Single Commodity Stochastic Network Design Under Probabilistic Constraint with Discrete Random Variables
Published Online:7 Dec 2015https://doi.org/10.1287/opre.2015.1434
References
- (1975) Disjunctive programming: Cutting planes from logical conditions. Mangasarian OL, Meyer RR, Robinson SM, eds. Nonlinear Programming 2 (Academic Press, New York), 279–312.Crossref, Google Scholar
- (1969) Duality theory of linear programs: A constructive approach with applications. SIAM Rev. 11:347–377.Crossref, Google Scholar
- (2003) An intersection inequality for discrete distributions and related generation problems. Automata, Languages and Programming, 30th Internat. Colloquium, ICALP, Lecture Notes in Computer Science, Vol. 2719 (Springer, Berlin), 543–555.Crossref, Google Scholar
- (1952) Optimality and degeneracy in linear programming. Econometrica 20:160–170.Crossref, Google Scholar
- (2013) Regularization methods for optimization problems with probabilistic constraints. Math. Programming, Ser. A 138:223–251.Crossref, Google Scholar
- (2000) Concavity and efficient points of discrete distributions in probabilistic programming. Math. Programming, Ser. A 89:66–77.Crossref, Google Scholar
- (2002) Bounds for probabilistic integer programming problems. Discrete Appl. Math. 124(1-3): 55–65.Crossref, Google Scholar
- (1967) Association of random variables with applications. Ann. Math. Statist. 38:1466–1474.Crossref, Google Scholar
- (2002) On a dual method for a specially structured linear programming problem with application to stochastic programming. Optim. Methods Software 17:445–492.Crossref, Google Scholar
- (2012) The probability of a feasible flow in a stochastic transportation network. Accessed December 8, 2012, http://rutcor.rutgers.edu/Fanelli.pdf.Google Scholar
- (1962) Flows in Networks (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
- (2012) Flow-based capacity allocation in the CEE region: Sensitivity analyses, multiple optima, real income. RRR 8-2012.Google Scholar
- (1957) A theorem on flows in network. Pacific J. Math. 7: 1073–1082.Crossref, Google Scholar
- (1873) Uber die auflosung linearer gleichungen mit reellen koeffizienten. Mathematische Annalen 6:23–28.Crossref, Google Scholar
- (1965) Best possible inequalities for the probability of a logical function of events. Amer. Math. Monthly 72:343–359.Crossref, Google Scholar
- (1960) Some recent applications of the theory of linear inequalities to external combinatorial analysis. Proc. Symposia Appl. Math. Vol. X. Combinatorial Analysis (American Mathematical Society, Providence, RI), 113–127.Google Scholar
- (2012) Combinatorial results on the fitting problems of the multivariate gamma distribution introduced by Prékopa and Szántai. Ann. Oper. Res. 200:265–278.Crossref, Google Scholar
- (2010) Mathematical programming generation of p-efficient points. Eur. J. Oper. Res. 207(2):590–600.Crossref, Google Scholar
- (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19(2): 674–699.Crossref, Google Scholar
- (2010) An integer programming approach for linear programming with probabilistic constraints. Math. Programming 122:247–272.Crossref, Google Scholar
- (1995) A minimal algorithm for the multiple-choice knapsack problem. Eur. J. Oper. Res. 83:394–410.Crossref, