewandte Mathematik and Mechanik 53, 1973, 635–636.
Anand, P., and K. Swarup: The Procedure for Local Separable Programming.Zeitschrift für Angewandte Mathematik und Mechanik 50, 1970, 320–321.
Anzai, Y.: On Integer Fractional Programming.Journal of the Operations Research Society of Japan 17, 1974, 49–66.
Arbuzova, N.I.: Interdependence of the Stochasticε-Stabilities of Linear and Linear Fractional Programming Problems of a Special Form (Russian).Ekonom. i Mat. Metody 4, 1968, 108–110.
Arisawa, S., and S.E. Elmaghraby: Optimal Time-Cost Trade Offs in GERT-Networks.Management Science 18, 1972, 589–599.
Armstrong, R., et al.: Effective Solution of Non-Convex Multi-Objective Ratio Goal Problems.Research Report CCS 390, Center for Cybernetic Studies, University of Texas, Austin, 1980.
Arora, S.R.: A Set Partitioning Problem with Linear Fractional Objective Function.Indian Journal of Pure and Applied Mathematics 8, 1977, 961–968.
—: A Note on Fractional Fixed Charge Problems.New Zealand Operational Research 5, 1977, 66–71.
Arora, S.R., and S.P. Aggarwal: Dynamic Programming Approach to Linear Fractional Functional Programming.Revue Belge de Statistique d'Informatique et de Recherche Opérationelle 17, 1977, 10–23.
—: Linear Fractional Functional Programming with a Parameter in an Activity Vector.Economic Computation and Economic Cybernetics Studies and Research 3, 1977, 37–56.
Arora, S.R., and M.C. Puri: Enumeration Technique for the Set Covering Problem with a Linear Fractional Functional as the Objective Function.Zeitschrift für Angewandte Mathematik und Mechanik 57, 1977, 181–186.
Arora, S.R., M.C. Puri and K. Swarup: The Set Covering Problem with Linear Fractional Functionals.Indian Journal of Pure and Applied Mathematics 8, 1977, 578–588.
—: Cutting Plane Technique for Set Covering Problem with Linear Fractional Functional.Zeitschrift für Angewandte Mathematik und Mechanik 57, 1977, 597–602.
Artjuhin, A.V.: An Algorithm for the Solution of the Distribution Problem of Parametric Fractional Linear Programming (Russian).Izdat. “Ilim”, Frunze, 1973, 30–36.
-: Some Applications of Parametric Fractional Linear Programming (Russian).Izdat., “Ilim”, Frunze, 1973, 37–54.
Ashton, D.J., and D.R. Atkins: Multi-Criteria Programming for Financial Planning.Journal of the Operational Research Society 30, 1979, 259–270.
Avriel, M.:Nonlinear Programming: Analysis and Methods, Prentice-Hall, Englewood-Cliffs, N.J., 1976.
Avriel, M., et al.: Introduction to Concave and Generalized Concave Functions. In: Schaible, S., and W.T. Ziemba, (eds.),Generalized Concavity in Optimization and Economics, Academic Press, New York, 1981, 21–50.
Avriel, M., and S. Schaible: Second-Order Characterizations of Pseudo-Convex Functions.Mathematical Programming 14, 1978, 170–185.
Awerbuch, S., J.G. Ecker and W.A. Wallace: A Note: Hidden Nonlinearities in the Application of Goal Programming.Management Science 22, 1976, 918–920.
Babayev, D.A.: Mathematical Models for Optimal Timing of Drilling on Multilayer Oil and Gas Fields.Management Science 21, 1975, 1361–1369.
—: A General Fractional Programming Problem (Russian).Central. Èkonom.-Mat. Inst., Akad. Nauk SSSR, Moscow, 1976.
Bakhshi, H.C.: Sensitivity Analysis in Linear Fractional Functional Programming Problems with Extreme Point Restriction.SCIMA, Journal of Management Science and Applied Cybernetics 8, 1979, 6–15.
Bakhshi, H.C., and M.C. Puri: An Efficient Technique for Extreme Point Mathematical Programming Problems.Cahiers du Centre d'Etudes de Recherche Opérationelle 21, 1979, 257–268.
Baluta, M., V. Dobrescu and G. Paun: Algorithm for Solving a Combinatorial Problem of Optimal Selection.Economic Computation and Economic Cybernetics Studies and Research 1, 1979, 87–95.
