Literaturverzeichnis

ABADIE, J. M., 1963-1: On decomposition principle. Operations Res. Center, Univ. California, Berkeley, ORC·63-20, 1963.

-, and A. C. WILLIAMS, 1963-1: Dual and parametric methods in decomposition. In R. GRAVES, and P. WOLFE (Ed.): Recent advances in mathematical pro­gramming. New York, Toronto, London: McGraw-Hill 1963.

ABLOW, C. M., and GEORGES BRIGHAM, 1955-1: An analog solution of programming problems. Operations Res. 3, 388-394 (1955).

ADAM, A., F. FERSCHL, A. KLAMECKER, A. KLINGST, O. PICHLER, J. ROPPERT, H. SCHOLZ, K. WENKE und W. WETZEL, 1963-1: Anwendung der Matrizen­rechnung auf wirtschaftliche und statistische Probleme, 2. Auf!. Wiirzburg: Physica-Verlag 1963.

AGMON, SHMUEL, 1954--1: The relaxation method for linear inequalities. Canad. J. Math. 6, 382-392 (1954).

ALBACH, HORST, 1960-1: Lineare Programmierung als Hilfsmittel betrieblicher Investitionsplanung. Z. f. Handelsw. Forsch. 12, 526 (196(1).

ALLEN, R. G. D., 1959-1: Mathematical economics. London: Macmillan 1959. ALLENDOERFER, C. B., and C. O. OAKLEY, 1955-1: Principles of mathematics.

New York: Me Graw-Hill 1955. ANTOSIEWICZ, H. A. (Ed.), 1955-1: Proceedings of the Second Symposium in Linear

Programming 1 and 2. National Bureau of Standards and Directorate of Management Analysis. DCS/Comptroller, UASF, Washington, D. C., 1955.

ARROW, K. J., HI51-1: Alternative proof of the substitution theorem for Leontief models in the general cases. In T. C. KOOPMANS (Ed.): Activity analysis of production and allocation. New York: John Wiley & Sons, Inc. 1951.

-, T. E. HARRIS, and J. MARSCHAK, 1951-1: Optimal inventory policy. Econo­metrica 19, 250-272 (1951).

-, L. HURWICZ, and H. UZAWA, 1958-1: Studies in linear and non-linear pro­gramming. Stanford, Cal.: Stanford University Press 1958.

-, L. HURWICZ, and H. UZAWA, 1961-1. Constraint qualifications in maximization problems. Naval Res. Logist. Quart. 8, 175-191 (1961).

-, S. KARLIN, and H. SCARF, 1958-1: Studies in the mathematical theory of inven­tory and production. Stanford, Cal.: Stanford University Press 1958.

-, S. KARLIN, and P. SUPPES (Eds.), 1960-1: Mathematical methods in the social sciences. Proc. of the First Stanford Symposium. Stanford, Cal.: Stanford Univer­sity Press 1960.

BABBAR, M. M., 1955-1: Distribution of solutions of a set of linear equations (with applications to linear programming). J. Amer. Statist. Assoc. riO, 854--869 (1955).

BALAS, E., 1963-1: Solution of large-scale transportation problems through aggregation. Bukarest: Mathemat. Inst., Rumanische Akademie der Wissen­schaften, November 1963.

-, 1964--1: Extension de l' algorithme additif it la programmation en nombres entiens et it la programmation nonlim\aire. C. R. Acad. Sci. (Paris) 2M,5139 (1964).

672 LiteraturverzeiC'hnis

BARANKIN, E. W., and R. DORFMAN, 1958-1: On quadratic programming. Univ. of. Cal. Publ. in Statistics 2, 13. Berkeley, Cal.: University of California Press 1958.

BATCHELOR, JAMES H., 1963-1: Operations research, An annotated bibliography. St. Louis: St. Louis Press 1963.

BAUMOL, WILLIMf J., 1959-1: Economic dynamics - An introduction. 2nd ed. New York: The Macmillan Co. 1959.

-, 1961-1: Economic theory and operations analysis. Englewood Cliffs, N. J.: Prentice-Hall, Inc. 1961.

BEALE, E. M. L., 1954-1: Linear programming by the method of leading variables. Rep. of the Conference on Linear Programming. May 1954 (arranged by Ferranti Ltd., London.)

-, 1955-1: Cycling in the dual simplex algorithm. Naval. Res. Logist. Quart. 2, 269-276 (1955).

-, 1955-2: On minimizing a convex function subject to linear inequalitis. J. Roy. Statist. Soc., Ser. B, 17, 173-184 (1955).

-, 1958-1: A method of solving linear programming problems when some but not all of the variables must take integral values. Princeton, N. J. : Statist. Techniques Res. Group. Princeton University 1958.

-, 1959-1: An algorithm for solving the transportation problem when the shipping cost over each route is convex. Naval Res. Logist. Quart. 6, 43-56 (1959).

-,1959-2: On quadratic programming. Naval Res. Logist. Quart. 6, 227-243 (1959).

BECKENBACH, E. F., 1948-1: Convex functions. Bull. Amer. Math. Soc. 04, 439-460 (1948).

BECKMANN, M. J., 1955-1: Comparative studies in linear programming and the Giffen paradox. Rev. Econ. Studies 23, 232-235 (1955).

-,1959-1: Lineare Planungsrechnung: LudwigshafenjRhein. Fachverlag f. Wirt­schaftstheorie u. Okonometrie 1959.

-, C. B. MCGUIRE, and C. WINSTEN, 1956-1: Studies in the economics of trans­portation. The RAND Corp., Res. Memorandum RM-1488, May 12, 1955. New Haven: Yale Univ. Press 1956.

BELAKREK6, 1964-1: Lehrbuch der linearen Optimierung. Berlin: VEB Deutscher Verlag der Wissenschaften 1964.

BELLMANN, RICHARD, 1954-1: Dynamic programming of continuous processes. Santa Monica, Cal.: The RAND Corp., Rep. R-271, July, 1954.

-,1957-1: Dynamic programming. Princeton: Princeton Univ. Press 1957. -, 1958-1: On a routing problem. Quart. Appl. Math. XVI, 87 -90 (1958). -, and DAVID BLACKWELL, 1951-1: Red dog, blackjack, poker. Sci. American 184,

44-47 (1958). -,1. GLICKSBERG, and O. A. GROSS, 1958-1: Some aspects of the mathematical

theory of control processes. Santa Monica Cal. : The RAND Corp. Rep. R-313 (1958). -, and W. KARUSH, 1962-1: Mathematical programming and the maximum

transform. J. Soc. Indust. Appl. Math. 10, 550-566 (1962). BEREANY, B., 1963-1: On stochastic linear programming. Rev. Math. Pures et

Appliqm\es, 8, 683-697 (1963). BERGE, CLAUDE, 1958-1: Theorie des graphes et ses applications. Paris: Dunod 1958. -, 1962-1: The theory of graphs and its applications. Translated by A. Doig.

New York: John Wiley 1962. BERNHOLTZ, B., 1964-1: A new derivation of the Kuhn-Tucker conditions. Opera­

tions Res. 12, 295-299 (1964). BmKHOFF, GARRETT, 1946-1: Three observations on linear algebra. Rev. univ. naco

Tucuman, Ser. A., 0, 147-151 (1946).

Literaturverzeichnis 673

BIRKHOFF, GARRETT, andSAuNDERsJ.\I[AcLANE, 1953-1: A survey of modern algebra. (Rev.ed.) New York: The Macmillan Co. 1953.

BITTNER, L., und H. JUTTLER, 1962-1: Eine Variante der Simplex.Methode. Unternehmensforsch. 6, 137 (1962).

BLACKWELL, DAVID, and M. A. GIRSHICK, 1954-1: Theory of games and statistical decisions. New York: John Wiley & Sons 1954.

BLANKENSHIP, W. A., 1963-1 : A new version of the Euclidean algorithm. Amer. Math. MtWy. 70 (1963).

BODEWIG, E. ,1959-1: Matrix calculus. Amsterdam: North-Holland Publ. Co. 1959. BOELTER, L.lVI., 1955-1: Some reflections on automation. Symp. on Electronics and

Automatic Production. San Francisco 1955. BOHNENBLUST, H. F., S. KARLIN, and L. S. SHAPLEY, 1950-1: Solutions of discrete,

two-person games. InH. W. KUHN andA. W. TUCKER (Eds.): Contributions to the theory of games. Ann.Math. Study I,N 0.24. Princeton: Princeton Univ. Press1950.

BOLDYREFF, A. W., 1955-1: Determination of the maximal steady state flow of traffic through a railroad network. The RAND Corp. Res. Memorandum RM-1532. JORSA 3, 443-465 (1955).

BOREL, Emile, 1921-1: La theorie dujeu et les equations integrales it noyau syme­trique. C. R. Acad. Sci. 173, 1304-1308 (1921).

-, 1924-1: Sur les jeux ou interviennent Ie hasard et l'habilete des joueurs. Theorie des probabilites. Librairie scientifique. Paris: Hermann 1924.

-, 1927-1: Sur les systemes de formes lineaires a determinant symetrique gauche et la theorie generale du jeu. C. R. Acad. Sci. 184, 52-53 (1927).

-, 1953-1: Translation of three papers by Borel on the theory of games, with commentary. In MAURICE FRl!JCHET; Emile Borel, Initiator of the theory of psychological games and its application. Econometrica 21, 95-127 (1953).

BOULDING, K.E., and W.A.SPIVEY, 1960-1; Linear programming and the theory of the firm. New York: The Macmillan Co. 1960.

BOWMAN, E. H., 1960-1: Assembly-line balancing by linear programming. Opera­tions Res. 8, 385-389 (1960).

-, and R. B. FETTER (Eds.), 1959-1: Analyses of industrial operations. Home­wood, m.: Richard D. Irwin, Inc. 1959.

BRIGGS, F. E. A., 1962-1: A dual labelling method for the Hitchcock problem. Operations Res. 10, 507-517 (1962).

BROWN, G. W., 1951-1: Iterative solution of games by fictitious play. In T. C. KOOPMANS (Ed.):Activity analysis of production and allocation. New York: John Wiley & Sons., Inc. 1951.

-, and T. C. KOOPMANS, 1951-1; Computational suggestions for maximizing a linear function subject to linear inequalities. In T. C. KOOPMANS (Ed.): Activity analysis of production and allocation. New York : John Wiley & Sons, Inc. 1951.

-, and J. VON NEUMANN, 1950-1: Solutions of games by differential equations. The RAND Corp., Paper P-142. Published in H. W. KUHN and A. W. TUCKER (Eds.); Contributions to the theory of games. 1, Ann. Math. Study No. 24. Princeton: Univ. Press 1950.

CARN, A. S., 1948-1: The warehouse problem. Bull. Amer. Math. Soc. 54, 1073 (1954) (Abstract).

CANDLER, W., 1960-1: A short· cut method for the complete solution of game theory and feed-mix problems. Econometrica 28, 618-639 (1960)_

CHARNES, A., 1952-1; Optimality and degeneracy in linear programming_ Econo­metrica 20,160-170 (1952). Operations Res_ Quart. 3, 54 (1952) (Abstract).

-, and W. W. COOPER, 1955-1: Generalizations of the warehousing model. Operations Res. Quart. 6, 131-172 (1955).

Dant,7.1g. Lincarc Prograrnmierung 43

674 Literaturverzei chnis

CHARNES, A., 1957-1: Management models and industrial applications in linear programming. Management Sci. 4, 38-91 (1957).

- -, 1959-1: Chance· constrained programming. Management Sci. 6, 73-79 (1959).

- -,1959-2: Some uses of model prototypes in an operations research study. Reprint No. 35 Carnegie Institute of Technology, Pittsburgh 1959.

- -, 1961-1: Management models and industrial applications of linear pro· gramming. New York: John Wiley & Sons, Inc. 1961.

- -, and A. HENDERSON, 1953-1: An introduction to linear programming. New York: John Wiley & Sons, Inc. 1953.

- -, and B. MELLON, 1952-1: Blending aviation gasolines - A study in pro· gramming interdependent activities in an integrated oil company. Econome· trica 20, 2 (1952). -, 1963-1: Deterministic equivalents for optimizing and satisficing under chance constraints. Operations Res. 11, 18-39 (1963). -, and G. L. THOMPSON, 1962-1: Some properties of redundant constraints and extraneous variables in direct and dual linear programming problems. Opera. tions Res. 10, 711-723 (1962). -, 1964-1: Critical path analysis via chance constrained and stochastic pro· gramming. Operations Res. 12, 460-470 (1964).

-, and H. J. GREENBERG, 1951-1: Plastic collapse and linear programming -Preliminary report. Bull. Amer. Math. Soc. 57, 480 (1951) (Abstract).

-, and C. E. LEMKE, 1954-1: Minimization of non·linear separable convex fune· tionals. Naval Res. Logist. Quart. 1, No.4 (1954).

CHUNG, AN·MIN, 1963-1: Linear Programming. Columbus, Ohio: Charles and Merrill Books 1963.

CHURCHMAN, C. W., R. L.AcKOFF, E. L. ARNOFF, and E. L. ARNOFF, 1960-1: Operations Research, eine Einfiihrung in die Unternehmensforschung. Wien und Miinchen: R. Oldenbourg 1960.

CKENERY, H. B., and P. G. CLARK, 1959-1: Interindustry economics. New York: John Wiley & Sons 1959.

CLARKE, G. B., and 1. G. SIMPSON, 1959-1: A theoretical approach to the profit maximization problems in farm management. J. Agric. Econ.13, 150-164(1959).

CLASEN, R. J., 1963-1: The linear logarithmic programming problem. Santa Monica, Cal.: The RAND Corp.,RM·3707·PR, June 1963.

CLINE, R. E., 1963-1: Representations for the generalized inverse of matrices partitionedasA = [U, V]. In R. GRAVES andP. WOLFE (Ed.): Recent advances in mathematical programming. New York·Toronto·London: McGraw·Hilll963 (Abstract).

CORNFIELD, J., W. D. EVANS, and M. HOFFENBERG, 1947-1: Full employment pattern. Parts I and II. Mth. Labor Rev. 64, 163-190; 420-432 (1947).

COTTLE, R. W., 1963-1: Symmetric dual quadratic programs. Quart. Appl. Math. 21, 237 -243 (1963).

-, 1963-2: A theory of Fritz John in mathematical programming. Santa Monica, Cal.: The RAND Corp. RM·3858.PR, 1963.

-,1963-3: Formal self· duality in nonlinear programming. Notes on operations research I. Operations Res. Center, University of California, Berkeley, California, ORC 63-19, 1963.

-,1964-1: Nonlinear programs with positively boundedjacobians. Thesis. Univer· sity of California, Berkeley, 1964.

-, 1964-2: A fundamental theorem in quadratic programming. J. Soc. Indust. Appl. Math. 12, 663-665 (1964).

Literaturverzeichnis 675

COURANT, R., und D. HILBERT, 1931-1: Methoden der Mathematischen Physik, Berlin: Springer-Verlag, 1931.

CRAMER, H., 1955-1: The elements of probability theory and some of its applica­cations. New York: John Wiley & Sons, Inc. 1955.

CURTES, H. A., 1963-1: Use of decomposition theory in the solution of the state assignment problem of sequential machines .• J. A. C. M., 386 (1963).

DAKIN, R. J., 1964-1: A mixed-integer programming algorithm. Basser Computing Department, School of Physics, The University of Sidney, Technical Report No. 31, September 1964.

DANO, SVEN, 1965-1: Linear programming in industry, 3rd Edition. Wien: Springer-Verlag 1965.

DANTZIG, GEORGE B., 1948-1: Programming in a linear structure. WASHINGTON, D. C.: Comptroller, USAF, 1948.

-, 1949-1: Programming of interdependent activities. II. Mathematical model. In T. C. KOOPMANS (Ed.): Activity analysis of production and allocation. New York: John Wiley & Sons 1951.

-,1951-1: A proof of the equivalence of the programming problem and the game problem. In T. C. KOOPMANS (Ed.): Activity analysis of production and alloca­tion. New York: John Wiley & Sons 1951.

-,1951-2: Application of the simplex method to a transportation problem. In T. C. KOOPMANS (Ed.): Activityanalysis of production and Allocation. New York: John Wiley & Sons 1951.

-, 1951-3: Maximization of a linear function of variables subject to linear inequali­ties. In T. C. KOOPMANS (Ed.): Activity analysis of production and allocation­New York: John Wiley & Sons 1951.

-,1954-1: Notes on linear programming: Part XI, Composite simplex-dual simplex algorithm - I. Santa Monica, Cal.: The RAND Corp. RM-1274, 1954; The RAND Corp. P-516.

-, 1954-2: Notes on linear programming: Part VII - The dual simplex algorithm. Santa Monica, Cal.: The RAND Corp. RM-1270, 1954.

-,1954-3: Notes on linear programming: Parts VIII, IX, X - Upper bounds, secondary constraints, and block triangularity in linear programming. Santa Monica, Cal.: The RAND Corp. RM-1954, 1954. Econometrica 23, 174-183(1955).

-,1955-1: Linear programming under uncertainty. Management Sci. 1, 196-206 (1955).

-,1955-2: Notes on linear programming: Part XIII - Optimal solution of a dynamic Leontief model with substitution. Santa Monica, Cal.: The RAND Corp. RM-1281-1, 1955,Econometrica 23, 295-302 (1955).

-, 1956-1: Constructive proof of the min-max theorem. Pacific J. Math. 6, 25-33 (1956).

-,1956-2: Recent advances in linear programming. Management Sci. 2, 131-144 (1956).

-, 1957-1: Thoughts on linear programming and automation. SantaMonica, Cal.: The RAND Corp. P-824, 1956. Management Sci. 3, 131-139 (1957).

-,1957-2: Discrete variable extremum problems. Operations Res. 5, 266-277 (1957).

