[prev] [prev-tail] [tail] [up]

References

Principal texts

1.
Sharma, J. K. (2012), Operations Research: Problems and Solutions (3rd ed.), New Delhi, Macmillan.
2.
Hillier, F. S., and Lieberman, G. J. (2015), Introduction to Operations Research (10th ed.), New York, McGraw-Hill.
3.
Bertsimas, D., and Tsitsiklis, J. N. (1997), Introduction to Linear Optimization, Belmont, Athena Scientific.

Recommended texts

1.
Chvátal, V. (1983), Linear Programming, New York, W. H. Freeman.
2.
Taha, H. A. (2017), Operations Research: An Introduction (10th ed.), Harlow, Pearson.
3.
Winston, W. L. (2004), Operations Research: Applications and Algorithms (4th ed.), Belmont, Brooks/Cole.

Software

1.
Harris, C. R., et al. (2020), Array programming with NumPy, Nature, 585, 357–362.
2.
Virtanen, P., et al. (2020), SciPy 1.0: fundamental algorithms for scientific computing in Python, Nature Methods, 17, 261–272.
3.
Huangfu, Q., and Hall, J. A. J. (2018), Parallelizing the dual revised simplex method, Mathematical Programming Computation, 10, 119–142.

Further reading

1.
Arrow, K. J., Harris, T., and Marschak, J. (1951), Optimal inventory policy, Econometrica, 19, 250–272.
2.
Beale, E. M. L. (1955), Cycling in the dual simplex algorithm, Naval Research Logistics Quarterly, 2, 269–275.
3.
Bellman, R. (1957), Dynamic Programming, Princeton University Press.
4.
Bellman, R. (1957), A Markovian decision process, Journal of Mathematics and Mechanics, 6, 679–684.
5.
Bellman, R. (1958), On a routing problem, Quarterly of Applied Mathematics, 16, 87–90.
6.
Birkhoff, G. (1946), Tres observaciones sobre el álgebra lineal, Universidad Nacional de Tucumán, Revista, Serie A, 5, 147–151.
7.
Blackett, P. M. S. (1962), Studies of War: Nuclear and Conventional, Edinburgh, Oliver and Boyd.
8.
Bland, R. G. (1977), New finite pivoting rules for the simplex method, Mathematics of Operations Research, 2, 103–107.
9.
Box, G. E. P., and Muller, M. E. (1958), A note on the generation of random normal deviates, Annals of Mathematical Statistics, 29, 610–611.
10.
Bradley, S. P., Hax, A. C., and Magnanti, T. L. (1977), Applied Mathematical Programming, Reading, Addison-Wesley.
11.
Charnes, A. (1952), Optimality and degeneracy in linear programming, Econometrica, 20, 160–170.
12.
Charnes, A., and Cooper, W. W. (1961), Management Models and Industrial Applications of Linear Programming, New York, Wiley.
13.
Charnes, A., Cooper, W. W., and Ferguson, R. O. (1955), Optimal estimation of executive compensation by linear programming, Management Science, 1, 138–151.
14.
Cyert, R. M., Davidson, H. J., and Thompson, G. L. (1962), Estimation of the allowance for doubtful accounts by Markov chains, Management Science, 8, 287–303.
15.
Dantzig, G. B. (1951), Maximization of a linear function of variables subject to linear inequalities, in T. C. Koopmans (ed.), Activity Analysis of Production and Allocation, New York, Wiley, 339–347.
16.
Dantzig, G. B. (1955), Upper bounds, secondary constraints, and block triangularity in linear programming, Econometrica, 23, 174–183.
17.
Dantzig, G. B., and Orchard-Hays, W. (1954), The product form for the inverse in the simplex method, Mathematical Tables and Other Aids to Computation, 8, 64–67.
18.
Dantzig, G. B., Fulkerson, D. R., and Johnson, S. M. (1954), Solution of a large-scale traveling-salesman problem, Journal of the Operations Research Society of America, 2, 393–410.
19.
Derman, C. (1963), On optimal replacement rules when changes of state are Markovian, in R. Bellman (ed.), Mathematical Optimization Techniques, Berkeley, University of California Press, 201–210.
20.
Dijkstra, E. W. (1959), A note on two problems in connexion with graphs, Numerische Mathematik, 1, 269–271.
21.
Edgeworth, F. Y. (1888), The mathematical theory of banking, Journal of the Royal Statistical Society, 51, 113–127.
22.
Edmonds, J. (1965), Maximum matching and a polyhedron with 0,1-vertices, Journal of Research of the National Bureau of Standards, 69B, 125–130.
23.
Edmonds, J., and Karp, R. M. (1972), Theoretical improvements in algorithmic efficiency for network flow problems, Journal of the ACM, 19, 248–264.
24.
Egerváry, J. (1931), Mátrixok kombinatorius tulajdonságairól, Matematikai és Fizikai Lapok, 38, 16–28.
25.
Erlang, A. K. (1909), Sandsynlighedsregning og telefonsamtaler, Nyt Tidsskrift for Matematik B, 20, 33–39.
26.
Erlang, A. K. (1917), Løsning af nogle problemer fra sandsynlighedsregningen af betydning for de automatiske telefoncentraler, Elektroteknikeren, 13, 5–13.