Banker, R.D.: A Gametheoretic Approach to Measuring Efficiency.European Journal of Operational Research 5, 1980, 262–266.
Banker, R.D., et al.: A Bi-Extremal Principle for Frontier Estimation and Efficiency Evaluations.Management Science 27, 1981, 1370–1382.
Bansal, S.: Absolute Value Linear Fractional Programming.Cahiers du Centre D'Etudes de Recherche Opérationelle 23, 1981, 43–52.
Barlow, R.E., and F. Proschan:Mathematical Theory of Reliability. Wiley, New York, 1965.
Barrodale, I.: Best Rational Approximation and Strict Quasiconvexity.SIAM J. of Numerical Analysis 10, 1973, 8–12.
Bazaara, M.S., and C.M. Shetty:Nonlinear Programming, Theory and Algorithms. J. Wiley, New York, 1979.
Beale, E.M.L.: Fractional Programming with Zero-One Variables. In: Fiacco, A.V., and K.O. Kortanek (Eds.),Extremal Methods and Systems Analysis. Springer, Berlin, 1980, 430–432.
Becher, O.: Das Problem der optimalen Routenwahl einer Transporteinheit bei Beschäftigung mit Gelegenheitsfahrten.Zeitschrift für die gesamte Staatswissenschaft 121, 1965, 196–221.
Bector, C.R.: Nonlinear Fractional Functional Programming with Nonlinear Constraints.Zeitschrift für Angewandte Mathematik und Mechanik 48, 1968, 284–286.
—: Duality in Fractional and Indefinite Programming.Zeitschrift für Angewandte Mathematik und Mechanik 48, 1968, 418–420.
—: Programming Problems wiht Convex Fractional Functions.Operations Research 16, 1968, 383–391.
—: Some Aspects of Nonlinear Indefinite Fractional Functional Programming.Cahiers du Centre d'Etudes de Recherche Opérationelle 12, 1970, 22–34.
—: Indefinite Quadratic Fractional Functional Programming.Metrika 18, 1971, 21–30.
—: Duality in Nonlinear Fractional Programming.ZOR — Zeitschrift für Operations Research 17, 1973, 183–193.
—: On Convexity, Pseudo-Convexity and Quasi-Convexity of Composite Functions.Cahiers du Centre d'Etudes de Recherche Opérationelle 15, 1973, 411–428.
—: Duality in Linear Fractional Programming.Utilitas Mathematica 4, 1973, 155–168.
—: A Note on a Dual Fractional Program.Cahiers du Centre d'Etudes de Recherche Opérationelle 16, 1974, 107–115.
Bector, C.R., M.K. Bector and J.E. Klassen: Duality for a Nonlinear Programming Problem.Utilitas Mathematica 11, 1977, 87–99.
Bector, C.R., and S.K. Bhatt: A Linearization Technique for Solving Interval Linear Fractional Programs. In: Proceedings of the Fifth Manitoba Conference on Numerical Mathematics, Congressus Numerantium. No. XVI, Winnipeg,Utilitas Mathematica, 1976, 221–229.
—: Pseudo-Monotonic Interval Programming.Naval Research Logistics Quarterly 25, 1978, 309–314.
Bector, C.R., S. Chandra and T.R. Gulati: Duality for Complex Nonlinear Fractional Programming Over Cones. In: Proceedings of the Third Manitoba Conference on Numerical Mathematics, Winnipeg,Utilitas Mathematica 1974, 87–103.
-: Duality for Fractional Control Problems. In: Proceedings of Fifth Manitoba Conference on Numerical Mathematics, Winnipeg,Utilitas Mathematica, 1976, 231–241.
—: A Lagrangian Approach to Duality for Complex Nonlinear Fractional Programming Over Cones.Mathematische Operationsforschung und Statistik, Series Optimization 8, 1977, 17–25.
Bector, C.R., and T.R. Grover: Minimizing Certain Nonconvex Quadratic Fractional Programs by Ranking the Extreme Points. In: Proceedings of the Second Manitoba Conference on Numerical Mathematics, Congressus Numerantium, Winnipeg,Utilitas Mathematica, 1973, 95–100.
Bector, C.R., and P.L. Jolly: Pseudo Monotonic Integer Programming. In:Proceedings of the Manitoba Conference on Numerical Mathematics and Computing, 1979, 211–218.