-, 1957-3: On the status of multistage linear programs. Santa Monica Cal.: The RAND Corp. P-1028, 1957. Proc. Intern. Statist. Inst., Stockholm, 1957; Management Sci. 6,53-72 (1959).

-,1958-1: On integer and partial integer linear programming problems. Santa Monica, Cal.: The RAND Corp. P-14lO, 1958.

43*

676 Literaturverzeichnis

DANTZIG, GEORGE B., 1958-2: Solving two-move games with perfect information. Santa Monica, Cal.: The RAND Corp. P-1459.1958.

-, 1959-1: Inductive proof of the simplex method. Santa Monica, Cal. : The RAND Corp. P-1851, 1959. IBM J. Res. Develop. 4,505-506 (1960).

-,1960-1: On the shortest route through a network. Management Sci. 6,187-190 (1960).

-, 1960-2: On the significance of solving linear programming problems with some integer variables. Econometrica 28,30-44 (1960).

-,1960-3: General convex objective forms. In K. J. ARROW, S. KARLIN, and P. SUPPES (Eds.): Mathematical methods in the social science. Stanford: Stanford Univ. Press. 1960.

-,1960-4: A machine-job scheduling model. Management Sci. 6, 191-196 (1960). -, 1963-1: Compact basis triangularization for the simplex method. In R GRAVES

und P. WOLFE (Ed.): Recent advances in mathematical programming. New York-Toronto-London: McGraw-Hill 1963.

-, 1964-1: Linear control processes and mathematical programming. Operations Res. Center, University of California, Berkeley, ORC 64-31, December 1964. und R W. COTTLE, 1963-1: Positive (semi-)definite matrices and mathematical programming. Operations Res. Center, University of California, Berkeley, ORC 63-18, 1963.

-, E. EISENBERG, and R. W. COTTLE, 1965-1: Symmetric dual nonlinear pro­grams. Pacific J. Math. (in press.).

-, LESTER R. FORD, JR., and DELBERT R. FULKERSON, 1956-1: A primal-dual algorithm for linear programs. In H. W. KUHN and A. W. TUCKER (Eds.): Linear inequalities and related systems. Ann. Math. Study No. 38. Princeton: Prince­ton Univ. Press 1956.

-, and DELBERT R. FULKERSON, 1954-1: Minimizing the number of tankers to meet a fixed schedule. Naval Res. Logist. Quart. 1, 217 -222 (1954).

- -,1956-1: On the max-flow min-cut theorem of networks. In H. W. KUHN and A. W. TUCKER (Eds.): Linear inequalities and related systems. Ann. Math. Study No. 38. Princeton: Princeton Univ. Press 1956.

- -, and SELMER M. JOHNSON, 1954-1: Solution of a large-scale traveling -salesman problem. JORSA 2, 393-410 (1954).

- -, 1959-1: On a linear programming combinatorial approach to the traveling­salesman problem. Operations Res. 7,58-66 (1959).

-, Roy HARVEY, and R. McKNIGHT, 1964-1: Updating the product form of the inverse for the reversed simplex method. Operations Res. Center, University of California, Berkeley, ORC 64-33, 1964.

-, and D. L. JOHNSON, 1964-1: Maximum payloads per unit time delivered through an air network. Operations Res. 12, 230-236 (1964).

-, and ALBERT MADANSKY, 1960-1: On the solution of twostage linear programs under uncertainty. Santa Monica, Cal.: The RAND Corp., P-2039, 1960; ebenfalls in J. NEYMAN (Ed.): Proceedings, Fourth Berkeley Symposium on mathematical Statictics and Probability. 1, 165-176 (1961).

-, and WILLIAM ORCHARD-HAYS, 1953-1: Notes on linear programming: Part V -Alternate algorithm for the revised simplex method using product form for the inverse. Santa Monica, Cal.: The RAND Corp. RM-1268, 1953.

-, and ALEX ORDEN, 1953-1: Notes on linear programming: Part II - Duality theorems. Santa Monica Cal.: The RAND Corp. RM-1265, 1953.

- -. and PHILIP WOLFE, 1954-1: Notes on linear programming: Part I - The generalized simplex method for minimizing a linear form under linear inequality restraints. The RAND Corp. RM-1264, 1954. Pacific J. Math. 0, 183-195 (1955).

Literaturverzeichnis 677

DANTZIG, GEORGE B., and J. H. RAMSER, 1959-1: The truck dispatching problem. Management Sci. 6, SO-91 (1959).

-, andR. M. VAN SLYKE, 1964-1: Generalized upper bounded techniques for linear programming I, II. Operations Res. Center, University of California, Berkeley, ORC 64-17, 1964 und ORC 64-lS, 1965.

-, and A. WALD, 1951-1: On the fundamental lemma of Neyman and Pearson. Ann. Math. Statist. 22, S7 -93 (1951).

-, and PHILIP WOLFE, 1960-1: Decomposition principle for linear programs. Operations Res. 8, 101-111 (1960).

- -, 1961-1: The decomposition algorithm for linear programming. Econometrica, 29, 4 (1961).

DEBREU, G., 1963-1: Non.negative solutions of linear inequalities. Center for Research in Management Science, University of California, Berkeley, Technical Report Nr. 10, 1963.

DENNIS, J. B., 1959-1: Mathematical programming and electrical networks. New York: John Wiley & Sons 1959.

DILWORTH, R P., 1950-1: A decomposition theorem for partially ordered sets. Ann. Math. 01, 161-166 (1950).

DINES, L. L., and N. H. MyCoY, 1933-1: On linear inequalities. Trans. Roy. Soc. Can., Sect. III, 37 -70 (1933).

DINKELBAOH, W., und H. HAX, 1962-1: Die Anwendung der gemischt ganzzahligen Programmierung auf betriebswirtschaftliche Entscheidungsprobleme. Z. Han· delsw. Forsch. 14, 179-195 (1962).

-, und F. STEFFENS, 1961-1: Gemischt ganzzahlige lineare Programme zur LOsung gewisser Entscheidungsprobleme. Unternehmensforsch. 0,3 (1961).

DOIG, A. G., and M. H. BELZ, 1956-1: Report on trim problems for May 1956. Dept. of Statistics, Univ. Melbourne, 1956.

-, and A. H. LAND, 1960-1: An automatic method of solving discrete programming problems. Econometrica 28, 497 -520 (1960).

DORFMAN, R, 1951-1: Application of linear programming to the theory of the firm. Berkeley, Cal.: Univ-. of Cal. Press 1951.

-,1951-2: Application of the simplex method to a game theory problem. In T. C. KOOPMANS (Ed.): Activity analysis of production and allocation. New York: John Wiley & Sons 1951.

-, P. A. SAMUELSON, and R M. SOLOW, 1955-1: Linear programming and eco· nomic analysis. New York: McGraw·HillI95S.

DORN, W. S., 1961-1: On Lagrange multipliers and inequalities. Operations Res. 9, 95-104 (1961).

-,1963-1: Nonlinear programming. A survey. Management Sci. 9, 171-20S (1963).

-, and H. J. GREENBERG, 1955-1: Linear programming and plastic limit analysis of structures. Technical Rep. No.7, Carnegie Inst. of Techn. Pittsburgh 1955.

DRESHER, MELVIN, 1961-1: Strategische Spiele (Theorie und Praxis). Deutsche Bearbeitung von H. P. KUNZI. Ziirich: Verlag Industrielle Organisation 1961.

-, S. SHAPLEY, and A. W. TUOKER (Ed.), 1964-1: Advances in game theory. Princeton: Princeton Univ. Press 1964.

-, A. W. TUOKER, and PHILIP WOLFE (Eds.), 1957-1: Contributions to the theory of games. Ann. Math. Study, m, No. 39. Princeton: Princeton Univ. Press. 1957.

DUFFIN, R J., 1956-1: Infinite programs. In H. W. KUHN, and A. W. TUOKER (Eds.): Linear inequalities and related systems. Ann. Math. Study No. 3S. Princeton: Princeton Univ. Press 1956.

678 Literaturverzeichnis

DUFFIN, R. J., 1961-1: The extremal length of a network. Office of Tech. Services, Doc. No. AD.253665, 1961.

-,1962-1: Dual programs and minimum costs. J. Soc. Indust. Appl. Math. 10, 119-123 (1962).

DVORETZKY, A., J. KIEFER, and J. WOLFOWITZ, 1952-l. The inventory problem: I. Case of known distributions of demand; II. Case of unknown distributions of demand. Econometrica 20,187-222; 450-466 (1952).

DWYER, PAUL S., 1955-1: The solution of the Hitchcock transportation problem with the method of reduced matrices. Eng. Res. Inst. Rep. Univ. of Michigan. Ann Arbor 1955.

DZIELINSKI, B. P., and R. E. GOMORY, 1963-1: Lot size programming and the decomposition principle. Econometrica 31, 595 (1963) (Abstract).

EASTERFIELD, THOMAS E., 1946-1: A combinatorial algorithm. J. London. Math. Soc. 21, 219-226 (1946).

EDMONDS, J., 1962-1: Covers and packings in a family of sets. Bull. Amer. Math. Soc. 68, 494-499 (1962)

EDMONDSON, J. H., 1951-1: Proof ofthe existence theorem of an epsilon transforma­tion. Lasung einer Ubungsaufgabe zu einer Vorlesung von GEORGE B. DANTZIG (Exemplare erhaltlich von GEORGE B. DANTZIG). March 28, 1951.

EFROYMSON, M. A., 1962-1: Some new algorithms for linear programming. Presented at Symposium on Mathematical Programming, University of Chicago, June 18-22, 1962.

EGERVARY, E., 1931-1: Matrixok Kombinatorius Tulajfonsagair61. Matematikai es Fizikai Lapok 38,16-28 (1931). Ubersetzung von H. W. KUHN: On combina­torial properties of matrices. Logistics Papers 11, Appendix to Quarterly Progress Report No. 21, 1954,

EGGLESTON, H. G., 1958-1: Convexity. Cambridge Tracts in Mathematics and Mathematical Physics, No. 47. Cambridge: Cambridge Univ. Press 1958.

EISEMANN, KURT, 1957-1: The trim problem. Management Sci. 3, 279-284 (1957). -, 1964-1: The primal-dual method for bounded variables. Operations Res. 12,

110-121 (1964). -, 1964-2: The generalized stepping stone method for the machine loading problem.

Management Sci. 11, 1 (1964). -, and J. R. LOURIE, 1959-1: The machine loading problem. IBM 704 Program.

New York: IBM Applications Library 1959. EISENBERG, E., 1961-1: Duality in homogeneous programming. Proc. Amer. Math.

Soc. 12, 783-787 (1961). EL AGIZY, M., 1964-1: Programming under uncertainty with discrete d. f.

Operation Res. Center, University of California, Berkeley, ORC 64-13, 1964. EL-MAGHRABY, S. E., 1959-1: An approach to linear programming under uncer­

tainty. Oper. Res. 7,208-216 (1959). -, 1960-1: Allocation under uncertainty when the demand has continous d. f.

Management Sci. 6, 270 (1960). -,1963-1: An algorithm for the solution of the 0-1 problem of integer linear

programming. Yale University 1963. EVERETT, H., 1963-1: Generalized Lagrange multiplier method for solving problems

of optimum allocation of resources. Operations Res. 11, 399-417 (1963).

FABIAN, TIBOR, 1954-1: Process type analysis of the iron and steel industry. Part IV: Programming open hearth steel production. Discussion Paper No. 46, Management Sci. Res. Project. Univ. of Calif., Los Angeles 1954.

Literaturverzeiclmis 679

FABIAN, TIBOR, 1955-1: Process analysis of the iron and steel industry: a model. Res. Rep. No. 47. Management Sci. Res. Project. Univ. of. Calif., 1955. Econometrica 23,347-348 (1955) (Abstract).

-, 1958-1: A linear programming model of integrated iron and steel production. Management Sci. 4, 415-449 (1958).

FAN, K., 1953-1: Minimax theorems. Proc. Nat. Acad. Sci. U. S. A. 39, 42-47 (1953). FARKAS, J., 1902-1: "Ober die Theorie der einfachen Ungleichungen. J. reine angew.

Math. 124, 1-24 (1902). FELLER, WILLIAM, 1957-1: An introduction to probability theory and its applica­

tions. 2nd ed., vol. 1. New York: John Wiley and Sons 1957. FENCHEL, W., 1953-1: Convex cones, sets, and functions. In D. W. BLACKETT:

Lecture Notes. Princeton: Princeton University 1953. FERGUSON, ALLEN R., and G. B. DANTZIG, 1954-1: Notes on linear programming:

Part XVI. The problem of routing aircraft - a mathematical solution. Aeronaut. Eng. Rev. 14, 51-55 (1955).

-, 1956-1: The allocation of aircraft to routes - an example of linear programming under uncertain demand. Management Sci. 3,45-73 (1956).

FIACCO, A. V., N. SMITH, and D. BLACKWELL, 1960-1: A more general method for nonlinear Programming. Presented to the 17th National Meeting of O. R. S. A., May 20, 1960.

FISHER, WALTER D., and LEONARD W. SCHRUBEN, 1953-1: Linear programming applied to feed-mixing under different price conditions. J. Farm Econ. XXXV, 471-483 (1953).

FISZ, M., 1958-1: Wahrscheinlichkeitsrechnung und mathematische Statistik. Berlin: VEB Deutscher Verlag der Wissenschaften 1958.

FLOOD, MERRILL M., 1953-1: On the Hitchcock distribution problem. Pacific. J. Math. 3, 369-386 (1953).

-, 1956-1: The traveling salesman problem. In J. F. MCCLOSKEY and J. M. COPPIN­GER (Eds.): Operations research for management, Vol. II. Baltimore: Johns Hopkins Press 1956; Operations Res. 4, 61-75 (1956).

-,1960-1: An alternative proof of a theorem of Konig as an algorithm for the Hitchcock distribution problem. In R. BELLMAN and MARSHALL HALL, JR. (Eds.): Proceedings of Symposia in Applied Mathematics, Vol. X. Combinatorial analysis. Providence: Amer. Math. Soc. 1960.

-,1962-1: A symposium on game theory. Behavioral Sci. 7, 1-102 (1962). FOERSTNER, KARL, und RUDOLF HENN, 1956-1: Die Anwendung okonomischer

Verfahren in der Unternehmensplanung. Z. Betriebswirtsch.12, 700 -71 0 (1956). -,1957-1: Dynamische Produktionstheorie und lineare Programmierung. Meisen­

heim am GIan, 1957. FORD, LESTER R., JR., and DELBERT R. FULKERSON, 1954-1: Maximal flow through

a network. Canad. J. Math. 8, 399-404 (1956). -,1955-1: Notes on linear programming: Part XXIX. A simple algorithm for

finding maximal network flows and an application to the Hitchcock problem. The RAND Corp. Res. Memo. RM-1604, 1955; The RAND Corp. P-743, 1955.

-, 1956-1 : Notes on linear programming: Part XXXII. Solving the transportation problem. The RAND Corp. Res. Memo. RM-1736, 1956. Management Sci. 3, 24-32 (1956).

-,1956-2: Dynamic network flow. The RAND Corp. P-967, 1956. -,1957-1: A primal-dual algorithm for the capacitated Hitchcock problem. Naval.

Res. Logist. Quart. 4, 47-54 (1957). -, 1958-1: Constructing maximal dynamic flows from static flows. Operations Res.

6,419-433 (1958).

680 Literaturverzei chnis

FORD, LESTER R., JR., 1958-2: Suggested computation for maximal multi­commodity network flows. Management Sci. 5, 97-101 (1958).

-, 1960-1: Flows in networks. Princeton: Princeton Univ. Press 1962. FORSYTHE, G. E., 1953-1: Solving linear algebraic equations can be interesting.

Bull. Amer.Math. Soc. 59, 299-329 (1953). -,1955-1: Computing constrained minima with Lagrange multipliers. J. Soc.

Indust. Appl.Math. 3, 173-178 (1955). FOULKES, J., 1955-1: Linear programming and structural design. In H. A. ANTO­

SIEWICZ (Ed.): Proceedings of the Second Symposium in Linear Programming, Vol. 2. Nat. Bur. of Stand., Washington 1955.

FOURIER, JEAN BAPTISTE JOSEPH, 1826-1: SoluLion d'une question particuliere du calcul des inegalites, 1826, und Ausziige aus Histoire de l'Academie, 1823, 1824. Oeuvres II, 317-328.

Fox, L., 1954-1: Practical solution of linear equations and inversion of matrices. In OLGA TAUSSKY (Ed.): Contributions to the solution of systems of linear equa­tions and the determination of eigenvalues. Nat. Bur. of Stand. Appl. Math. Ser. 39, 1-54 (1954).

FRANK, M., and P. WOLFE, 1956-1: An algorithm for quadratic programming. Naval Res. Logist. Quart. 3, 95-110 (1956).

FREDRICK, F. P., 1964-1: Experience with the staged-pivot product form algo­rithm. Houston: Booner and Morre Associates, Inc., 1964.

FREIMER, M., and S. DREYFUS, 1961-1: A new approach to the duality theory of mathematical programming. lVIIT Lincoln Laboratory, Lexington, Mass., Report 55G-0036, May 1961.

FREUND, R., 1956-1: The introduction of risk into a programming model. Econo­metrica 24, 253-263 (1956).

FRISCH RAGNAR, 1954-1: Principles of linear programming with particular refe­rence to the double gradient form of the logarithmic potential network. Oslo: Univ. Inst. of Economics 1954.

-,1957-1: Linear dependencies and a mechanized form of the multiplex method for linear programming. Oslo: Univ. IllSt-. of Economics 1957.

-, 1962-1: Tentative formulation of the multiplex method for the case of a large number of basic variables. Institute of Economics, University of Oslo, 1962.