27.
Farkas, J. (1902), Theorie der einfachen Ungleichungen, Journal für die reine und angewandte Mathematik, 124, 1–27.
28.
Fiacco, A. V., and McCormick, G. P. (1968), Nonlinear Programming: Sequential Unconstrained Minimization Techniques, New York, Wiley.
29.
Ford, L. R., and Fulkerson, D. R. (1956), Maximal flow through a network, Canadian Journal of Mathematics, 8, 399–404.
30.
Forrest, J. J. H., and Tomlin, J. A. (1972), Updated triangular factors of the basis to maintain sparsity in the product form simplex method, Mathematical Programming, 2, 263–278.
31.
Gal, T., and Greenberg, H. J. (eds.) (1997), Advances in Sensitivity Analysis and Parametric Programming, Boston, Kluwer.
32.
Gale, D., Kuhn, H. W., and Tucker, A. W. (1951), Linear programming and the theory of games, in T. C. Koopmans (ed.), Activity Analysis of Production and Allocation, New York, Wiley, 317–329.
33.
Garey, M. R., Johnson, D. S., and Sethi, R. (1976), The complexity of flowshop and jobshop scheduling, Mathematics of Operations Research, 1, 117–129.
34.
Gass, S. I., and Saaty, T. L. (1955), The computational algorithm for the parametric objective function, Naval Research Logistics Quarterly, 2, 39–45.
35.
Goldfarb, D., and Reid, J. K. (1977), A practicable steepest-edge simplex algorithm, Mathematical Programming, 12, 361–371.
36.
Gomory, R. E. (1958), Outline of an algorithm for integer solutions to linear programs, Bulletin of the American Mathematical Society, 64, 275–278.
37.
Halfin, S., and Whitt, W. (1981), Heavy-traffic limits for queues with many exponential servers, Operations Research, 29, 567–588.
38.
Hammersley, J. M., and Morton, K. W. (1956), A new Monte Carlo technique: antithetic variates, Mathematical Proceedings of the Cambridge Philosophical Society, 52, 449–475.
39.
Harris, F. W. (1913), How many parts to make at once, Factory, The Magazine of Management, 10, 135–136, 152.
40.
Harris, P. M. J. (1973), Pivot selection methods of the Devex LP code, Mathematical Programming, 5, 1–28.
41.
Hitchcock, F. L. (1941), The distribution of a product from several sources to numerous localities, Journal of Mathematics and Physics, 20, 224–230.
42.
Hoffman, A. J., and Kruskal, J. B. (1956), Integral boundary points of convex polyhedra, in H. W. Kuhn and A. W. Tucker (eds.), Linear Inequalities and Related Systems, Annals of Mathematics Studies 38, Princeton University Press, 223–246.
43.
Howard, R. A. (1960), Dynamic Programming and Markov Processes, Cambridge, MIT Press.
44.
Hull, T. E., and Dobell, A. R. (1962), Random number generators, SIAM Review, 4, 230–254.
45.
Jackson, J. R. (1955), Scheduling a Production Line to Minimize Maximum Tardiness, Research Report 43, Management Science Research Project, University of California, Los Angeles.
46.
Jackson, J. R. (1957), Networks of waiting lines, Operations Research, 5, 518–521.
47.
Johnson, S. M. (1954), Optimal two- and three-stage production schedules with setup times included, Naval Research Logistics Quarterly, 1, 61–68.
48.
Kantorovich, L. V. (1939), Mathematical Methods of Organizing and Planning Production (in Russian), Leningrad State University; English translation (1960), Management Science, 6, 366–422.
49.
Karmarkar, N. (1984), A new polynomial-time algorithm for linear programming, Combinatorica, 4, 373–395.
50.
Karp, R. M. (1972), Reducibility among combinatorial problems, in R. E. Miller and J. W. Thatcher (eds.), Complexity of Computer Computations, New York, Plenum, 85–103.
51.
Karush, W. (1939), Minima of Functions of Several Variables with Inequalities as Side Conditions, M.Sc. dissertation, University of Chicago.
52.
Kelley, J. E., and Walker, M. R. (1959), Critical-path planning and scheduling, Proceedings of the Eastern Joint Computer Conference, 160–173.
53.
Kemeny, J. G., and Snell, J. L. (1960), Finite Markov Chains, Princeton, Van Nostrand.
54.
Kendall, D. G. (1953), Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain, Annals of Mathematical Statistics, 24, 338–354.
55.
Khachiyan, L. G. (1979), A polynomial algorithm in linear programming, Soviet Mathematics Doklady, 20, 191–194.
56.
Khintchine, A. Y. (1932), Mathematical theory of a stationary queue (in Russian), Matematicheskii Sbornik, 39, 73–84.
57.
Klee, V., and Minty, G. J. (1972), How good is the simplex algorithm?, in O. Shisha (ed.), Inequalities III, New York, Academic Press, 159–175.
58.
König, D. (1931), Gráfok és mátrixok, Matematikai és Fizikai Lapok, 38, 116–119.