Bedi, M.K.: Duality for a Special Class of Quasi-Convex Programming Problems.Zeitschrift für Angewandte Mathematik und Mechanik 58, 1978, 165–166.
Behringer, F.A.: Lexicographic Quasiconcave Multiobjective Programming.ZOR — Zeitschrift für Operations Research 21, 1977, 103–116.
Belen'Kij, A.S.: Minimax Problem with Linear Constraints.Automation and Remote Control 41, 1980, 562–568; translated fromAvtom. Telemekh 4 (Russian), 1980, 151–158.
Bell, E.J.: Primal-Dual Decomposition Programming.Ph.D. Thesis, Operations Research Center, University of California, Berkeley, 1965.
Bellman, R.:Dynamic Programming. Princeton University Press, Princeton, 1957.
Belykh, V.M., and M.K. Gavurin: Minimization Algorithm for a Linear-Fractional Function (Russian).Vestnik Leningradskogo Universiteta, Matematika, Mehanika, Astronomija 4, 1980, 10–15.
Bereanu, B.: Distribution Problems in Stochastic Linear Programming and Minimum Risk Solutions, (Roumanian).Dissertation Abstract, Faculty of Mathematics and Mechanics, Bucharest, 1963.
—: Solutions of Minimum Risk in Linear Programming (Roumanian).Analele Universitatii Bucuresti, Seria Stiintele Naturii, Matematica-Mecanica 13, 1964, 121–140.
-: Programme de Risque Minimal en Programmation Linéaire Stochastique.Compte Revue Academie Science, Paris, 1964, 981–983.
—: Decision Regions and Minimum Risk Solutions in Linear Programming. In: Prekopa, A. (ed.),Colloquium on Applications of Mathematics to Economics, Hungarian Academy of Sciences, Budapest, 1965, 37–42.
-: Quasi-Convexity, Strict Quasi-Convexity and Pseudo-Convexity of Composite Objective Functions.Revue Francaise d'Automatique, Informatique et Recherche Opérationelle, 1972, 15–26.
Bergthaller, C.A.: Quadratic Equivalent of the Minimum Risk Problem.Revue Roumaine de Mathematiques Pures et Appliquees 15, 1970, 17–23.
Bessent, A., and W. Bessent: Determining the Comparative Efficiency of Schools through Data Envelopement Analysis.Research Report CCS 361, Center for Cybernetic Studies, University of Texas, Austin, December 1979.
Bessent, A., et al.: An Application of Mathematical Programming to Assess Managerial Efficiency in the Houston Independent School District.Research Report CCS 373, Center for Cybnertic Studies, University of Texas, Austin, November. 1981.
Bhatia, D., and B. Gupta: Efficiency in Certain Nonlinear Fractional Vector Maximization Problems.Indian Journal of Pure and Applied Mathematics 11, 1980, 669–672.
Bhatia, H.L.: Solid Transportation Problem in Linear Fractional Programming.Revue Belge de Statistique d'Informatique et de Recherche Opérationelle 18, 1978, 35–50.
Bhatt, S.K.: Sequential Unconstrained Minimization Technique for a Non-Convex Program.Cahiers du Centre d'Etudes de Recherche Opérationelle 15, 1973, 429–435.
—: An Existence Theorem for a Fractional Control Problem.Journal of Optimization Theory and Applications 11, 1973, 379–385.
—: Generalized Pseudo-Convex Programming in Real Banach Space and Duality.Cahiers du Centre d'Etudes de Recherche Opérationelle 16, 1974, 7–16.
—: Linearization Technique for Linear Fractional and Pseudo-Monotonic Programs Revisited.Cahiers du Centre d'Etudes de Recherche Opérationelle 23, 1981, 53–56.
Bitran, G.R.: Experiments with Linear Fractional Problems.Naval Research Logistics Quarterly 26, 1979, 689–693.
Bitran, G.R., and T.L. Magnanti: Duality and Sensitivity Analysis for Fractional Programs.Operations Research 24, 1976, 675–699.
Bitran, G.R., and A.G. Novaes: Linear Programming with a Fractional Objective Function.Operations Research 21, 1973, 22–29.
Blau, R.A.: Decomposition Technique for the Chebychev Problem.Operations Research 21, 1973, 1157–1162.