FULKERSON, D. R., 1956-1: Note on Dilworth's decomposition theorem for partially ordered sets. Proc. Amer. Math. Soc. 7,701-702 (1956).

-, 1959-1: A network flow feasibility theorem and combinatorial applications. Canad. J. Math. 11, 440-451 (1959).

-, 1959-2: Increasing the capacity of a network: The parametric budget problem. Management Sci. 5, 472-483 (1959).

-, 1959-3: An out-of-kilter method for minimal cost flow problems. The RAND Corp. Paper P 1825, 1959. J. Soc. Indust. Appl.Math. 9,18-27 (1961).

-,1960-1: Zero-one matrices with zero trace. Pacific J.Math. 10, 831-836 (1960). -, 1961-1: A network flow computation for project cost curves. Management Sci. 7,

167 -178 (1961). -,1964-1: Expected critical path lengths in PERT networks. The RAND Corp.

Memorandum, RM-437-PR, 1964. -, and G. B. DANTZIG, 1955-1: Computations of maximal flows in networks. Naval

Res. Logist. Quart. 2, 277 -283 (1955). -, and P. WOLFE, 1962-1: An algorithm for scaling matrices. Notes on linear

programming and extensions. Part 28. The RAND Corp. RM-2956-PR, February 1962.

Literaturvel'zeichnis 58]

GADDUM, J. W., 1952-1: A theorem on convex cones with applications to linear inequalities. Proc. ArneI'. Math. Soc. 3, 957 -960 (1952).

-, A. J. HOFFMAN, and D. SOKOLOWSKY, 1954-1: On the solution of the caterer problem. Naval. Res. Logist. Quart. 1, 223-229 (1954).

GAINEN, LEON, 1955-1: Linear programming in bid evaluations. In H. A. ANTO­SIEWICZ (Ed.): Proceedings of the Second Symposium in Linear Programming, Vol. 2. Nat. Bureau of. Standards, Washington, D. 0.1955.

GALE, DAVID, 1951-1: Convex polyhedral cones and linear inequalities. In T. C. KOOPMANS(Ed.): Activity analysis of production and allocation. New York: John Wiley and Sons 1951.

-,1956-1: Neighboring vertices on a convex polyhedron. In H. W. KUHN and A. W. TUCKER (Eds.): Linear inequalities and related systems. Princeton: Princeton Univ. Press 1956.

-, 1956-2: The basic theorems of real linear equations, inequalities, linear pro-gramming and game theory. Naval. Res. Logist. Quart. 3, 193-200 (1956).

-,1957-1: A theorem on flows in networks. Pacific J. Math. 7, 1073-1082 (1957). -, 1959-1: Transient flows in networks. Michigan Math. J. 6, 59-63 (1959). -,1960-1: The theory of linear economic models. New York: McGraw-Hill 1960. -, 1962-1: On the number of faces of a convex polytope. Department of Mathe-

matics, Brown University, Technical Report Nr. 1, 1962. -, H. W. KUHN, andA. W. TUCKER, 1950-1: On symmetric games. InH. W. KUHN

and A. W. TUCKER (Eds.): Contributions to the theory of games, Vol. 1. Prince­ton: Princeton Univ. Press 1950.

- - -,1950-2: Reductions of game matrices. In H. W. KUHN, and A. W. TUCKER (Eds.): Contributions to the theory of games, Vol. 1. Princeton: Princeton Univ. Press 1950.

- - -,1951-1: Linear programming and the theory of games. In T. C. KOOPMANS (Ed.): Activity analysis of production and allocation. New York: John Wiley and Sons 1951.

GARVIN, WALTER, 1960-1: Introduction to linear programming. New York: McGraw-Hill 1960.

-, H. W. CRANDALL, J. B. JOHN, and R. A. SPELLMAN, 1957-1: Applications of linear programming in the oil industry. Management Sci. 3, 407 -430 (1957).

GASS, SAUL, 1964-1: Linear programming: Methods and applications. New York­Toronto-London: McGraw-Hill 1964.

-, and T. L. SAATY, 1955-1: The computational algorithm for the parametric objective function. Naval Res. Logist. Quart. 2, 39-45 (1955).

GASSNER, BETTY J., 1964-1: Cycling in the transportation problem. Naval Res. Logistics Quart. 11, 1 (1964).

GAUSS, KARL FRIEDRICH, 1826-1: Theoria combinationis observationum erroribus minimis obnoxiae. Supplementum, Bd. 4. Werke. Gottingen 1826.

GAUTillER, J. M., 1961-1: Le principe de decomposition de Dantzig et Wolfe. Groupe de Travail, Mathematiques de Programmes Economiques, 1961.

GEARY, R. C., and M. D. MCCARTHY, 1964-1: Elements of linear programming, with economic applications. London: Charles Griffin and Company Ltd. 1964.

GEISSLER, S., 1960-1: Bestimmung einer ersten BasislOsung beim linearen Pro­grammieren. Unternehmensforschung 4, 80-88 (1960).

GERSTENHABER, MURRAY, 1951-1: Theory of convex polyhedral cones. In T. C. KOOPMANS (Ed.): Activity analysis of production and allocation. New York: John Wiley and Sons 1951.

-, 1958-1: A solution method for the transportation problem. J. Soc. Indust. Appl. Math. 6, 312-316 (1958).

682 Literaturverzeiehnis

GIESEN, G., 1961-1: Die kombinierte Simplex-Methode. Unternehmensforschung 5, 132 (1961).

GILMORE, P. C., 1963-1: Optimal and sub-optimal algorithms for the quadratic assignment problem. J. Soc. Indust. Appl. Math. 10, 305-313 (1963).

-, and R. E. GOMORY, 1961-1: A linear programming approach to the cutting stock problem. 1. B. M. Watson Research Center, Research Report, RC-408, March 1961; Operations Research 9,849-859 (1961) und 11, 863-887 (1963).

- -, 1964-1: Sequencing, a one state variable machine: A solvable case of the travelling salesman problem. 1. B. M. Watson Research Center, Research Paper, RC-lI03, January 1964.

GLICKSMAN, M. A., 1963-1: Linear programming and theory of games. New York: John Wiley 1963.

GLOVER, F., 1964-2: Generalized cuts in diophantine programming. Graduate School of Industrial Administration, Carnegie Institute of Technology, October 1964.

GNEDENKO, B. V., 1957-1: Lehrbuch der Wahrscheinlichkeitsrechnung. Berlin: Akademie-Verlag 1957.

GOLDMAN, A. J., 1956-1: Resolution and separation theorems for polyhedral convex sets. In H. W.KUHN and A. W. TUCKER (Eds.): Linear inequalities and related systems. Princeton: Princeton Univ. Press 1956.

-, A. J., and A. W. TUCKER, 1956-1: Polyhedral convex cones. In H. W. KUHN und A. VV. TUCKER: Linear inequalities and related systems. Princeton: Prince­ton Univ. Press 1956.

-,1956-2: Theory of linear programming. In H. W. KUHN und A. W. TUCKER: Linear inequalities and related Systems. Princeton: Princeton Univ. Press 1956.

GOLDSTEIN, A. A., and B. R. KRIPKE, 1964-1: Mathematical programming by minimizing differentiable functions. Numerische Math. 6, 47 -48 (1964).

GOLDSTEIN, LEON, 1952-1: Problem of contract awards. In ALEX ORDEN and LEON GOLDSTEIN (Eds.): Symposium on Linear Inequalities and Programming_ Washington, D. C. 1952.

GOL'SHTEYN, E. G., and D. B. YUDIN, 1961-1: Concerning one class of problems in planning of the national economy. English Translation Office of Technical Service, Doc. No. JPRS: 11175.

GOllIORY, R. E., 1958-1: Outline of an algorithm for integer solutions to linear programs. Bull. Amer. Math. Soc. 64, 275-278 (1958).

-, 1958-2: An algorithm for integer solutions to linear programs. Princeton-IBM Math. Res. Project, Techn. Rep. No.1, 1958.

-,1958-3: An algorithm for the mixed integer problem. Amer. Math. Soc. Notices 6,52 (1959).

-,1960-1: AIl-integer programming algorithm. 1.B.M. Research Center, Yorktown Heights, New York, RC 189 (1960).

-, 1965-1: On the relation between integer and noninteger solutions to linear programs. Proc. Nat. Acad. Sci. U.S.A., 53, 2, 260-265 (1965).

-, and W. J. BANMOL, 1960-1: Integer programming and pricing. Econometrica 28,3(1960).

-, and T. C. Hu, 1960-1: Multi-terminal network flows. IBM Res. Rep. RC-318, 30 (1960).

- -, 1960-2: An application of generalized linear programming to network flows. IBM Res. Rep. 50 (1960).

- -,1964-1: Synthesis of a communication network. J. Soc. Indust. Appl. Math. 12,2(1964).

Literaturverzeichnis 683

GOOD, R. A., 1959-1: Systems oflinear relations. J. Soc. Indust. App!. Math. 7,1-31 (1959).

GORDAN, P., 1873-1: trber die Auflosung linearer GIeichungen mit reellen Coeffi­cienten. Math. Ann. 6, 23-28 (1873).

GRAVES, ROBERT L., 1963-1: Parametric linear programming. In R. GRAVES und P. WOLFE (Eds.) : Recent advances in linear programming. New Y ork-Toronto­London: McGraw-Hill 1963.

-, and PHILIP WOLFE (Eds.): Recent advances in mathematical programming. New York: McGraw-Hill 1963.

GREENE, J. H., K. CHATTO, C. R. HICKS, and C. B. Cox, 1959-1: Linear program­ming in the packing industry. J. Indust. Eng. X, 364-372 (1959).

GROSS, 0., 1959-1: The bottleneck assignment problem. The RAND Corp. Paper P-1630. The RAND Symp. on Math. Programming 1959.

-,1962-1: A linear program of Prager's. Notes on linear programming and exten­sions. Part 60. The RAND Corp. RM-2993-PR (1962).

GULICHER, H., 1960-1: Die Anwendung des Linear Programming auf ein Transport­problem. Operations Res. (AKOR), 5, 104 (1960).

-,1962-1: Linear Programming zur Losungvon Verladeproblemen. APF, 1, 16-17 (1962).

GUNTHER, PAUL, 1955-1: Use of linear programming in capital budgeting. JORSA 3,219-224 (1955).

HADLEY, G., 1961-1: Linear alg!jbra. Reading, Mass.: Addison-Wesley Pub!. Co., Inc. 1961.

-,1961-2: Linear programming. Reading, Mass.: Addison-Wesley Pub!. Co. Inc. 1961.

-, 1964--1: Nonlinear and dynamic programming. Reading, Mass.: Addison-Wesley Publishing Company, Inc. (1964).

-, and M. A. SIMONNARD, 1959-1: A simplified two-phases technique for the simplex method. Naval Res. Logist. Quart. 6, 221-226 (1959).

HAKIMI, S. L.: On simultaneous flows in a communication network. Office of Technical Services Doc. Nr. AD-267 090 (1961).

HALDI, J., 1962-1: Solving fixed charge problems by means of integer programming. Graduate School of Business, Stanford University, May 1962.

HALMOS, P. R., and HERBERT E. VAUGHAN, 1950-1: The marriage problem. Amer. J. Math. 72,214-215 (1950).

HANSON, M. A., 1964--1: Duality and self-duality in mathematical programming. J. Soc. Indust. App!. Math., 12, 446-449 (1964).

HARTLEY, H. 0., 1959-1: Nonlinear programming by the simplex method. Econo­metrica 29, 223-237 (1959).

-, and R. R. HOCKING, 1963-1: Convex programming by tangential approxima­tion. Management Sci. 9, 600-612 (1963).

-, and L. D. LOFTSGARD, 1958-1: Linear programming with variable restraints. J. Sci. Iowa State College 33, 161-172 (1958).

HEADY, E. 0., and \V. CANDLER, 1958-1: Linear programming methods. Ames: Iowa State College Press 1958.

HEALY, W. C., JR., 1964-1: Multiple choice programming. Operations Res. 12, 122-138 (1964).

HEINHOLD, J., und K. KUNTZE, 1964--1: Ein Verfahren derlinearen Optimierung. Z. Wahrscheinlichkeitstheorie 2, 255-272 (1964).

684 Literaturverzeiclmis

HELLER, 1., 1955-1: On the traveling salesman problem. In H. A. ANTOSIEWICZ (Ed.): Proc. of the Second Symposium in Linear Programming 2, 643-665 (1955).

-, 1957-1: Constraint matrices of transportation type problems. Naval Res. Logist. Quart. 4, 73-76 (1957).

-, 1964-1: On linear programs equivalent to the transportation problem. J. Soc. Indust. Appl. Math. 12, 31-42 (1964).

-, and C. B. TOMPKINS, 1956-1: An extension of a theorem of Dantzig's paper 14. In H. W. KUHN and A. W. TUCKER (Eds.): Linear inequalities and related systems. Princeton: Princeton Univ. Press 1956.

HENDERSON, A., and R. SCHLAIFER, 1954-1: Mathematical programming. Harvard Business Rev. 32, 73-100 (1954).

HENDERSON, J. lVI., 1955-1: A short·run model for the coal industry. Rev. Econ. Statist. 37, 336-346 (1955).

HERMANN, C. C., and J. F. MAGEE, 1953-1: Operations research for management. Harvard Business Rev. 31, 110-112 (1953).

HEYMANN, J., 1951-1: Plastic design of beams and plane frames for minimum material consumption. Quart. Appl. Math. 8, 373-381 (1951).

HICKS, J. R., 1960-1: Linear theory. Econ. J. (London) LXX, 671-709 (1960). HILDRETH, C. G., 1955-1: Economic implications of some cotton fertilizer experi.

ments. Econometrica 23, 88-98 (1955). -, and STANLEY REITER, 1951-1: On the choice of crop rotation plan. In T. C.

KooPMANs (Ed.): Activity analysis of production and allocation. New York: John Wiley and Sons, Inc. 1951.

HILLS, R., 1961-1: An electrical analogue for solving transportation problems. Internat. J. Production Res. 1, 56-62 (1961).

HIRSCH, WARREN M., and GEORGE B. DANTZIG, 1954-1: The fixed charge problem. The RAND Corp. Paper P·648, 1954.

-, and A. J. HOFFMAN, 1961-1: Extreme varieties, concave functions and the fixed charge problem. Comm. Pure Appl. Math. 14, 355-369 (1961).

HITCHCOCK, FRANK L., 1941-1: The distribution of a product from several sources to numerous localities. J. Math. Phys. 20, 224-230 (1941).

HOFFMAN, A. J., 1953-1: Cycling in the simplex algorithm. Nat. Bur. Stand. Rep. N. 2974, 1953.

-,1956-1: Systems of distinct representatives and linear programming. Amer. Math. lVIthly 63, 455-460 (1956).

-,1960-1: Some recent applications of the theory oflinear inequalities to extremal combinatorial analysis. In R. BELLMAN and MARSHALL HALL, JR. (Eds.): Proc. of Symposia in Applied Math. X. Combinatorial Analysis. Amer. Math. Soc. 113-127 (1960).

-,1963-1: On abstract dual linear programs. 1.B.M. Watson Research Center, Research Note NC·214, March 1963.

-, and R. E. GOMORY, 1962-1: Finding optimum combinations. Int. Science and Tech. 26-33 (1962).

-, and J. G. KRUSKAL, 1956-1: Integral boundary points of convex polyhedra. In H. W. KUHN and A. W. TUCKER (Eds.): Linear inequalities and related sy· stems. Princeton: Princeton Univ. Press 1956.

-, and H. W. KUHN, 1956-1: On systems of distinct representatives. Amer. Math. Mthly 63, 455-460 (1956).

-, M. MANNOS, D. SOKOLOWSKY, and N. WIEGMANN, 1953-1: Computational experience in solving linear programs. J. Soc. Indust. Appl. Math. 1, 17 -33 (1953).

Literaturverzeichnis 685

HOFFMAN, A. J., and H. M. MARKOWITZ, 1963-1: A note on the shortest path, assignment, and transportation problems. Naval Res. Logistics Quart. 10, 4 (1963).

HOUTHAKKER, H. S., 1955-1: On the numerical solution of the transportation problem. JORSA 3, 210-214 (1955).

-,1959-1: The capacity method of quadratic programming. In P. WOLFE(Ed.): The RAND symposium on mathematical programming. The RAND Corp. Rep. R-351, 1959.

Hu, T. C., and W. PRAGER, 1958-1: Network analysis of production smoothing. Providence: Brown Univ. 1958.

-, 1961-1: Parallel sequencing and assembly line problems. Operations Res. 9, 841-848 (1961).

-, 1961-2: The maximum capacity route problem. Operations Res. 9, 898-900 (1961).

-,1963-1: Multi-commodity network flow. LB.M. Watson Research Center, Research Report RC-865, 1963; Operations Res. 11, 344-360 (1963).

-, 1964--1: On the feasibility of simultaneous flows in networks. Operations Res. 12,359-360 (1964).

HUARD, P., 1963-1: Dual programs. In R. GRAVESundP. WOLFE (Eds.): Recent advances in mathematical programming. New York-Toronto-London: McGraw-Hill 1963.

-, 1964--1: Resolution de programmes mathematiques a contraintes nonlineaires par la methode de centre. ElectriciM de France, Direction des Etudes et Recher­ches (1964). (Ed.), 1964--2: MatMmatiques des programmes economiques. Collection des Monographies de Recherche Operationelle, Tome 1. AFIRO. Paris: Dunod 1964.

IRI, M., 1960-1: A new method of solving transportation network problems. J. Operations Res. Soc. Japan 3, 27-87 (1960).

IVANESCU, P. L., 1963-1: Some network flow problems solved with pseudo­boolean programming. Mathematisches Institut, Rumiinische Akademie der Wissenschaften, Bukarest 1963.