59.
Koopmans, T. C. (ed.) (1951), Activity Analysis of Production and Allocation, New York, Wiley.
60.
Kuhn, H. W. (1955), The Hungarian method for the assignment problem, Naval Research Logistics Quarterly, 2, 83–97.
61.
Kuhn, H. W., and Tucker, A. W. (1951), Nonlinear programming, in J. Neyman (ed.), Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, University of California Press, 481–492.
62.
Land, A. H., and Doig, A. G. (1960), An automatic method of solving discrete programming problems, Econometrica, 28, 497–520.
63.
Law, A. M. (2015), Simulation Modeling and Analysis (5th ed.), New York, McGraw-Hill.
64.
Lehmer, D. H. (1951), Mathematical methods in large-scale computing units, Proceedings of the Second Symposium on Large-Scale Digital Calculating Machinery, Cambridge, Harvard University Press, 141–146.
65.
Lemke, C. E. (1954), The dual method of solving the linear programming problem, Naval Research Logistics Quarterly, 1, 36–47.
66.
Lindley, D. V. (1952), The theory of queues with a single server, Mathematical Proceedings of the Cambridge Philosophical Society, 48, 277–289.
67.
Little, J. D. C. (1961), A proof for the queuing formula \(L = \lambda W\), Operations Research, 9, 383–387.
68.
MacCrimmon, K. R., and Ryavec, C. A. (1964), An analytical study of the PERT assumptions, Operations Research, 12, 16–37.
69.
Malcolm, D. G., Roseboom, J. H., Clark, C. E., and Fazar, W. (1959), Application of a technique for research and development program evaluation, Operations Research, 7, 646–669.
70.
Manne, A. S. (1960), Linear programming and sequential decisions, Management Science, 6, 259–267.
71.
Markov, A. A. (1906), Rasprostranenie zakona bol’shih chisel na velichiny, zavisyaschie drug ot druga, Izvestiya Fiziko-matematicheskogo obschestva pri Kazanskom universitete, 15, 135–156.
72.
Markowitz, H. (1952), Portfolio selection, Journal of Finance, 7, 77–91.
73.
Metropolis, N., and Ulam, S. (1949), The Monte Carlo method, Journal of the American Statistical Association, 44, 335–341.
74.
Minkowski, H. (1896), Geometrie der Zahlen, Leipzig, Teubner.
75.
Nash, J. F. (1950), Equilibrium points in n-person games, Proceedings of the National Academy of Sciences, 36, 48–49.
76.
von Neumann, J. (1928), Zur Theorie der Gesellschaftsspiele, Mathematische Annalen, 100, 295–320.
77.
von Neumann, J. (1947), Discussion of a maximum problem, unpublished manuscript, in A. H. Taub (ed.), John von Neumann: Collected Works, Vol. VI (1963), Oxford, Pergamon, 89–95.
78.
von Neumann, J., and Morgenstern, O. (1944), Theory of Games and Economic Behavior, Princeton University Press.
79.
Padberg, M., and Rinaldi, G. (1991), A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems, SIAM Review, 33, 60–100.
80.
Park, S. K., and Miller, K. W. (1988), Random number generators: good ones are hard to find, Communications of the ACM, 31, 1192–1201.
81.
Pollaczek, F. (1930), Über eine Aufgabe der Wahrscheinlichkeitstheorie, Mathematische Zeitschrift, 32, 64–100.
82.
Raiffa, H., and Schlaifer, R. (1961), Applied Statistical Decision Theory, Boston, Harvard Business School.
83.
Savage, L. J. (1951), The theory of statistical decision, Journal of the American Statistical Association, 46, 55–67.
84.
Scarf, H. (1960), The optimality of (S, s) policies in the dynamic inventory problem, in K. J. Arrow, S. Karlin and P. Suppes (eds.), Mathematical Methods in the Social Sciences, Stanford University Press, 196–202.
85.
Slater, M. (1950), Lagrange multipliers revisited, Cowles Commission Discussion Paper: Mathematics, 403.
86.
Smith, W. E. (1956), Various optimizers for single-stage production, Naval Research Logistics Quarterly, 3, 59–66.
87.
Spielman, D. A., and Teng, S.-H. (2004), Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time, Journal of the ACM, 51, 385–463.
88.
Stigler, G. J. (1945), The cost of subsistence, Journal of Farm Economics, 27, 303–314.
89.
Vogel, W. R. (1958), A short-cut solution to the transportation problem, cited in N. V. Reinfeld and W. R. Vogel, Mathematical Programming, Englewood Cliffs, Prentice-Hall.
90.
Wald, A. (1950), Statistical Decision Functions, New York, Wiley.
91.
Weyl, H. (1935), Elementare Theorie der konvexen Polyeder, Commentarii Mathematici Helvetici, 7, 290–306.
92.
Wilson, R. H. (1934), A scientific routine for stock control, Harvard Business Review, 13, 116–128.
93.
Wolfe, P. (1959), The simplex method for quadratic programming, Econometrica, 27, 382–398.

[prev] [prev-tail] [front] [up]