Böhm, H.H.: Die Maximierung der Kapitalrentabilität.Zeitschrift für Betriebswirtschaft 32, 1962, 489–512.
Borwein, J.M.: Fractional Programming Without Differentiability.Mathematical Programming 11, 1976, 283–290.
Bradley, S.P., and S.C. Frey: Fractional Programming with Homogeneous Functions.Operations Research 22, 1974, 350–357.
Brender, D.M.: A Surveilance Model for Recurrent Events.IBM Watson Research Center Report, 1963.
Bühler, W.: A Note on Fractional Interval Programming.Zeitschrift für Operations Research 19, 1975, 29–36.
Bühler, W., und R. Dick: Stochastische lineare Optimierung. Teil I,Zeitschrift für Betriebswirtschaft 42, 1972, 667–692; Teil II,Zeitschrift für Betriebswirtschaft 43, 1973, 101–120.
Bühler, W., and N. Newinger: On the Convergence of Martos' Hyperbolic Programming Algorithm.Arbeitsbericht, Lehrstuhl für Unternehmensforschung, Rheinisch — Westfälische Technische Hochschule, Aachen, 1973.
Cabot, A.V.: Maximizing the Sum of Certain Quasiconcave Functions Using Generalized Benders Decomposition.Naval Research Logistics Quarterly 25, 1978, 473–482.
Callahan, J.R., and C.R. Bector: Optimization with General Stochastic Objective Functions.Proceedings of the Third Manitoba Conference on Numerical Mathematics, 1973, 127–137.
Cambini, A.: Un Algoritmo per il Massimo del Quoziente di Due Forme Affini con Vincoli Lineari.Paper No. A-42, Department of Operations Research, University of Pisa, Italy, 1977.
—: Sulla Programmazione Lineare Frazionaria Stocastica.Paper No. A-50, Dipartimento di Recerco Operativa e Scienze Statistiche, Università di Pisa, Italy, 1978.
—: An Algorithm for a Special Class of Fractional Programs. In: Schaible, S., and W.T. Ziemba (eds.),Generalized Concavity in Optimization and Economics, Academic Press, New York, 1981, 491–508.
Cambini, A., L. Martein and L. Pellegrini: Decomposition Methods and Algorithms for a Class of Non-linear Programming Problems.First Meeting AFCET-SMF Palaiseau, Ecole Polytechnique Palaiseau Paris, 1978, 179–189.
Černov, J.P.: Several Problems of Parametric Fractional Linear Programming (Russian).Optimal. Planirovanie Vyp. 16, 1970, 98–111.
—: A Certain Problem of Parametric Linear-Fractional Programming (Russian).Izvestija Akademii Nauk Kirgizskoi SSR 3, 1970, 20–27.
—: The Problems of Fractional Programming with Linear Separable and Quadratic Functions (Russian).Èconom. i Mat. Metody 7, 1971, 721–732.
—: An Application of the δ-Method to the Solution of Fractional Programming Problems with Separable Functions (Russian).Mathematical Methods for the Solution of Economic Problems (Suppl. to Èkonom. i Mat. Metody 3), 1972, 68–73.
Černov, J.P., and E.G. Lange: A Transport Problem of Fractional Programming (Russian).Optimal. Planirovanie Vyp. 16, 1970, 112–132.
Černov, J.P., and E.G. Lange: An Application of the Method of Successive Computations to the Solution of a Certain Class of Fractional Concave Programming Problems (Russian).Mathematical Methods of Solution of Economic Problems (Suppl. to Èkonom. i Mat. Metody 5), 1974, 37–49.
Černov, J.P., E.G. Lange and A. Žusupbaev: Application of the Successive Calculation Method to Solving a Production Allocation Problem with a Fractional-Convex Functional (Russian).Izvestija Akademii Nauk Kirgizskoi SSR 2, 1979, 27–34.
Chadha, S.S.: A Decomposition Principle for Fractional Programming.Opsearch 4, 1967, 123–132.
—: An Extension of Upper Bounded Technique for a Linear Fractional Program.Metrika 20, 1969, 25–35.
—: A Linear Fractional Functionals Program with Variable Coefficients.Revue de la Faculte des Sciences de l'Universite d'Instanbul, Serie A 36, 1971, 7–13.
—: A Dual Fractional Program.Zeitschrift für Angewandte Mathematik und Mechanik 51, 1971, 560–561.