-, 1964--1: Programmation polynomiale en nombresentiers. C. R. Acad. Sci. (Paris), 21)8,424-427 (1964).

JACKSON, J. R., 1957-1: Simulation research on job shop production. Naval Res. Logist. Quart. 1, 287 (1957).

JACOBS, W. W., 1954-1: The caterer problem. Naval Res. Logist. Quart. 1, 154-165 (1954).

-,1955-1: Military applications of linear programming. In H. A. ANTOSIEWICZ (Ed.): Proc. of the Second Symposium in Linear Programming, 2. Nat. Bur. of Standards, USAF, Washington, D. C. 1955.

JAEGER, ARNO, 1964--1: Introduction to analytic geometry and linear algebra. New York: Holt, Rinehart, and Winston 1964.

-, and BERTRAM MOND, 1964--1: On direct sums and tensor products of linear programs. Z. Wahrscheinlichkeitstheorie, 3, 19-31 (1964).

-, und KLAUS WENKE, 1966-1: Lineare Wirtschaftsalgebra. Stuttgart: Teubner Verlagsgesellschaft 1966 (in Vorbereitung).

JEWELL, W. S., 1957-1 : Warehousing and distribution of a seasonal product. Naval. Res. Logist. Quart. 4, 29-34 (1957).

686 Literaturverzeichnis

JEWELL, W. S., 1958-1: Optimal flow through networks. Massachusetts Inst. of Technology. Cambridge, Mass. 1958.

-,1960-1: Optimal flow through networks with gains. 2nd Int. Conference on Oper. Res. Aix-en-Provence (France) 1960.

-,1960-2: A classroom example of linear programming. Operations Res. 8, 565 - 570 (1960).

JOHN, F., 1948-1: Extremum problems with inequalities as subsidiary conditions. New York: Interscience Publ., Inc. 1948.

JOHNSON, E., 1965-1: Network flows, graphs and integer programming. Operations Research Center, University of California, Berkeley, California, ORC 65-1,1965.

JOHNSON, S., 1954-1: Optimal two-and three-stage production schedules with setup times included. Naval Res. Logist. Quart. 1, 61-68 (1954).

-,1958-1: Discussion: Sequencing n jobs on two machines with arbitrary time lags: Alternate proof and discussion of general case. Management Sci. 5, 299-303 (1959).

JOKSCH, H. C., 1962-1: Lineares Programmieren. Tiibingen: J. C. B. Mohr 1962. -, 1964-1: Programming with fractional linear objective functions_ The Mitre

Corporation, paper presented to Joint CORS-ORSA Meeting, Montreal, May 28. 1964.

JORDAN, W., 1920-1: Handbuch der Vermessungskunde, Bd.1. Stuttgart: Met­clersche Buchhandlung 1920 (7. Aufl.); 1904 (5. Auti.).

KALABA, R. E., and M_ L_ JUNCOSA, 1956-1: Optimal design and utilization of communication networks. Management Sci. 3, 33-44 (1956).

KANTOROWICZ, L. V., 1939-1: Mathematical methods in the organization and planning of production. Ubersetzung in Management Sci. 6, 366-422 (1960).

-, 1942-1: On the translocation of masses. C. R. Acad. Sci. URSS 37, 199-201 (1942).

-, 1959-1: Economicheskii Raschet Nailuchshego Ispol Zovaniia Resursov. Akad. Nauk SSSR (1959).

-, 1963-1: Calcul economique et utilisation des ressources. Ubersetzung aus dem Russischen. Paris: Dunod 1963.

-, and M. K. GAVURIN, 1949-1: The application of mathematical methods to problems of freight flow analysis. Akad. Nauk SSSR (1949).

KAPLANSKY, IRVING, 1945-1: A contribution to von Neumann's theory of games. Ann. Math. 46, 474-479 (1945).

KARLIN, SAMUEL, 1959-1: Mathematical methods and theory in games, pro­gramming, and economics. Vols 1 and 2. Cambridge, Mass.: Addison-Wesley Publ. Co., Inc. 1959.

KARUSH, W., 1963-1: Duality and network flow. System Development Corporation, TM-1042-201-00, March 15, 1963.

KAUFMANN, A., 1962-1: Methodes et modeles de la recherche operationnelle. Paris: Dunod 1962. Englische Ubersetzung: Methods and models in operations Research. Englewood Cliffs: Prentice Hall, 1963.

KAWARATANI, T. K., R. J. ULLMAN, and G. B. DANTZIG, 1960-1: Computing tetra­aethyl-Iead requirements in the linear programming format. Operations Res. 8, 1 (1960).

KELLEY, J. E., Jr., 1960-1: The cutting plane method for solving convex programs. J. Soc. Indust. Appl. Math. 8, 703-712 (1960).

-,1961-1: Critical-path planning and scheduling; mathematical basis. Operations Res. 9, 296-320 (1961).

Literaturverzeichnis 687

KELLY, R. J., and W. A. THOMPSON, JR., 1963-1: Quadratic programs in real Hilbert space. J. Soc. lndust. Appl. Math.U, 1063-1070 (1963).

KEMENY, J. G., H. MIRKIL, J. C. SNELL, and G. L. THOMPSON, 1959-1: Finite mathematical structures. Englewood Cliffs, N. J.: Prentice-Hall, Inc. 1959.

-, J. C. SNELL, and G. L. THOMPSON, 1963-1: Einfiihrung in die endliche Mathe­matik. Ludwigshafen (Rhein): Fachverlag fUr Wirtschaftstheorie und Oekono­metrie 1963.

KENDALL, DAVID G., 1960--1: On definite doubly-stochastic matrices and Birkhoff's problem III. J. London Math. Soc. 31), 81-84 (1960).

KLEE, VICTOR, 1964-1: A string algorithm for shortest paths in networks. Opera­tions Res. 12,428-432 (1964).

-,1964-2: Convex polytopes and linear programming. Mathematics Research Laboratory, Boeing Scientific Research Laboratories, Math. Note Nr. 366, August 1964.

KONIG, DINES, 1936-1: Theorie der endlichen und unendlichen Graphen. Leipzig: Akad. VerI. 1936.

KOOPMANS, T. C., 1947-1: Optimum utilization of the transportation system. Supplement to Economctrica 17, (1949).

-,1951-1: (Ed.) Activity analysis of production and allocation. New York: John Wiley and Sons 1951.

-,1951-2: Analysis of production as an efficient combination of activities. New York: John Wiley and Sons 1951.

-,1954-1: Uses of prices. Proc. Conf. on Operations Res. in Production and Inventory Control. Cleveland: Case lnst. Technology 1954.

-, and S. REITER, 1951-1: A model of transportation. New York: John Wiley and Sons 1951.

KRELLE, WILHELM, 1958-1: Ganzzahlige Programmierungen; Theorie und An­wendungeninderPraxis. Unternehmensforschung 2, 161-175 (1958).

-, 1960-1: Linear programming under uncertainty. Econometrica 28, 664-665 (1960) (Abstract).

- und KtrnZI, H. P.: 1958-1: Lineare Programmierung. Ziirich: Verlag Industr. Organisation (1958).

KRICKEBERG, K., 1963-1: Wahrscheinlichkeitstheorie, Stuttgart: Teubner Ver­lagsgesellschaft 1963.

KROMPHARDT, WILHELM, RUDOLF HENN und KARL FORSTNER, 1962-1: Lineare Entscheidungsmodelle. Berlin-Heidelberg-New York: Springer 1962.

KRUSKAL, J. B., 1956-1: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Amer. Math. Soc. 7, 48-50 (1956).

KUENNE, R., 1963-1: Theory of economic general equilibrium. Princeton, N. J.: Princeton University Press (1963).

KUNZI, H. P., 1958-1: Die Simplexmethode zur Bestimmung einer Ausgangslosung bei bestimmten linearen Programmen. Unternehmensforschung 2, 60-69 (1958).

-,1963-1: Die Duoplex-Methode. Unternehmensforschung 7, 103-U6 (1963). -, und W. KRELLE, 1962-1: Nichtlineare Programmierung. Berlin-Heidelberg-

New York: Springer 1962. -, and W. OETTLI, 1963-1: Integer quadratic programming. In R. GRAVES und

P. WOLFE: Recent advances in mathematical programming. New York-Toronto­London: McGraw-Hill, 1963.

-, and H. TZSCHACH, 1965-1: The duoplex algorithm. Numerische Mathematik 7,222-225 (1965).

-,1965-2: Numerische Methoden der Mathematischen Optimierung mit FOR­TRAN- und ALGOL-Programmen. Stuttgart: Teubner 1965.

688 Literaturverzeichnis

KUHN, H. W., 1955-1: The Hungarian method for the assignment problem. Naval Res. Logist, Quart. 2, 83-97 (1955).

-, 1956-1: Solvability and consistency for linear equations and inequalities. Amer. Math. Monthly 63, 217 -232 (1956).

-,1957-1: A note on Prager's transportation problem. J. Math. Phys. 36, 107-111 (1957).

-, and A. W. TUCKER (Eds.) , 1950-1: Contributions to the theory of games. Princeton: Princeton Univ. Press 1950. -, 1950-2: Nonlinear programming. Econometrica 19, 50-51 (1951) (Abstract). - (Eds.), 1953-1: Contributions to the theory of games, Vol. II. Princeton: Princeton Univ. Press 1953. -,1955-1: Theory of games. Encyclopaedia Britannica 10, 5-10 (1955).

-, -, (Eds.), 1956-1: Linear inequalities and related systems. Princeton: Princeton Univ. Press 1956.

- -, 1958-1: John von Neumann's work in the theory of games and mathematical economics. Bull. Amer. Math. Soc. 64, 100-122 (1958).

KUNZ, K. S., 1957-1: Numerical analysis. New York: McGraw-Hill 1957.

LAMBERT, F., 1960-1: Programmes lineaires mixtes. Cah. centre d'etudes oper. Brussels 1960.

LAND, A. H., and A. G. Dow, 1957-1: An automatic method of solving discrete programming problems. British Trading Co., Ltd., London School of Economics and Political Science.

-, 1963-1: A problem of assignment with inter-related costs. Operations Res. 14, 185-199 (1963).

LAVALLEE, R. S., 1955-1: The application of linear programming to the problem of scheduling traffic signals. JORSA 3, 562 (1955) (Abstract).

LAWLER, E. L., 1963-1: The quadratic assignment problem. Management Sci. 9, 586 (1963).

LEHMANN, R. S., 1954-1: On the continuous simplex method. The RAND Corp., RM-1386,1954.

LEMKE, C. E., 1954-1: The dual method of solving the linear programming problem. Naval Res. Logist. Quart. 1, 36-47 (1954).

-,1961-1: The constrained gradient method of linear programming. J. Soc. Indust. AppI. Math. 9, 1-17 (1961).

LEONTIEF, \VASSILY, 1951-1: The structure of American economy, 1919-1939. New York: Oxford Univ. Press 1951.

-, 1953-1: Studies in the structure of the American economy. New York: Oxford Univ. Press. 1953.

LESOURNE, 1960-1: Technique economique gestion industrielle. 2. Auf!.. Paris: Dunod 1960.

LEWIS, ROBERT E., 1955-1: Top managment looks at linear programming and inventory management. Proc. of the Linear Programming and Inventory Management Seminar, Pittsburgh, 1955.

LOURIE, JANICE R., 1964-1: Topology and computation of the generalized transpor­tation problem. Management Sci. 11, 177 -187 (1964).

LUCE, R. DUNCAN, and HOWARD RAIFFA, 1957-1: Games and decisions, intro­duction and critical survey. New York: John Wiley 1957.

MAcDONALD, J., 1950-1: Strategy in poker, business and war. New York: W. W. Norton 1950.

Literaturverzeiclmis 689

MACGUIRE, C. B., 1963-1: Some extensions of the Dantzig-Wolfe decomposition scheme. Center for Research in Management Science, University of California, Berkeley, Working Paper Nr. 66, March 1963.

MADANSKY, ALBERT, 1959-1: Some results and problems in stochastic linear programming. The RAND Corp. Paper P-1596 1959.

-, 1960-1: Inequalities for stochastic linear programming problems. Management Sci. 6, (1960).

-, 1960-2: Methods of solution of linear programs under uncertainty. The RAND Corp. Paper P-2132 1960.

-, 1963-1: Dual variables in two-stage linear programming under uncertainty. J. Math . .Ana!. App!. 6, 98-108 (1963).

MAGHOUT, K., G. COMES, et N. STEINBERG, 1962-1: Generalisation it n dimensions du probleme de transport. Rev. franc. de Recherche Operationelle 6, 21-34 (1962).

J\ilALINVAUD, E., 1963-1: Decentralized procedures for planning. Center for Research in Management Science, University of California, Berkeley, Technical Report Nr. 15, 1963.

MANGASARIAN, O. L., 1962-1: Duality in nonlinear programming. Quart. AppJ. Math. 20, 300-302 (1962).

-, 1964-1: Nonlinear programming problems with stochastic objective functions. Management Sci.lO, (1964).

-, and J. PONSTEIN, 1963-1: Minimax and duality in nonlinear programming. Shell Development Company, Emeryville, Calif., P-1l82 (1963).

MANNE, ALAN S., 1956-1: Scheduling of petroleum refinery operations. Cam­bridge, Mass.: Harvard Univ. Press 1956.

-, 1956-2: .An application of linear programming to the procurement of transport aircraft. Management Sci. 2, 190-191 (1956) (Abstract).

-, 1960-1: On the job.shop scheduling problem. Operations Res. 8, 219-223 (1960).

-,1961-1: Economic analysis for business decisions. New York-Toronto-London: McGraw-Hill, 1961.

MARcus, M., 1960-1: Some properties of doubly stochastic matrices. Amer. Math. Monthly 67, 215-221 (1960).

MARKOWITZ, HARRY M., 1952-1: Portfolio selection. J. Finance VII, 1952. -,1954-1: The nature and applications of process analysis. The RAND Corp. 1954. -,1954-2: Concepts and computing procedures for certain Xli programming

problems. In H. A. ANTOSIEWICZ: Proceedings of the Second Symposium in Linear Programming, Vol. 2, Washington 1955; The RAND Corp. Paper P-602, 1954.

-, 1956-1: The optimization of a quadratic function subject to linear constraints. Naval Res. Logist. Quart. 3, (1956).

-, 1959-1: Portfolio Selection: Efficient diversification of investments. New York: John Wiley 1959.

-, and A. S. MANNE, 1957-1: On the solution of discrete programming problems. Econometrica 25, 19 (1957).

MARSCHAK, J., 1962-1: Computation, decomposition, and internal pricing. Center for Research in Management Science, University of California, Berkeley, Working Paper Nr. 56, December 1962.

MARTIN, G. T., 1963-1: .An accelerated Euclidean algorithm for integer linear programming. In R. GRAVES und P. WOLFE (Eds.): Recent advances in linear programming. New York-Toronto·London: McGraw-Hill 1963.

Dantzig, LitH'are PrngrammicI'nniX 44

690 Literaturverzeichnis

MAsSE, PIERRE, 1946-1; Les reserves et la regulation de l'avenir dans la vie econo­mique, 1. Avenir determine. II. Avenir aleatoire. Paris: Hermann 1946.

-,1963-1: Le choix des investiments. Paris: Dunod, 2. Auf!. Englische Dber­setzung: Optimal investment decisions. Englewood Cliffs, N. J.: Prentice Hall (1963).

-, and R. GIBRAT, 1957-1: Applications of linear programming to investments in the electric power industry. Management Sci. 3, 149-166 (1957).

MAYNARD, HAROLD B., 1955-1: Putting new management tools to work. Proc. of the Linear Programming and Inventory Management Seminar. Pittsburgh 1955.

McILLROY, M. D., 1962-1: Transportation problems with distributed loads. Murray Hill, N. J.: Bell Telephone Laboratories, Inc. (1962).

McKINSEY, J. C. C., 1952-1: Introduction to the theory of games. New York: McGraw-Hill 1952.

MILLER, C. E., 1960-1: The simplex method for local separable programming. Standard Oil Co. of California 1960.

-, 1963-1: The simplex method for local separable programming. In R. GRAVES und P. WOLFE (Eds.) : Recent advances in mathematical programming. New York­Toronto-London: McGraw-Hill (1963).

-, A. W. TUCKER, and R. A. ZEMLIN, 1960-1: Integer programming formulation of traveling salesman problems. J. Assoc. Comput. Mach. 7.4 (1960).

MILLER, L. B., and H. M. WAGNER, 1964-1: Chance programming with joint constraints. Graduate School of Business, Stanford University, Technical Report Nr. 9, October 1964.

MILLS, HARLAN, 1956-1: Marginal values of matrix games and linear programs. In H. W. KUHN and A. W. TUCKER: Linear inequalities and related systems. Princeton: Princeton Univ. Press 1956.

-, 1960-1: Equilibrium points in finite games. J. Soc. Indust. Appl. Math., 8, 397 -402 (1960).

MINKOWSKI, H., 1896-1: Geometrie der Zahlen. Leipzig und Berlin: B. G. Teubner 1910.

MINTY, GEORGE J., 1962-1: On an algorithm for solving some network-programming problems. Operations Res. 10,403-405 (1962).

MONROE, ARTHUR ELI, 1924-1: Early economic thought; selections from economic literature prior to Adam Smith. Cambridge, Mass.: Harvard Univ. Press 1924.

MOORE, E. F., 1957-1: The shortest path through a maze. Bell Telephone Labora­tories.

MORGENSTERN, DIETRICH, 1934-1: Einfiihrung in die Wahrscheinlichkeitsrech­nung und mathematische Statistik. Berlin: Springer-Verlag 1964.

MORGENSTERN, OSKAR, 1949-1: The theory of games. Sci. American 180, 22-25 (1949).

-, Economic activity analysis. New York: John Wiley & Sons 1954. MORIN, GEORGE, 1955-1: More effective production planinng with linear pro­

gramming. Paper F from Proc. of the Linear Programming and Inventory Management Seminar. Pittsburgh 1955.

MOTZKIN, T. S., 1936-1: Beitrage zur Theorie der linearen Ungleichungen. Disser­tation Universitat Zurich 1936.

-, 1952-1: The multi-index transportation problem. Bull. Amer. Math. Soc. 68, 494 (1952) (Abstract).

-,1956-1: The assignment problem. In Proceedings of the Sixth Symposium in Applied Mathematics New York: McGraw-Hill 1956.

Li teraturverzeichnis 691

MOTZKINT.S., H. RAIFFA, G. L. THOMPSON, andR. M. THRALL, 1953-1: The double description method. In H. W. KUHN and A. W. TUCKER (Eds.): Contributions to the theory of games. Princeton, N. J.: Princeton Univ. Press 1953.

-, and I. J. SCHOENBERG, 1954-1: The relaxation method for linear inequalities. Canad J. Math. 6, 393-404 (1954).

MULLER.MERBACH, H., 1962-1: Die optimale Zuordnung von Produkten und Ma· schinen mittels linearer Planungsrechnung. Fortschr. Betriebsfiihr. 1, 15-18 (1962).

-, 1964-1: A parametric linear programming approach for the project cost curves. Operations Res. Center, University of California, Berkeley, Working Paper, 1964.

-,1964-2: The symmetric product form of the revised simplex method. Operations Res. Center, University of California, Berkeley, 1964.

MUNKRES, JAMES, 1957-1: Algorithms for the assignment and transportation problems. J. Soc. Indust. Appl. Math. 0, 32-38 (1957).

NASLUND, BERTIL, and A. WHINSTON, 1962-1: A model of multi.period invest· ment under uncertainty. Management Sci. 8, 184-200 (1962).

N ATRELLA JOSEPH V., 1955-1: New applications oflinear programming. Computers and Automation 4, 11, 22 (1955) (Abstract).

NELSON, RICHARD R., 1957-1: Degeneracy in linear programming: A simple geometric interpretation. Rev. Econ. Statist. 39, 402-407 (1957).

NEWMAN, P., 1955-1: Some calculations on least·cost diets using the simplex method. Oxford: Bulletin, Oxford Univ. Inst. of Statistics 17, 303-320 (1955).

New York Times, 1959-1: Russian assails soviet economics, by Harry Schwartz, May 29, 1959.

NEYMAN, J., 1950-1: First course in probability and statistics, Vol. 1. New York: Henry Holt and Co., Inc. 1950.

-, and E. S. PEARSON, 1936-1: Contributions to the theory of testing statistical hypotheses. Statist. Res. Mem., Parts I and II, 1936, 1938.

NORMAN, R. Z., 1955-1: On the convex polyhedra of the symmetric traveling sales· man problem. Bull. Amer. Math. Soc. 61, 559 (1955) (Abstract).

-, and M. O. ROBIN, 1958-1: An algorithm for a minimum cover of a graph. Notices Amer. Math. Soc. 0, 36 (1958).

OLLMERT, HANS·JOACHIM, 1965-1: Zur Theorie des Simplex.Verfahrens im ausge· arteten Fall. Diplomarbeit. Universitat des Saarlandes, Saarbriicken, 1965.

ONIGKEIT, D., 1962-1: Ein lineares Programmierungsverfahren. Z. Wahrschein· lichkeitstheorie 1,82-108 (1962).

ORCHARD·HAYS, 1954-1: A composite simplex algorithm, II. The RAND Corp. Research Memorandum RM·1275, 1954.

-, 1955-1: The RAND code for the simplex. The RAND Corp. Research Memo· randum RM·I440, 1955.

-,1956-1: Evolution of computer codes for linear programming. The RAND Corp. Paper P·810, 22-24 (1956).

-, LEOLA CUTLER, and HAROLD JUDD, 1956-1: Manual for the RAND IBM code for linear programming on the 704. The RAND Corp. Paper P·842, 24-26 (1956).

ORDEN, ALEX, 1952-1: Application of the simplex method to a variety of matrix problems. In ALEX ORDEN and LEON GOLDSTEIN (Eds.): Symposion on Linear Inequalities and Programming, Project ScooP No. 10 Washington 1952.

-, 1955-1: Survey of research on mathematical solutions of programming problems. Management Sci. 1, 170-172 (1955).

-,191)6-1: The transshipment problem. Management Sci. 2,276-285 (1956).

44*

692 Literaturverzeichnis

PARISOT, G. R., 1961-1: Resolution numerique approchee du probleme de pro­grammation lineaire par application de la programmation logarithmique. UniversiM de Lille, These Numero d'Ordre 52, 1961.

PAULL, A. E., and JOHN R. WALTER, 1955-1: The trim problem: An application of linear programming to the manufacture of newsprint paper. Econometrica 23, 336 (1955) (Abstract).

PHIPPS, C. G., 1952-1: Maxima and minima under restraint. Amer. Math. Mthly 59, 230-235 (1952).

PIEHLER, J., 1962-1: Einfiihrung in die lineare Optimierung. Leipzig: B. G. TEUBNER, (1962).

POLLACK, MAURICE, 1961-1: Solutions of the k-th best route through a network -a review. J. Math. Anal. Appl. 3, 547 -559 (1961).

POUSSIN, M. CH. J. DE LA VALLEE, 1911-1: Sur la methode de l'approximation minimum. Ann. soc. sci. de Bruxelles 35,1-16 (1911).

PRAGER, WILLIAM, 1956-1: On the caterer problem. Management Sci. 3, 15-23 (1956); 3, 209 (1957) (Abstract).

-, 1957-1: A generalization of Hitchcock's transportation problem. J. Math. Phys. (M.l. T.) 36,99-106 (1957).

-, 1963-1: A structural method for computing project cost polygons. Management Sci. 9, 394-404 (1963).

PYNE, INSLEY B., 1956-1: Linear programming on an electronic analogue computer. AlEE Transactions Annual 1956.

RADNER, RoY, 1955-1: The linear team: An example of linear programming under uncertainty. In H. A. ANTOSIEWICZ (Ed.): Proc. of the Second Symp. in Linear Programming, Vol. 2. Washington 1955.

-,1959-1: The application of linear programming to team decision problems. Management Sci. 5, 143-150 (1959).

RAIFFA, H. G., L. THOMPSON, and R. M. THRALL, 1952-1: An algorithm for the determination of all solutions of a two-person zero-sum game with a finite num­ber of strategies (double descriptive method). In A. ORDEN and LEON GOLDSTEIN (Eds.): Symp. on Linear Inequalities and Programming. Washington 1952.

REISCH, E., and L. ErSGRUBER, 1960-1: Bibliography of linear programming and ist application to agricultural economic problems. Purdue University 1960.

REITER, S., 1957-1: Surrogates for uncertain decision problems: Minimal informa­tion for decision making. Econometrica 25, 339-345 (1957).

RENYI, ALFRED, 1962-1: Wahrscheinlichkeitsrechnung. Berlin: Deutscher Verlag der Wissenschaften 1962.

RICHARDSON, MOSES, 1958-1: Fundamentals of mathematics. New York: The Macmillan Co. 1958.

RICHTER, HANS, 1956-1: Wahrscheinlichkeitstheorie. Berlin: Springer-Verlag, 1956.

RILEY, VERA, and SAUL I. GASS, 1958-1: Linear programming and associated techniques, a comprehensive bibliography on linear, nonlinear and dynamic programming. Baltimore: Johns Hopkins Press 1958.

RITTER, K., 1962-1: Ein Verfahren zur L6sung parameterunabhangiger, niaht­linearer Maximumprobleme. Unternehmensforschung 6,149-166 (1962).

ROBINSON, JULIA, 1951-1: An iterative method of solving a game. Ann. Math. 54, 296-301 (1951).

ROCKAFELLAR, R. T., 1963-1: Convex functions and dual extremum problems. Ph. D. Dissertation, Harvard University, Cambridge, Mass., 1963.

Literaturverzeichnis 693

ROCKAFELLAR, R. T., 1964-1: A combinatorial algorithm for linear programs in the general mixed form. J. Soc. Indust. Appl. Math. 12, 215-225 (1964).

ROSEN, J. B., 1960-1: Gradient projection method for non·linear programming, Part I: Linear constraints. J. Soc. Indust. Appl. Math. 8, 181-217 (1960). Part II: Non·linear constraints. J. Soc. Indust. Appl. Math. 9, 514-532 (1961).

-, 1961-1: The gradient projection method for non-linear projection. Part II. ,T. Soc. Indust. Appl. Math. 9, 514-532 (1961).

-,1963-1: Convex partition programming. In R. GRAVES and P. WOLFE (Eds.): Recent advances in mathematical programming. New York, Toronto, London: McGraw·HillI963.

-,1963-2: Primal partition programming for block diagonal matrices. Computer Science Division, School of Humanities and Sciences, Stanford University, Technical Report Nr. 32, 1963.

ROUBAULT, M., 1963-1: Etude d'un algorithme de resolution pour les programmes nonlineaires convexes. Thesis, Faculte des Sciences, Universite de Paris, 1963.

RYSER, H. J., 1961-1: Matrices of zeros and ones. Bull. Amer. Math. Soc. 66, 442-464 (1960).

-,1963-1: Combinatorial mathematics. The Carus Math. Monographs, Nr. 14, Math. Assoc. New York: John Wiley and Sons, Inc., 1963.

SAATY, T. L., 1955-1: The number of vertices of a polyhedron. Amer. Math. Mthly 65,327 -331 (1955).

-,1959-1: Mathematical methods of operative research. New York: McGraw Hill 1959.

SALVESON, M. E., 1953-1: A computational technique for the fabrication scheduling problem. Management Sci. Res. Project, Univ. of California, Los Angeles, 1953.

SAMUELSON, P. A., 1955-1: Linear programming and economic theory. In H. A. ANTOSIEWICZ (Ed.): Proc. of the Second Symposium in Linear Programming. Vol. 2. Washington 1955.

SASIENI, M. W., A. YASPAN, and L. FRIEDMAN, 1962-1: Methoden und Probleme der Unternehmensforschung, deutsch herausgegeben von H. P. KUNZI. Wiirzburg: Physica-Verlag 1962.

SCHELLING, T. C., 1960-1: The strategy of conflict. Cambridge, Mass.: Harvard University Press, 1960.

SCHMETTERER, LEOPOLD, 1956-1: Einfiihrung in die mathematische Statistik. Wien: Springer-Verlag 1956.

SHAPLEY, L. S., 1959-1: On network flow functions. Naval Res. Logist. Quart. 8, 2 (1961).

-,1961-1: On network flow functions. The RAND Corp., Paper P·2185, 1961. -, and R. N. SNOW, 1950-1: Basic solutions in discrete games. In H. W. KUHN and

A. W. TUCKER (Ads.): Contributions to the theory of games. Princeton, N. J.: Princeton Univ. Press 1950.

SHERMAN, H. C., H. L. CAMPBELL, and C. S. LANFORD, 1939-1: Experiments on the relation of nutrition to the composition of the body and the length of life. Proc. Nat. Acad. Sci. U. S. A. 25,16-20 (1939).

SllETTY, C. M., 1959-1: A solution to the transportation problem with non-linear costs. Operations Res. 7, 571-580 (1959).

SHUBIK, MARTIN, 1959-1: Strategy and market structure; competition, oligopoly, and the theory of games. New York: John Wiley and Sons 1959.

-, (Ed.), 1964-1: Game theory and related approaches to social behavior. New York: John Wiley and Sons, Inc. 1964.

694 Literaturverzeichnis

SIMON, H. A., 1956-1: Dynamic programming under uncertainty with a quadratic criterion function. Econometrica 24, 74-81 (1956).

SIMONNARD, M., 1962-1: Programmation lillElaire. Paris: Dunod 1962. -, and G. F. HADLEY, 1959-1: Maximum number of iterations in the transportation

problem. Naval Res. Logist. Quart. 6, 125-129 (1959). SINDEN, F. W., 1963-1: Duality in convex programming and in projective space.

J. Soc. Indust. Appl. Math. 11, 535-552 (1963). SINHA, S. M., 1963-1: Stochastic programming. Operations Res. Center, University

of California, Berkeley, ORC 63-22,1963. SLATER, M., 1950-1: Lagrange multipliers revisited. Cowles Commission Discussion

Papers, Math. 403, 1950; The RAND Corp. RM-676, 1951. SMITH, D. M., and W. ORCHARD-HAYS, 1963-1: Computational efficiency in

product form LP codes. In R. GRAVES and P_ WOLFE (Eds.), Recent advances in mathematical programming. New York, Toronto, London: McGraw-Hill 1963.

SMITH, L. W. JR., 1956-1: Current status of the industrial use of linear programming. Management Sci. 2, 156-158 (1956).

SMI'm, V. E., 1959-1: Linear programming models for the determination of pala­table human diets. J. Farm Econ. 41, 272-283 (1959).

SOLOW, R. M., 1952-1: On the structure oflinear models. Econometrica 20, 29-46 (1952).

SPIVEY, W. A., 1963-l: Linear programming. New York: The Macmillan Company 1963.

SPURKLAND, S., 1963-2: Error control. Norwegian Computer Center, LP-Note 8, Blindern, 1963.

STIEFEL, E., 1960-1: Note on Jordan elimination, linear programming and Tcheby­cheff approximation. Numer. Math. 2 and 4 (1960).

STIEMKE. E., 1915-1: mer positive Losungen homogener linearer Gleichungen. Math. Ann. 76,340-342 (1915).

STIGLER, GEORGE, J., 1945---1: The cost of subsistence. J. Farm Econ. 27, 303-314 (1945).

STOER, J., 1964-1: On a duality theorem in nonlinear programming. Numerische Math. 6,55-58 (1964).

STOKES, R. W., 1931-1: A geometric theory of solution oflinearinequalities. Trans. Amer. Math. Soc. 33, 782-805 (1931).

SWANSON, E. R., 1955-1: Integrating crop and livestock activities in farm manage­ment activity analysis. J. Farm Econ. 37, 1249-1258 (1955).

-,1955-2: Solving minimum-cost feed mix problems. J. Farm Econ. 37, 135-139 (1955).

SYMONDS, G. H., 1955-1: Linear programming: The solution of refinery problems. New York: Esso Standard Oil Co. 1955.

-,1955-2: Mathematical programming as an aid to decision making. Advanced Management 20,11-17 (1955).

SZWARC, vY., 1963-1: The mixed integer linear programming problem when the integer variables are zero or one. Gruaduate School of Industrial Administration, Carnegie Institute of Technology, May 1963.

TALACKO, J. V., 1959-1: On stochastic linear inequalities. Trab. Estadist. 10, 89-112 (1959).

TEREBESI, M., 1961-1: Bemerkungen zum Verfahren von Gomory zur Bestimmung ganzzahliger Losungen von linearen Programmen. Unternehmensforschung 5, 197 -215 (1961).

Literaturverzeichnis 695

THEIL, H., 1957-1: A note on certainty equivalence in dynamic planning. Econo· metrica 25, 346-349 (1957).

-,1961-1: Some reflections on static programming IDIder uncertainty. Welt­wirtschaftliches Archiv. 87, 124-138 (1961).

-, und C. VAN DE PANNE, 1960-1: Quadratic programming as an extension of classical quadratic maximization. Management Sci. 7, 1-20 (1960).

THRALL, R. M., 1955-1: Some results in non-linear programming. The RAND Corp. RM-909, 6, 17 (1952).

-, and L. TORNHEIM, 1957-1: Vector spaces and matrices. New York: John Wiley and Sons 1957.

TINTNER, G., 1955-1: Stochastic linear programming with applications to agricul­tural economics. In H. A. ANTOSIEWICZ (Ed.): Proc. of the Second Symp. in Linear Programming, Vol. 1, 197-228. Washington 1955.

-, C. MILLHAlVI and J. K. SENGUPTA, 1963-1: A weak duality theorem for stochastic linear programming. Unternehmensforschung 7,1-8 (1963).

TOMPKINS, C. B., 1955-1: Projection methods in calculation. In H. A. ANTOSIEWICZ (Ed.): Proc. of the Second Symp. in Linear Programming, Vol. 2,425-448. Washington 1955.

-, 1957-1: Some methods of computational attack on programming problems, other than the simplex method. Naval Res. Logist. Quart. 4, 95-96 (1957).

TORNGVIST, L., 1961-1: On distribution fIDIction for quantities related to networks. Bull. Internat. Statistic. Inst. 38, Teil4, Tokio, 609-612 (1961.)

TOTSCHEK, R., and R. C. WOOD, 1961-1: An investigation of real-time solution of the transportation problem. Journal of A.C.M., April 1961, S. 230.

TUCKER, A. VV., 1950-1: Linear programming and theory of games. Econometrica 18, 189 (1950).

-,1950-2: Analogues of Kirchoff's laws. George Washington Univ. Logistic Papers 3, 4 (1950).

-, 1955-1: Linear inequalities and convex polyhedral sets. In H. A. ANTOSIEWICZ (Ed.): Proc. of the Second Symp. in Linear Programming, Vol. 2, 569-602. Washington 1955.

-,1955-2: Game theory and programming. Stillwater: Oklahoma A and M College 1955.

-,1956-1: Dual systems of homogeneous linear relations. In H. W. KUHN and A. W. TUCKER (Eds.): Linear inequalities and related systems. Princeton, N. J.: Princeton Univ. Press 1956.

-, 1957-1: Linear and nonlinear programming. Operations Res. 5, 244-257 (1957).

-, 1960-1: On directed graphs and integer programs. Princeton, N. J.: Princeton Univ. Press 1960.