—: A Linear Fractional Functional Program with a Two Parameter Objective Function.Zeitschrift für Angewandte Mathematik und Mechanik 51, 1971, 479–481.
—: A Generalized Upper Bounded Technique for a Linear Fractional Program.Metrika 20, 1973, 25–35.
—: Duality Theorems for a Generalized Linear and Linear Fractional Program.Cahiers du Centre d'Etudes de Recherche Opérationelle 15, 1973, 167–173.
—: A Decomposition Principle for a Generalized Linear and Piece-wise Linear Program.Trabajos de Estadistica e Investigacion Operativa 28, 1977, 85–92.
Chadha, S.S., and J.M. Gupta: Sensitivity Analysis of the Solution of a Generalized Linear and Piece-Wise Linear Program.Cahiers du Centre d'Etudes de Recherche Opérationelle 18, 1976, 309–321.
Chadha, S.S., and R.N. Kaul: A Dual Nonlinear Program.Metrika 19, 1972, 18–22.
—: A Linear Fractional Functional Program with Variable Coefficients.Journal of Mathematical Sciences 7, 1972, 15–20.
Chadha, S.S., and S. Shivpuri: A Simple Class of Parametric Linear Fractional Functionals Programming.Zeitschrift für Angewandte Mathematik und Mechanik 53, 1973, 644–646.
—: Parametrization of a Generalized Linear and Piece-wise Linear Programming Problem.Trabajos de Estadisticae Investigation Operativa 28, 1977, 151–160.
—: Enumerative Technique for an Extreme Point Fractional Program.European Journal of Operational Research 4, 1980, 54–59.
Chambers, D.: Programming the Allocation of Funds Subject to Restrictions on Reported Results.Operational Research Quarterly 10, 1967, 407–431.
Chandra, S.: Linear Fractional Functional Programming.Journal of the Operations Research Society of Japan 10, 1967, 1–2.
—: The Capacitated Transportation Problem in Linear Fractional Programming.Journal of the Operations Research Society of Japan 10, 1967, 18–26.
—: Decomposition Principle for Linear Fractional Functional Programs.Revue Francaise d'Informatique et de Recherche Opérationelle 2, 1968, 65–72.
—: Strong Pseudo-Convex Programming.Indian Journal of Pure and Applied Mathematics 3, 1972, 278–282.
Chandra, S., and M. Chandramohan: Duality and Algorithmic Aspects of Integer Linear Fractional Programming.Research Report, Department of Mathematics, Indian Institute of Technology, New Delhi, 1976.
—: An Improved Branch and Bound Method for Mixed Integer Linear Fractional Programs.Zeitschrift für Angewandte Mathematik und Mechanik 59, 1979, 575–577.
—: Duality in Mixed Integer Nonconvex and Nondifferentiable Programming.Zeitschrift für Angewandte Mathematik und Mechanik 59, 1979, 205–209.
—: A Branch and Bound Method for Integer Non-linear Fractional Programs.Zeitschrift für Angewandte Mathematik und Mechanik 60, 1980, 735–737.
—: A Note on Integer Linear Fractional Programming.Naval Research Logistics Quarterly 27, 1980, 171–174.
Chandra, S., and T.R. Gulati: A Duality Theorem for a Nondifferentiable Fractional Programming Problem.Management Science 23, 1976, 32–37.
Chandrasekaran, R.: Minimum Ratio Spanning Trees.Networks 7, 1977, 335–342.
Charnes, A., and W.W. Cooper: Programming with Linear Fractional Functionals.Naval Research Logistics Quarterly 9, 1962, 181–186.
—: Systems Evaluation and Repricing Theorems.Management Sciences 9, 1962, 33–49.
—: Programming with Linear Fractional Functionals, a Communication.Naval Research Logistics Quarterly 10, 1963, 273–274.
—: Deterministic Equivalents for Optimizing and Satisficing Under Chance Constraints.Operations Research 11, 1963, 18–39.
—: An Explicit General Solution in Linear Fractional Programming.Naval Research Logistics Quarterly 20, 1973, 449–467.
—: Goal Programming and Multi-Objective Optimization, Part I.European Journal of Operational Research 1, 1977, 39–54.
—: Auditing and Accounting for Program Efficiency and Management Efficiency in Not-for-Profit Entities.Accounting, Organizations, and Society 5, 1980, 87–107.