-, 1960-2: A combinatorial equivalence of matrices. In R. BELLMAN and MARSHALL HALL JR. (Eds.): Proc. of Symposia in Applied Mathematics, Vol. X. Combina­torial Analysis. Providence: Amer. Math. Soc. 1960.

-,1960-3: Solving a matrix game by linear programming. IBM J. Res. Develop. 4,507 -517 (1960).

-,1963-1: Combinatorial theory IDIderlying linear programs. In R. GRAVES und P. WOLFE (Eds.). Recent advances in mathematical programming. McGraw-Hill, New York, Toronto, London, 1963.

-, IDId R. D. LUCE (Eds.), 1959-1: Contributions to the theory of games. Princeton University Press, Princeton, New Jersey, 1959.

TUTTE, W. T., 1946-1: On Hamiltonian circuits. J. London Math. Soc. 21, 98-101 (1946).

696 Literaturverzeichnis

USAF, (Hq., Comptroller, computational division) 1954-1: The appreciation of linear programming techniques of Air Force problems. 1954.

UZAWA, HIROFUMI, 1958-1: The KUHN-TuOKER theorem in concave programming. In KENNETH J. ARROW, LEONID HURWIOZ, and HIROFUMI UZAWA (Eds.): Studies in linear and non-linear programming. Stanford: Stanford Univ. Press 1958.

-, 1960-1: Market mechanisms and mathematical programming. Economctrica 28, 872-881 (1960).

VAJDA, S., 1958-2: Inequalities in stochastic linear programming. Bull. Internat. Statist. Inst. 36, 357 -363 (1958).

-. 1960-1: Lineare Programmierung, Beispiele. Aus dem Englischen iibertragen von H. P. KUNZI: Ziirich: Verlag Industrielle Organisation 1960.

-, 1961-1: Mathematical programming. Reading, Mass.: Addison-Wesley Pub!. Comp.1961.

-, 1961-2: Einfiihrung in die Linearplanung und die Theorie del' Spiele. Deutsche Ubersetzung von W. RIEDLER. Miinchen und Wien: R. Oldenbourg 1961.

-,1963-1: Pourquoi est-il necessaire de developper les methodes actuelles de planification matMmatique? Econometrica 31, 257 -259 (1963) (Abstract).

VAN DEN BOGARD, P. J. M., 1960-1: On the static theory of certainty equivalence. Internat. Center for Management Science, Rotterdam, Report 6010, 1960.

VAN DE PANNE, C., and ANDREW WHINSTON, 1963-1: The simplex and dual method for quadratic programming. Internat. Center for Management Science, Rotterdam, Report 6010, 1963.

VAN MOESEKE, P., and G. TINTNER, 1964-1: Base duality theorem for stochastic and parametric linear programming. Unternehmensforschung 8, 75-79 (1964).

VAN DER WAERDEN, B. L., 1957-1: Mathematische Statistik. Berlin: Springer­Verlag 1957.

VAN SLYKE, R., 1963-1: Monte Carlo methods and the PERT Problem. Operations Research 11, 839-860 (1963).

-, and ROGER WETS, 1962-1: On diagonalization methods in integer programming. Operations Research Center, University of California, Berkeley, California, RR 27,1962.

VAZSONYI, ANDREW, 1955-1: Optimizing a function of additively separated va­riables subject to a simple restriction. In H. A. ANTOSIEWIOZ (Ed.): Proc. of the Second Symp. in Linear Programming, Vol. 2, 453-469. Washington 1955.

-, 1962-1: Die Planungsrechnung in Wirtschaft und Industrie. Deutsche Uber­setzung von W. RIEDLER. Wien und Miinchen: R. Oldenbourg 1962.

VEINOTT, A. F. Jr., and H. M. WAGNER, 1962-1: Optimum capacity scheduling, I and II. Operations Research 10, 518-546 (1962).

VILLE, JEAN A., 1938-1: Sur la tMorie generale des jeux ou intervient l'habiliw des joueurs. Applications aux jeux de hasard it Emile Borel et Jean Ville. Tome 4, Fasc. 2. In EMILE BOREL: Traite du calcul des probabiliws de ses applications. 1938.

VON NEUMANN, JOHN, 1928-1: Zur Theorie del' Gesellschaftsspiele. Math. Ann. 100, 295-320 (1928).

-,1937-1: Uber ein 6konomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes. Ergebn. Math. Koll. 8, 1937.

-,1947-1: On a maximization problem. Princeton, N. J.: Inst. Advanced Study 1947 (Manuscript).

-, 1948-1: A numerical method for determination of the value and best strategies of a zero-sum, two-person game. Princeton, N. J.: lnst. Advanced Study 1948.

Literaturverzeichnis 697

VON NEUMANN, JOHN, 1953-1: A certain zero-sum two-person game equivalent to the optimal assignment problem. In H. W. KUHN and A. W. TUCKER (Eds.): Contributions to the theory of games. Princeton, N. J.: Princeton Univ. Press 1953.

-,1954--1: A numerical method to determine optimum strategy. Naval Res. Logist. Quart. 1, 2 (1954).

-, and OSKAR MORGENSTERN, 1961-1: Spieltheorie und wirtschaftliches Verhalten. Deutsch herausgegeben von F. SOMMER. Wiirzburg: Physica-Verlag 1961.

VOTAW, D. F., JR. 1952-1: Methods of solving Bome personnel classification problems. Psychometrika 17, 255-266 (1952).

-,1955-1: Programming under conditions of uncertainty. In H. A. ANTOSIEWICZ (Ed.): Proc. of the Second Symp. in Linear Programming, Vol. 2, 187-195. Washington 1955.

-,1960-1: Statistical programming. Ann. Math. Statist. 31, 1077-1083 (1960). -, and A. ORDEN, 1952-1: Personnel assignment problem. In ALEX ORDEN and

LEON GOLDSTEIN (Eds.): Symp. on Linear Inequalities and Programming. Washington 1952.

WAGNER, H. M., 1957-1: A comparison of the original and revised simplex methods. Operations Res. 5, 361-369 (1957).

-,1957-2: A linear programming solution to dynamic Leontief type models. Management Sci. 3, 234-254 (1957).

-, 1958-1: The dual simplex algorithm for bounded variables. Naval Res. Logist. Quart. 5, 257 -261 (1958).

-, 1958-2: On the distribution of solutions in linear programming problems. J. Amer. Statist. Ass. 53,161-163 (1958).

-, 1959-1: On a class of capacitated transportation problems. Management Sci. 5, 304-318 (1959).

W ALD, ABRAHAM, 1935-1: Dber die eindeutige positive Losbarkeit der neuen Pro­duktionsgleichungen; auch: Dber die Produktionsgleichungen der okonomischen Wertlehre. Ergebn. Math. Koll. 6,12-18 (1936); 7, 1-6 (1936).

-, 1950-1: Statistical decision functions. New York: John Wiley and Sons 1950. WALRAS, LEON, 1874-1: Elements d'economie politique pure ou theorie de la

richesse sociale. Fasc. 1, Tome 8. Lausanne, Paris, Basel 1874; weitere Hinweise aufW ALRAS siehe bei DORFMAN, SAMUELSON und SOLOW, 1958-1.

~W ARGA, J., 1963-1: A convergent procedure for convex programming. J. Soc. Indust. Appl. Math. 11, 579-587 (1963) (siehe auch 588-593).

WAUGH, F. V., 1951-1: The minimum-cost dairy feed. J. Farm Econ. 33, 299-310 (1951).

-, 1958-1: Alligations, forerunner of linear programming. J. Farm Econ. 40, 89-101 (1958).

WBELL, J. R., and W. H. MARLOW, 1961-1: On an industrial programming problem of Kantorovich. Management Sci. 8, 13-17 (1961).

WEGNER, P., 1960-1: A nonlinear extension of the simplex method. Management Sci. 7, 43-55 (1960).

WENKE, KLAUS, 1956-1: Mathematische Modelle in der Betriebswirtschaft. Z. f. Betriebswirtsch. 26, 48-53 (1956).

-,1961-1: Zur Kalkulation von Kuppelprodukten, eine Anwendung des linearen Programmierens. Z. f. Betriebswirtsch. 31, 12-29 (1961).

-, 1964-1: Praktische Anwendung linearer Wirtschaftsmodelle. Unternehmens­forschung 8, 33-46 (1964).

VVETS, ROGER, 1964--1: Programming under uncertainty, the complete problem. Boeing Scientific Research Laboratories, 1964.

Dtlntzig, Lineare Progranlmierllng 45

698 Literaturverzeichnis

WETZEL, W., ]956-1: Lineare Verteilungsmodelle in der Betriebswirtschaft -Beispiele fiir den praktischen Einsatz der Linearplanung in Unternehmungen. Unternehmensforschung 1, 1956/7.

WEYL, H., 1935-1: Elementare Theorie der konvexen Polyeder. Comment. Math. Helv. 7, 290-306 (1935).

WHINSTON, S., 1962-1: Price coordination in decentralized systems. ONR Graduate School of Business Administration, Research Memorandum Nr.99, Carnegie Institute of Technology, 1962.

-, 1964-1: A decomposition algorithm for quadratic programming. Cowles Foundation for Research in Economics, Discussion Paper Nr. 172, Yale Uni­versity, June 1964.

WHITE, W. B., S. M. JOHNSON, and G. B. DANTZIG: Chemical equilibrium in com­plex mixtures. J. Chem. Phys. 28, 751-755 (1958). Siehe auch DANTZIG, JOHNSON, and WHITE: A linear programming approach to the chemical equili­brium problem. Management Sci. 0, 38-43 (1958).

WILDE, D. J., 1962-1: Differential calculus in nonlinear programming. Operations Research 10, 764-773 (1962).

WILLIAMS, A. C., 1960-1: The method of continuous coefficients. Socony Mobile Oil Co. Part I, Rep. No. ECC 60.3, March 1, 1960; Rep. No. ECC 60.4, March 21 1960.

-, 1962-1: A treatment oftransportation problems by decomposition. J. Soc. Indust. App!. Math. 10, 35-48 (1962).

-, 1963-1: A stochastic transportation problem. Operations Research 11, 759-770 (1963).

WILLIAMS, JOHN D., 1954-1: The compleat strategyst. New York: McGraw-Hill 1954.

WITTMANN, WALDEMAR, 1960-1: Lineare Programmierung und traditionelle Pro­duktionstheorie. Z. f. handelswissenschaft!. Forsch. 12, 1 (1960).

WITZGALL, C., 1963-1: An all-integer programming algorithm with parabolic constraints. Argonne National Laboratory, Argonne, Illinois. J. Soc. Indust. App!. Math. 11, 855-871 (1963).

'WOLFE, PHILIP, 1957-1: Computational techniques for non-linear programs. Princeton University Conference 1957.

-, 1959-1: The simplex method for quadratic programming. Econometrica 27, 3 (1959).

- (Ed.), 1959-2: The RAND symposium on mathematical programming. The RAND Corp. Report R-351 1959.

-, 1960-1: Accelerating the cutting plane method for non-linear programming. The RAND Corp. 1960; J. Soc. Indust. App!. Math. 9, 481-488 (1961).

-,1961-1: A duality theorem for nonlinear programming. Quart. Appl. Math. 19, 239-244 (1961).

-,1961-2: An extended composite algorithm for linear programming. The RAND Corporation, Paper P-2373, July 1961.

-,1961-3: Accelerating the cutting plane method for non-linear programming. J. Soc. Indust. App!. Math. 9, 481-488 (1961).

-,1962-1: Some simplex-like nonlinear programming procedures. Operations Res. 10, 438-447 (1962).

-, 1963-1: Methods of nonlinear programming. In R. GRAVES und P. WOLFE (Eds.): Recent advances in mathematical programming. New York, Toronto, London: McGraw-Hill 1963.

Literaturverzeichnis 699

WOLFE, PHILIP, 1963-2: A technique for resolving degeneracy in linear pro­gramming. J. Soc.Indust. Appl. Math. 11, 205-211 (1963).

-, and L. CUTLER, 1963-1: Experiments in linear programming. In R. GRAVES und P. WOLFE (Eds.): Recent advances in mathematical programming. New York, Toronto, London: McGraw-Hill 1963.

-, and G. B. DANTZIG, 1962-1: Linear programming in a Markov chain. Operations Res. 10, 702-710 (1962).

",VOLLIIIER, RICHARD, 1964-1: Removing arcs from a network. Operations Res. 12, November 1964.

WOOD, MARSHALL K., 1948-1: Scientific planning techniques. Project SCOOP, Discussion Paper No. I-DU. Planning Res. Div. Washington 1948.

-, and G. B. DANTZIG, 1949-1: The programming of interdependent activities: General Discussion. In T. C. KOOPIIIANS: Activity analysis of production and allocation. New York: John Wiley and Sons 1951; Econometrica 17,193-199 (1949).

-, and M. A. GEISLER, 1951-1: Development of dynamic models for program planning. In T. C. KOOPlIIANS (Ed.): Activity analysis of production and alloca­tion. New York: John Wiley and Sons 1951.

ZIlIIlIIERN, B., 1957-1: Resolution des programmes lineaires de transport par la methode de separation en etoile. Rev. rech. operationnelle 1, 117 -132 (1957).

ZOUTENDIJR, G., 1959-1: Maximizing a function in a convex region. J. Roy. Statist. Soc. Ser. B 21, 338-355 (1959).

-,1960-1: Methods offeasible directions. New York: Elsevier Publ. Co. 1960.

45*

Sachverzeichnis

Addition - von Matrizen, Definition der 213 - von Vektoren, Definition der 206 Additivitat 7, 39-40 Aktivitat 2, 4, 7 -, Grad der 4 -, permanent zulassige 567 -, variable Koeffizienten der 498-505

-, mit einem Kontroilparameter 498

-, mit mehreren Kontrollpara-metern 503

Aktivitatsanalyse 7, 22 Aktivitatsmenge 41 Algorithmus -, gemischter 276 -, primaler-dualer 283-289 -, selbstdualer parametrischer

280-283 Alternativen, k-fache 609 Alternativsatz fUr Matrizen 25, 161 Analogkomputer 31 .Aquivalente Systeme (s. Systeme) Ausbildung auf der Arbeitsstatte 5,

65-68 .AuBerer FluB 41 Auszahlung 319 -, erwartete 326 Automation 1

und mathematische Programmie­rung 11-13

Basis -, dreieckige 348, 370, 388 - eines linearen Programms 95 - eines Vektorraums 209 -, Inverse der 229,243 - -, Produktform der 232 -, komplementare 276-278, 559

- bei quadratischen Programmen 559

-, primale und duale 276

Basis und Baum 405 (s. auch Matrix, Systeme, lineare Gleichungen, Vektor)

Basisliisung 26 (s. auch zulassige Liisungen)

-, Definition der 95 -, entartete 95, 117 -, optimale, zulassige 111-112

des gewichteten Zuteilungs­problems 471

des kapazitierten Transport-problems 429

des Transportproblems 346, 439 des Umladeproblems 394, 439 mittels der Methode der oberen

Grenzen 420 Basisvariablen 85 -, abhangige, unabhangige 85 Baum 402, 405 Bedingungen von KUHN und TUCKER

535 Bureau of Labor Statistics 21, 629

Chemisches Gleichgewicht 10, 545 Circling 117 (s. Kreisen) Combined Shipping Board 344 Cowles Commission 1, 18, 22, 29 Cycling 30, 117 (s. Kreisen)

DALKS 517 Darstellung - einer Aktivitat 250 - eines Vektors 210 Dekompositionsprinzip 33, 490, 507

(s. auch verallgemeinertes Programm von \VOLFE)

-, Gesprach tiber das 515-523 -, Hauptprogramm beim 509 - -, beschranktes 511 -, Iterationsverfahren beim 511 -, Teilprogramm beim 510 - -, unbeschranktes 513 Dekompositionssatz fUr Ketten 392,

441

Sach verzeichnis 701

Deterministische Probleme 10 Diagramm von TUCKER 145, 148, 161,

277 (s. auch duales lineares Pro· gramm)

Dichotomie 609 Dimension eines Vektorraums 210 Diskrete Probleme 10 (s. auch nicht·

lineare Programmierung) Diskrete Programmierung 583-624 -, Iterationsverfahren fiir 601 -, Probleme lasbar durch 608 Doppelbeschreibungsmethode 30 Dreiecksmodelle 19, 31 Duales lineares Programm (System) 25,

57,71, 143-155 -, Beispiel des ehrgeizigen Industriel·

len und 301 eines gemischten Programms 146 eines Standardprogramms, eines

Programmsin Normalform 71,148 -, komplementare primale und duale

Basen und 276 -, Multiplikatoren von LAGRANGE und

167 -, Tucker-Diagramm fiir 145, 161,277 -, Zulassigkeit des 149 Duale Simplexmethode 276, 278 Dualitat 29 -, Fundamentalsatze iiber 155-163 Dualitatssatz 29, 139, 145 -, Beweis des 148-155 -, Matrixspiele und 329 -, schwache Form des 151 (s. auch

komplementarer Schlupf, Simplexmethode)

Dynamische Programmierung 10, 579 -, Funktionalgleichungsmethode fUr

588 -, Optimalitatsprinzip bei 111

zur Lasung des Rucksackproblems 588

Ecklasung (s. Extremlasung) Einheitsmatrix 224 Einheitsvektor 208 Einstufige Probleme 10 Eisen- und Stahlindustrie 35 Elektrizitatswerke -, Investitionsprogramm fiir 35 Elektroncnrechner -, Bedeutung zur Lasung des Er­

nahrungsproblems 632

Elementare Operationen 85-87 (s. auch Pivot-Operationen, Systeme

linearer Gleichungen) Eliminationsmethode zur Lasung von

Ungleichungssystemen 98 Endlichkeit (s. auch Entartungsfall)

des Algorithmus fUr diskrete Pro­gramme 606

des Algorithmus fUr verallge­meinerte Programme 496

des quadratischen Algorithmus 563 des Simplexalgorithmus 117, 139,

142, 270 ENIAC 15 Entartungsfall 30, 117, 141, 256, 262,

266 beim primalen oder dualen System

282 beim Transportproblem 351 beim Zuordnungsproblem 363

(s. auch Kreisen, lexikographische Regel, Zufalls-Auswahl-Regel)

Ernahrungsmodell 133, 137 -139 fUr die Hausfrau 3

- von STIGLER 625-643 - von THRALL 73 Ernahrungspillen -, Fabrikant von 301-304 Ersatzprozesse 249 Erwartungskosten 568 Erwartungswert 569 Exogener FluB 41 ExtremlOsung 26 (s. auch Extrem-

punkt) Extrempunkt( e) 179 -, Linearkombination von 198 -, nicht ganzzahliger 586

Farkassches Lemma 26, 144, 159, 169 Fehlervariable 151 (s. auch kiinstliche

Variablen) Firma 23 Fixe Kosten, Problem der 618 Flugrouten 35, 644-670 FluB -, auBerer, exogener 18, 41 (s. auch

Netzwerk) -, maximaler 438 - -, Gleichgewichtsbedingungen fiir

den 439 FluBdiagramm - der Simplexmethode 122

702 Sachverzeichnis

FluBdiagramm des Algorithmus fiir die quadratische Programmierung 563

FluBkapazitat 438 Fiihrender Koeffizient 267

Ganzzahlige Formen -, Methode der 590-608 (s. auch dis·

krete Programmierung) Ganzzahlige Programmierung 33

(s. auch diskrete Programmierung) Generische Spalte 493 Geschichte der linearen Programmie.

rung, Tabelle der 15 Gewichte einer Linearkombination 82,

206 - von Gleichungen 243 (s. auch Sim·

plexmultiplikatoren) Gestiirtes Problem 266, 270-272

beim Transportproblem 352 (s. auch lexikographische Anordnung, lexikographische Regel)

Gleichgewichtsbedingungen 41 Gradient 184, 198 Graph - linearer 27, 400 (s. auch Netzwerk)

Halbebene 175 Halbraum 175 Handlungsreisender -, Problem des 619-620 Hausfrauenproblem 4-5, 74 Heiratsspiel 367, 380, 586 Homogene Systeme (s. Systeme) Hyperebene 175 -, schneidende 589

IBM.Komputer 15, 31 Industrielle Anwendung der linearen

Programmierung 33-35 Industrieller -, Plan des eh:rgeizigen 299 Inkonsistentes Gleichungssystem 81 Inneres Produkt von Vektoren 213 Input.Qutput.Koeffizienten 41, 308,

312 Input.Qutput.Matrix 22 (s. auch

tableau economique) Inverse einer Matrix 219 Iterationen -, Anzahl der 117,185,283,418

Job·Shop·Produktion 34

Kanonische Form (s. Systeme)

Kante - eines konvexen Polyeders 180, 185 - eines Netzwerks 400 Kantenfolge 401 Kapazitiertes System 420 Kegel 194 Kette in einem Graphen 401 KettenfluB 441 Knotenpunkt 400 Koalitionstheorie 10 Kombinatorische Probleme 361, 584 Komplementare primare und duale

Basen 276 Komplementarer Schlupf -, Anwendung auf Matrixspiele 330 - in primalen und dualen Systemen

157 -, TUCKERS Satz yom 162 Konkave Funktion 534 -, glob ales Minimum fiir 614 Konservenfabrikant -, Beispiel des 3, 42 (s. Transport.

probleme) Konsistentes Gleichwlgssystem 81 Konstruktion eines Modells 40-41 Kontinuierliche Probleme 10 Kontrollparameter 503-505 Konvexe Funktion 178 Konvexe Gebiete 171-180 Konvexe Hiille 187 Konvexe Menge(n) 172 -, abgeschlossene 172 -, Durchschnitt von 173 -, polyed:rale 495, 509 - -, unbeschrankte 513 Konvexe Programmierung 10, 32, 497,

534-565 -, Annahme der Nichtentartung fUr

536 -, Bedingungen von KUHN und

TUCKER fiir 535 -, Reduktion der, auf ein verallge.

meinertes Programm 497 (s. auch Problem des chemischen Gleichgewichts, quad:ratische Programmierung)

Konvexes Polyeder 176 -, Kante eines 180, 185 Konvex.separable Zielfunktionen

547-555 Kosten 41, 70

Sachverzeichnis 703

Kostenfaktoren -, relative 11, 257-259, 307 Kostenkoeffizienten 70, 310-311 Kreis in einem Graphen 402 -, einfacher 402 Kreisen (circling, cycling) beim Sim­

plexalgorithmus 30, 117, 141, 244,262,265

-, Beispiele des 263, 264 (s. auch Entartungfall )

Kiinstliche Variablen 110, 119-120, 151, 152, 270, 279

Lagerhaltung 10, 63-65, 77, 476 -, Beispiel fiir 571-575 (s. auch

Planung) Lagrange-Multiplikatoren 163 -167,

243,534 -, Definition der 164 Lagrange-Parameter 163 Lateinische Quadrate -, orthogonale 621 Lebensmittelverarbeitungsindustrie 34 Leere Losungsmenge 81 Leontiefsches Modell (System) 10, 23,

242 Lexikographische Anordnung 266, 337

(s. auch gestiirtes Problem, Vektor) Lexikographische Regel 256, 269 Lineare Abhangigkeit und Unabhangig­

keit von Vektoren 207 Lineare Gleichung 2 (s. auch Systeme

linearer Gleichungen) -, inkonsistente, unlosbare, wider­

spruchsvolle 83, 119 -,leere 83 -, redundante, iiberfliissige, iiber-

zahlige 83, 118 Lineare Programmierung (s. auch

lineares l'rogramm) -, Annahmen bei der 7,38-40 -, Definition der 6-8 - bei UngewiBheit 566-582,644 -

670 -, Geschichte der 14-37 -, graphische Methoden bei der

40-63 -, mathematisches Problem der 42, 68

als Schwerpunktproblem 186 - - in N ormalform, Standardform 68 - - in Ungleichungsform 99-103 -, Methode der Lagrange-Multiplikato-

ren bei der 163-167

Lineare Programmierung -, parametrische 280-283 -, Standardproblem der 40,68 - und Spieltheorie 318-342 - und Wirtschaftsmodelle 19-24 Lineare Ungleichungen 2 -, Systeme von 24-25, 95-103 (s.

auch konvexe Gebiete, lineare GIeichung)

Lineares Programm -, Aquivalenz von Spiel und 328-334 -, Geometrie des 191-199

in abgekiirzter Koeffizientenform 82 - mit nach oben begrenzten Variablen

418-437 -, verallgemeinertes 490-498 (s. auah

lineare Programmierung, Simplex­methode)

Lineares Programmierungsmodell 7, 23, 24

-, Aufstellen eines 38-79, 625-632 -, Tableauform eines 49 -, vielstufiges 9 Lineares Ungleichungsproblem 10, 99 Linearitat 20, 23 - der Zielfunktion 40 Linearkombination 26 - von GIeichungen 82 - von Vektoren 206 Losbares GIeichungssystem 81

lUanagement Science 4 Manager einer Werkzeugmaschinen-

fabrik -, Beispiel des 292-299 Markoffsches Gleichungssystem 241 Markoffsche Ketten 10 Mathematische Programmierung 2 -, Beziehung zwischen Automation

und 11-13 (s. auch Programmie­rungsproblem)

Matrix, Matrizen -, Addition von 213 -, Alternativsatz fiir 25, 162 -, Definition der 212 -, doppelt stochastische 362 - eines Spieles 318 (s. auch Spiele) - eines Transportproblems 346 -, elementare 230 -, Inverse einer 219-225 -, Multiplikation von 216 -, nichtsingulare 219

704 Sachverzeiclmis

Matrix, Matrizen -, Produkt von 216 -, Produkt von Vektor und 214, 216 -, schiefsymmetrische 331 -, Transponierte einer 213, 224

(s. auch Vektor) Matrixalgebra 217-219 Matrixspiel 318-328 -, aquivalentes lineares Programm zu

einem 329 -, Definition des 319 -, Losung eines 330 - -, konstruktives 334-340 -, Wert eines 330 Matrizenoperationen 212-217 Metallegierung -, Herstellung einer optimalen 50-58 Metallindustrie 35 Minimallosung -, globale 166, 177 -, lokale 167, 177 Minimaxsatz 25, 29 -, Beweis des 329-330, 334-340 Mischstrategie 326, 328 -, optimale 328, 333, 337 Mischungsprobleme -, Anwendung der Simplexmethode

auf 128 -, Beispiele von 50, 54, 58, 186 Mittelwert mit Gewichten 55 Modell -, Aufstellung eines 6 -, Leontiefsches 20, 22 -, mathematisches 2,6 -, vielstufiges 9 -, Walrasisches 19 Morra 30 Multiplexmethode 31 lVlultiplikatoren 82 (s. auch Simplex.

multiplikatoren) - von LAGRANGE 163-167, 243, 534 - -, Definition der 164, 206

Nahrwerte von Lebensmitteln 630 National Bureau of Standards 30, 31 Netzwerk 10, 32, 343, 400-417,

438-457 -, Definition des 400 - in der Ebene «7 -, Knotenpunkt (Punkt) in einem 400 -, kiirzester Weg in einem (s. Problem

des kiirzesten Weges) - mit Kapazitaten 27

Netzwerk -, Problem des maximalen Flusses

in einem 385-403 -, Baummethode zur Losung des

452-457 -, Theorie von FORD und FULKER·

SON zum 438-457 -, zusammenhangendes 394 Nichtlineare Programmierung 10 (s.

auch konvexe Programmierung, dis· krete Programmierung)

Nichtnegativitat 7, 39 Nichttriviale Losung eines homogenen

Systems 159 Normalform eines linearen Programms

68,100-103

Olraffinerien 34 Operations Research 6 Optimalitatstest 111-112

Papiermiihlen 35 Permutation 360 Permutationsmatrix 362 Phase I der Simplexmethode llO, 120 -, anderes Kriterium fiir 289 Phase II der Simplexmethode llO, 121 -, gestortes Problem fiir 270 Pillenproblem 301-304 Pivot 89 Pivot·Blocke 233 Pivot·Gleichung 92 Pivot·Operationen 92, 139, 200-204 -, Eigenschaften von 200 - 204 - mit Pivot·Blocken 233 Pivot.Teilsystem 201 Pivot·Theorie 200-204 Pivot·Variable 92 Plan (s. Programm) Planung

bei variablen Kosten 566-571 - mittels diskreter Programmierung

583 -, Organisation der 26 - von Aktivitaten iiber einen Zeit·

raum 5 Polyeder 176 Posten 38, 69 Postenmenge 41 Preisbegriff in der linearen Program.

mierung 292-317 -, Vorzeichenvereinbarung beim 304

Sachverzeichnis 705

Preise 27, 243 -, implizite (s. Simplexmultiplikato-

ren) Preisfestsetzung (pricing out) 249, 305 Primale-duale Methoden 276,283-289 Primales System 25, 57, 144 -, beschranktes 283 - -, erstes 287 Primales und duales System, Beziehun­

gen zwischen 278 Problem

der Ausbildung auf der Arbeitsstatte 5,65-68,77-79

der tixen Kosten 584, 618 der KontraktwaW 35 der Lagerhaltung 63-65, 77, 476,

571-575 der lateinischen Quadrate 621 der leeren Behalter 584 der optimalen Zuordnung 361-367 der Produktemischung 58-63,

73-76, 186, 189 der Servietten 417 der Tankschiffbeschaffung 515 -, Gesprach tiber das 515-523 der vielstufigen Maschinenplanung

584 des chemischen Gleichgewichts 545 des Fabrikanten von Ernahrungs­

pilien 301-304 des Flugplans bei ungewisser Nach­

frage 644-670 des ehrgeizigen Industriellen

299-301 des Handlungsreisenden 584,

619-620 des Konservenfabrikanten 3 des ktirzesten Weges 382, 411-416,

584, 586 (s. auch Umladeproblem) des Managers einer Maschinenfabrik

292-299 des Managers mit fast unabhangigen

Betrieben 507 des Speiseplans 625-643 des Versandplans per Flugzeug 584 des Zeltplatzes 321-322 kombinatorischer Natur 361, 584

-, probabilistisches 10 Produkt von Matrizen -, Definition des 217 Produktemischung 58-63,73-76, 186,

189

Produktionskontrolle 12 Produktionsplanung, Produktionspro­

bleme 26 Program Monitoring (Programmkon­

trolle) 17 Programm2 -, Beziehung zwischen, und Automa-

tion 11-13 -, Definition des 2 -, Klassifizierung eines 8-11 -, konvexes 490-505, 534-565 -, mathematisches 2

mit veranderlichen Koeffizienten 490-506 (s. auch verallgemeiner­te Programme von WOLFE)

-, unendliches 28 -, umfangreiches 490 (s. auch De-

kompositionsprinzip) -, vielstufiges (s. vielstufige Pro­

gramme) -, zulassiges 41 (s. auch lineare Pro-

grammierung) Programmierung -, lineare (s. lineare Programmierung) -, mathematische 2 -, nichtlineare 10 (s. auch konvexe

Programmierung, diskrete Pro­grammierung)

-, parametrische 276 -, Algorithmus fUr 280-283 unter UngewiBheit 33, 566-582 -, Minimale Varianz bei festen Er­

wartungskosten bei 569-571 -, Minimierung der Erwartungs­

kosten bei 567 -568 Programmierungsmodell 6 Programmierungsproblem 2

(s. auch lineare Programmierung) -, deterministisches 8 -, Klassifizierung eines 8-11 -, lineares 38-40, 68 -, probabilistisches 9 (s. auch Pro-

grammierung unter UngewiBheit) Programmierungstableau 48-49 Projektionsmethode 30 Proportionalitat 7, 23, 38-39, 69 ProzeB 7 (s. Aktivitat) Punkt - in einem Graphen 400 - in n Dimensionen 173

Quadratische Form -, Konvexitat einer 556

706 Sach verzeichnis

Quadratische Form, positiv (semi-) definite 556

Quadratische Programmierung 32, 555-563

-, Algorithmus fur 563 -, Anwendungen der 555 -, Eigenschaft der Komplementaritiit

der Basen bei 559 -, Optimalitiitskriterien fUr 558

Rang einer Matrix 218

- eines Gleichungssystems 204 - eines Vektorraums 210 RAND-Corporation VIII, IX, X, 15, 29,

31 RAND-Kodes 15 Raum (s. Vektorraum) Rechenkodes 15, 31, 232, 250, 265 Rechentechniken 30 Reduktion

auf ein Ungleichungssystem 103 auf kanonische Form 224-225 eines Spieles auf ein symmetrisches

Spiel 331-333 eines Programms auf ein symmetri-

Bches Spiel 333-334 Regression 555 Relaxationsmethode 30 Rentable Produktion 555 Rucksackproblem 586

Sattelpunkt 325 Scheinvariable (s. kiinstliche Variable) Schema (s. Programm) Schiffsrouten 35 Schlinge eines linearen Graphen 477 Schlupf 157 Schlupfkante 477 Schlupfvariable 68, 100 Schnitt 447 - minimaler, und maximaler FluB 447 Schnittwert 447 Schwarzer Kasten 38 Schwerpunkt 56, 107, 186 Scoop 17,18 SEAC 15 Sensitivitiitsanalyse 305-316 Serviettenproblem 417 Simplex 189, 190 Simplexalgorithmus 110-117, 270 -, Endlichkeit des 117, 139, 142, 270

Simplexalgorithmus in Matrizenform 226-234

-, Induktionsbeweis fiir den 139-143 -, Varianten des 275-291

(s. auch Simplexmethode) Simplexmethode 1, 18,29-30,110-138

bei Variablen mit oberen Grenzen 420-423,427-428

beim Beweis des Dualitiitssatzes 150-155

-, duale 278-280 -, Endlichkeit der, bei Starung

262-274 -, FluBdiagramm fiir 122 -, geometrische Interpretation der

181-185 -, Lasung des Transportproblems mit

der 345-353 -, Lasung des Umladeproblems mit der

394-398 -, Methode der Lagrange-Multiplika­

toren und 167 mit Multiplikatoren 124, 243-261 - bei Variablen mit oberen Gren­

zen 427-428 -, rechentechnische Bemerkungen

zur 249-251 -, rechentechnische V orteile der

243-244 -, Preismechanismus der 292-317 -, reguliire 243 -, revidierte 243 (s. Simplexmethode

mit Multiplikatoren) -, Simplexinterpretation der 185-191

und Dekompositionsprinzip 510-511 (B. auch Phase lund Phase II der Simplexmethode, SimplexalgorithmuB)

Simplexmultiplikatoren 228, 243, 245, 249-250,254,271,490

beim gewichteten Zuteilungspro­blem 473-474

beim Transportproblem 349 Simplexmultiplikatoren beim

Umladeproblem 390 - beim Zuordnungsproblem 371 -, Definition der 254, 490 - interpretiert als Preise 292-317 Skalarkomponenten 205 Skalares Vielfaches 206 Spaltenspieler 320 -, Problem des 329

Sachverzeiclmis 707

Spaltenvektor 205 Spiele -, strikt determinierte 322 -, symmetrische 331 - -, Reduktion auf 331-334 -, Theorie der 28, 29 - und lineare Programme 318-342

(s. auch Matrixspiel) -, Zweipersonen-Nullsummen- 10

(s. auch Minimaxsatz) Spieler bei Matrixspiel 319 -, konservativer 325 Standardform eines linearen Programms