—: Management Science Relations for Evaluation and Management Accountability.Journal of Enterprise Management 2, 1980, 143–162.
Charnes, A., W.W. Cooper and E. Rhodes: Measuring the Efficiency of Decision Making Units.European Journal of Operational Research 2, 1978, 429–444: also: Corrections,op. cit. 3, 1979, 339.
—: Evaluation Program and Managerial Efficiency: An Application of Data Envelopement Analysis for Program Follow Through.Management Science 27, 1981, 668–697.
Charnes, A., L. Cox and M. Lane: A Note on the Redesigning of a Rate Structure for Allocation of State Funds to Educational Institutions.Working Paper 70-49 of Project GUM, University of Texas at Austin, May 1970.
Charnes, A., and D. Granot: Constrained Non-Cooperative von Neumann Ratio Games.Working Paper No. 368, Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, 1976.
Charnes, A., D. Granot and F. Granot: An Algorithm for Solving General Fractional Interval Programming Problems.Naval Research Logistics Quarterly 23, 1976, 53–65.
—: A Note on Explicit Solutions in Linear Fractional Programming.Naval Research Logistics Quarterly 23, 1976, 161–167.
—: On Solving Linear Fractional Interval Programming Problems.Cahiers du Centre d'Etudes de Recherche Opérationelle 20, 1978, 45–57.
Chong, J.H., and J.O. Kim: A Solution of Linear and Fractional Linear Programming with Both Restrictions (Korean).Su-hak kwa Mul-li 19, 1975, 9–15.
Choo, E.U.: Multicriteria Linear Fractional Programming.PhD. — Thesis, University of British Columbia, Vancouver, 1980.
Choo, E.U., and D.R. Atkins: An Interactive Algorithm for Multicriteria Programming.Computer and Operations Research 7, 1980, 81–87.
-: Connectedness in Multiple Linear Fractional Programming. To appear in Management Science.
—: Bicriteria Linear Fractional Programming.Journal of Optimization Theory and Applications 36, 1982, 204–220.
Climaco, J.C.N., E.Q.V. Martins and M.S. Rosa: A Simplex Based Algorithm for the Minimal Average Speed Path Problem. Dept. of Mathematics, University of Coimbra, Coimbra (Portugal), Dec. 1981.
Collatz, L., and W. Wetterling:Optimierungsaufgaben. 2. Ed., Springer, Berlin, 1971.
Cook, W.D., M. J.L. Kirby and S.L. Mehndiratta: A Linear Fractional Max-Min Problem.Operations Research 23, 1975, 511–521.
Corban, A.: Programming with Fractional Linear Objective Function.Revue Roumaine de Mathematique Pures et Appliquées 18, 1973, 633–637.
—: Duality in Transportation Problems in Fractional Programming (Roumanian).Studii si Cercetari Matematice 25, 1973, 347–357.
—: Duality in Non-Linear Programming (Roumanian).Studii si Cercetari Matematice 26, 1974, 375–399.
—: Non-linear Three-Dimensional Programming.Revue Roumaine de Mathématiques Pures et Appliquées 20, 1975, 1043–1059.
Craven, B.D.:Mathematical Programming and Control Theory. Chapman and Hall, London, 1978.
—: Duality for Generalized Convex Fractional Programs. In: Schaible, S., and W.T. Ziemba, (eds.),Generalized Concavity in Optimization and Economics. Academic Press, New York, 1981, 473–490.
Craven, B.D., and B. Mond: On Fractional Programming and Equivalence.Naval Research Logistics Quarterly 22, 1975, 405–410.
—: The Dual of a Fractional Linear Program.Journal of Mathematical Analysis and Applications 42, 1973, 507–512, andJournal of Mathematical Analysis and Applications 55, 1976, 807.
—: Duality for Homogeneous Fractional Programming.Cahiers du Centre d'Etudes de Recherche Opérationelle 18, 1976, 413–417.
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This research was supported by an earlier grant of Deutsche Forschungsgemeinschaft (West Germany), by Grant No. 4534 of Natural Sciences and Engineering Research Council (NSERC) and by the J.D. Muir Fund of the Faculty of Business, University of Alberta.
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Schaible, S. Bibliography in fractional programming. Zeitschrift für Operations Research 26, 211–241 (1982). https://doi.org/10.1007/BF01917115
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DOI: https://doi.org/10.1007/BF01917115