68,100-103 Standardproblem del' linearen Program­

mierung 40 Statistisches Kontrollsystem 16 Stochastische Programmierung (s. Pro-

grammierung unter UngewiBheit) Strahl 194 Strategie -, gemischte 326, 328 - -, optimale 328, 333, 337 -, reine 319 (s. auch Spiele) Streckenprobleme 19 Strukturmatrix 33 Summe -, gewichtete 206 - von Matrizen, Definition del' 213 - von Vektoren, Definition del' 206 Systeme linearer Gleichungen odeI' Un­

gleichungen 2,24,80-109 Systeme (s. auch lineare Gleichung,

lineare Ungleichungen) -, abhangige 83 -, aquivalente 85, 202-204 -, diagonale 89 -, dreieckige 89 -, homogene 26, 158,219

-, nichttriviale Lasung fiir 159 -, Satz von GORDAN fiir 158 -, Satz von STIEMKE fiir 160 - und unbeschraukte Lasungs-

mengen 513-514 -, inkonsistente 81, 95 -, Inkonsistenzsatz fiir 202 -, irredundante 83 -, kanonisch-aquivalente 93-94 -, kanonische 87 -95, 110, 201, 220,

251 -, konsistente 81, 95 -, lasbare 81, 95

Systeme, quadratische 87 -90 -, redundante 83 -, Redundanzsatz fiir 202 -, reduzierte 92 -, Rang bei 204 -, unabhangige 83 (s. auch

lineare Gleichung) -, unlasbare 81, 95 -, unzulassige, zulassige 81, 95, 149

Tableau economique 15, 19, 22 Theorie von FORD und FULKERSON

438-452 Transportproblem 22, 30, 32, 72,

118-119, 343-360 (s. auch Zu­ordnungsproblem, Umlade­problem)

-, Algorithmus fiir das 353-358 -, Definition des 343 -, Dreieckseigenschaft del' Basen beim

348 -, Entartungsfall beim 351-353 -, Ganzzahligkeit del' Basisvariablen

beim 349 -, Geschichtliche Ubersicht iiber das

343-344 -, klassisches 343 -, kapazitiertes 420-434 - -, Aquivalenz des Transportpro-

blems und des 433-434 -, Lasung des, durch die Simplex­

methode 346-353 -, Lasung des, mit beschrankten Vari­

ablen 428-436 - mit beschrankten Partialsummen

von Variablen 434-436 -, primale-duale Methode fiir das 458

-467 -, Problem des Konservenfabrikanten

als Beispiel fiir das 3-4. 42 -, Regel del' kleinsten Kosten fiir das

354,376 -, Tabelle fiir das 345-346 -, Variablen mit festen Werten fiir das

376 -, zulassige Lasungen fiir das (s. Basis-

lasung) Transpositionssatz 25, 161 Treppensysteme 529 Triviale Lasung eines homogenen Sy­

stems 159

708 Sachverzeichnis

Tucker-Diagramm 145, 148, 161, 277 (s. auch duales lineares Programm)

Umladeproblem 27, 382-399 (s. auch Problem des kiirzesten Weges)

-, Aquivalenz von Transportproblem und 390-393

-, Dreieckseigenschaft der Basen beim 388

-, Formulierung des 382-383 -, Losung des, mittels des zugehorigen

Graphen 406-410 -, Losung des, mit der Simplexmethode

394-398 -, Netzwerke und 384-385, 400-417 -, Standardform des 386-390 -, U mladeverfahren fur das 386 -, Verfahren des direkten Versands fiir

das 385 -, zulassige Losungen fiir das (s. Basis­

losung) Umladevariable 387 Ungarische Methode 283, 458 (s. auch

Zuordnungsproblem) UngewiJ3heit 9, 33, 566-582 Ungleichung (s. lineare Ungleichungen) UNIVAG31 Unlosbares Gleichungssystem 81 Unternehmungsforschung 6 Unternehmensfiihrung -, Wissenschaft von der 6 UnzuIassige Gleichung 103 Unzulassige Ungleichung 95 Unzulassigkeitsform 120, 270, 632, 634 Unzulassigkeitssatz 150, 159

Variablen -, diskrete 583 - 624 -, fiihrende 276 - -, Methode der 276 -, ganzzahlige (s. diskrete Variablen) -, kiinstliche 110, 119-120, 151, 252,

270 bei der dualen Simplexmethode

279-280 (s. auch Phase I der Simplexmethode)

mit oberen Grenzen 418-437 -, nichtganzzahlige 589 Varianten des Simplexalgorithmus

274-291 Varianz -, minimale 555, 569

Vektor -, Darstellung eines, in bezug auf eine

Basis 210 -, Definition des 205 -, lexiko-positiver 273, 337 -, linear abhangiger 207 -, Produkt von Matrix und 214 Vektoren -, linear abhangige Menge von 208 -, linear unabhangige Menge von 207 -, Rechenoperationen mit 205-206 Vektorgleichungen 208 Vektorraum 208-210 Verallgemeinertes Programm von

WOLFE 490-498 - als lineares Programm 491 -, aquivalente Formulierung eines 496 -, Definition des 491 -, Hauptprogramm fiir 491 - -, beschranktes 495 -, Hilfsprogramm (Teilprogramm) fUr

495 -, Spezialfalle 498-505 - zur Losung des Problems von KUHN

und TUCKER 535 Veranderung

der Input-Output-Koeffizienten 308, 312

der konstanten Koeffizienten 309 der relativen Kostenfaktoren 307,

310 Verbindungsstrecke 173 Vermutung von HIRSCH 186, 193 Verschnittproblem 584 Vertragsangebote 19 Vielstufige Modelle (Programme, Pro­

bleme) 9, 10 -, Anwendung des Dekompositions­

prinzips auf 528-532 bei UngewiJ3heit 575-580 (s. auch

Planung von Aktivitaten uber einen Zeitraum)

Vielzweckmaschinen 13 Vierfarbenproblem 622 V orzeichenvereinbarung bei Preisen 304

Walrasisches System 19 War Production Board 16 Wartungsplane 19 Welfare Economics 23 Werkzeugmaschinenfabrik -, Manager der 292-299

Sachverzeichnis 709

Wirtschaftsmodelle und lineare Pro-grammierung 19-24, 292

Zeilenspieler 320 -, Problem des 329 Zentralplanung ohne vollstandige In-

formation am Zentrum 523-527 Zielfunktion (Zielform) -, homogene 543-546 -, konvex-separable 547 -555 -, lineare 40, 70 -, nichtlineare, und diskrete Program-

mierung 613-615 -, unbeschrankte 139, 150 Zufall und Bluff 323-324 Zufallsereignis 9 Zufalls-Auswahl-Regel 117, 143, 256,

265 (s. auch Kreisen) Zulassige Losungen 70, 177, 179, 180

(s. auch Basislosung) -, Definition der 70

fiir Anfangsbasis 27, 111, 118 (s. auch Phase I der Simplexmethode)

fiir primales und duales System 149 -, konvexe Mengen von 176 (s. auch

Extrempunkte) -, optimale 71 Zulassiges Programm 41 Zuordnung mit Uberschu13 und Defizit

367-376 - als Transportproblem 368 -, Beispiel der, mit Schlupf 372

Zuordnungsproblem 283, 357, 361, 584, 586 (s. Zuteilungsprobleme, Zutei­lung von Flugzeugen zu Strecken)

-, Aquivalenz von Transportproblem und 364

-, Definition des 361 -, Entartung beim 363 -, typische Anwendungen des 366 Zuteilung von Flugzeugen zu Strecken

644-670 - bei fester Nachfrage 646-651 - bei ungewisser Nachfrage 652-670 -, Formulierung des Problems der 644 Zuteilungsprobleme 361-381,

418-419 (s. auch Zuordnungs­probleme)

mit festen Werten 376 mit Gewichten 26,468-489 -, Anfangslosung fUr 471 -, Beispiel fiir 650 -, fest dreieckige Form der Basen

fUr 474 -, Graphenstruktur der Basis fUr

476-481 -, Standardform der 468 -, Teilklasse mit optimalen Basen

von Dreiecksform bei 481-488

und primale-duale Methode 283 Zuwachs der Nachfrage 654 Zuwachsvariable 654 Zuwachswert 654

Namenverzeichnis

Ablow, C. 31 Aiken 15 Almon, C. IX, 292, 523 Arrow, K. J. 11, 22, 32

Babbage 15 Balinski, M. VIII Barankin, E. W. 32, 555 Barth, E. X Baumol, W. J. VIII, 24 Beale, E. M. L. 31, 32, 117, 141,262,

264, 265, 272, 273, 276, 591 Beckenbach, E. F. X Beckmann, M. J. 24 Bell, E. J. X Bellman, R. 11,414,579 Belz, M. H. 35, 584 Berge, C. 32 Birkhoff, G. 32, 363 Blattner, W. O. IX, 305 Boelter, L. M. K. 12 Borden, J. VIII Borel, E. 29, 319 Bose, R. C. 621 Bott, D.XII Brede, 1\'I. XII Brigham, G. 31 Brown, G. W. 22, 30. 31, 333 Burns, R. X

Cahn, A. 18, 30, 467 Carroll, L. 39 Charnes, A. 15. 24, 29, 30, 32, 34, 265,

273,467,547,615 Chatto, K. 137 Clark, J. IX Clasen, R. 459 Cooper, W. W. 15, 24, 29, 30, 34, 467 Cornfield, J. 21, 625 Cottle, R. X Cox, C. B. 137 Crandall, H. W. 24, 34 Curtiss, J. H. 18, 30 Cutler, L. IX, 276

Dalkey, N. C. 29 Dalks, F. M. 517 Dantzig, A. S. V, X Dantzig, G. B. XI, 2, 15, 28, 29, 31, 32,

33, 34, 35, 139, 243, 265, 266, 273, 276, 283, 289, 330, 333, 334, 348, 413, 414,418,452,467,490,503,508,534, 545,547,555,566,575,578,579,590, 608,615,618,619,644,645,646

Dantzig, T. V Diehl, H. XII Diehm, C. 31 Dines, L. L. 25 Doig, A. G. 35, 584 Dorfman, R. IX, 15, 18, 22, 23, 24, 32,

301, 334, 555 Dresher, M. IX, 29, 318 Duffin, R. J. 28 Dvoretsky, A. 11

Edmondson, J. H. 265 Eckert 15 Egervary, E. 32, 283, 344, 458 Einstein, H. IX Eisemann, K. 35, 584 El.Agizy, M. X Elmaghaby, S. E. 569 Eufinger, J. XII Euler, L. 621 Evans, W. D. 21, 22

Fabian, T. IX, 24, 35 Farkas,J. 15,26,144,159 Feller, W. 566 Ferguson, A. R. 35, 566, 644, 645, 646 Fisher, W. D. 35 Flood, M. M. 22, 458, 619 Ford, L. R. 15, 32, 276, 283, 289, 344,

438,447,458,459,508 Fourier, J. B. 14, 15, 25, 98, 108, 195,

198 Frisch, R. 31 Fulkerson, D. R. VIII, 15, 29, 32, 33,

35, 276, 283, 289, 344, 414, 438, 447, 452, 458. 459, 508, 590, 619

Namenverzeichnis 711

Gaddum, J. W. 417 Gainen, L. 35 Gale, D. 15, 22, 29, 144, 318, 330, 331,

414,621 Garvin, W. 24, 34 Gass, S. 276, 282 Gauss, K. F. 15,24,88 Gavurin, M. K. 27, 343 Geisler, M. A. 15, 17, 19, 22 Georgescu-Roegen, N. 22 Gibrat, R. 15, 24, 35 Glicksberg, 1. 11, 577 Goldman, A. J. 29,144 Goldstein, L. 35 Goldstine 15 Gomory, R. VIII, 33, 284, 490, 583, 590,

591,604,607 Gordan, P. 15, 25, 158, 159 Greene, J. H. 137 Gross, 0.11 Gunther, P. 659

Hahnos, P. R. 367, 380 Harary, F. 477 Harris, T. E. X, 11 Hartley, H. O. 534 Haydon,B. X Hehner, O. 29 Henderson, A. 30, 34 Hermann, C. C. 7 Hicks, C. R. 137 Hirsch, W. M. 186, 193, 618 Hitchcock, F. L. 15,234,344,356,382,

418,458 Hoffenberg, M. 21, 22 Hoffman, A. J. VIII, 30, 31, 32, 117,

141, 262, 263, 265, 272, 417, 586 Hogan, J. X Hollerith 15 Houthakker, H. S. 32 Hu, T. C. 490 Huppertsberg, B. XII Hurwicz, L. 22, 29, 32

Jackson, J. R. 34 Jacobs, W. W. 19,417 Jaeger, A. 513 Jaeger, E. XII Jewell, W. S. 508 Jochim, V. XII John, J. B. 24, 34 Johnson, S. 15, 33, 545, 555, 584, 590,

619 Jordan, W. 24

Judd, H. 276 Juncosa, M. L. 35 Kalaba, R. E. 35

Kantorowicz, L. V. 14, 15, 26, 27, 75, 343

Karlin, S. 29 Kawarantani, T. K. 503 Kelley, J. E. 197 Kemeny, J. G. 77 Kiefer, J. 11 Konig, D. 401, 477 Koopmans, T. C. 1,7,15,18,20,22,23,

24,29,30,234,344,385,390,400,418 KruskaI, J. B., Jr. 586 Kuhn, H. W. VIII, 15, 22, 28, 29, 32,

144, 276, 283, 318, 319, 330, 331, 344, 458,497,534

Kiinzi, H. P. XI

Laderman, J. 15, 30, 625 Lagrange, J. L. 163, 164, 167 Land, A. H. 35, 584 Lerned, E. P. 17 Lemke, C. E. 31, 32, 276, 289, 547, 615 Leontief, W. 15, 17, 20 Lerner, A. 22 Little, J. 459 Luce, R. D. 318

Madansky, A. IX, 33, 566, 575, 579 Magee, J. F. 7 Manne, A. S. 15, 24, 34, 434, 584, 615 Mannos, M. 30 Marek, M. R. X Marcus, M. 363 Markowitz, H. 15, 24, 32, 290, 481, 483,

489, 555, 556, 569, 571, 584, 615 Marschak, J. II, 22 Masse, P. 11, 15, 24, 35 Mauchley 15 Maynard, H. B. 35 McCoy, L. H. 25 McKinsey, J. C. C. 29 Mellon, B. 15, 24, 34 Minkowski, H. 15, 26, 198 Monroe, A. E. 19 Montalbano, M. 31 Moore, E. F. 414 Morgenstern, O. 15, 22, 25, 28, 319,331 Morin, G. 35 Motzkin, T. 15, 24, 25, 30, 98, 108, 161,

195,198 Munkres, J. 458

712 Namenverzeichnis

Nachtigal, E. X Natrella, J. V. 19 Neyrnan,J.15,21,28 Norton, J. 17

Ollmert, H.·J. 262, 265, 273 Orchard-Hays, W. IX, 15, 31, 78, 115,

232, 243, 276, 282 Orden, A. 15, 30, 31, 139, 232, 265, 266,

273, 359, 360, 382

Parker, E. T. 621 Pascal 15 Paull, A. E. 35, 584 Pearson, E. S. 28 Pearson, K. 21 Peters, K. XII Prager, W. 417, 467 Pyne, I. B. 31

Quade, E. S. X Quesnay 15, 19, 20

Rabusseau, R. XII Raiffa, H. 30, 318 Randolph, P. IX Rawlings, E. W. 17 Reiter, S. 22, 385, 390, 575 Renkewitz, H. XII Robacker, T. 131 Rosen, J. B. 33 Rutsch, M. XII Ryan, M. IX

Saaty, T. L. 276, 282 Salveson, M. E. 34 Samuelson, P. 15, 18, 22, 23, 24, 301 Scarf, H. 574 Schlaifer, R. 34 Schoenberg, I. J. 30 Schruben, L. W. 35 Schulmann, H. XII Shapiro, M. IX Shapley, L. S. IX, 29, 341 Shaw, C. 418 Shukhande,S.S.621 Simon, H. 22, 575 Slater, M. 534 Sokolowsky, D. 30, 417 Solow, R. M. 15,24,301 Spellman, R. A. 24, 34

Steinberg, D. A. X Steinitz, E. 198 Stewart, D. G. X Stibitz 15 Stiemke, E. 15, 25, 160 Stigler, G. J. 5, 30, 567, 625, 626, 627,

633 Stokes, R. W. 25 Sussman, B. X Symonds, G. H. 24, 34

Theil, H. 575 Thompson, G. L. 30 Thornton, C. B. 16 Thrall, R. M. 30, 73 Tompkins, C. B. 22, 30 Trinkl, F. IX Tucker, A. W. V, VIII, 15, 18, 22, 25,

28, 29, 32, 85, 100, 144, 145, 158, 161, 162, 180, 200, 232, 318, 319, 330, 331, 334, 337, 338, 497, 534, 620

Ullman, R. J. 503 Uzawa, H. 32, 534

Vajda, S. 31 Vallee Poussin, A. de la 25 Van Slyke, R. M. IX, X Vaughan, H. E. 367, 380 Ville, J. 25, 29, 161 Von Neumann, J. 7, 15, 18, 19, 25. 28,

29, 143, 144, 145, 318, 319, 328, 330, 331,363

Wade, B.L. X Wald, A. 11, 15, 28 Walras, L. 19 Walter, J. R. 35, 584 Waugh, F. V. 131, 261 Wenke, K. 513 Wets, R. X Weyl, H. 25 White, W. B. 545, 555 Wiegman, N. 30 Williams, J. D. V, VIII, 15, 29, 318,

319, 320, 321, 326, 534 Wolfe, P. IX, 15,32, 38, 139, 198,232,

265,266,273,276,324,490,508,534, 555, 556, 571, (j16

Wolfowitz, J. 11 Wood, M. K. 2, 15, 17, 19, 22

Gesamtherstellung: Konrad Triltsch, Graphischer Grofibetrieb, Wiirzburg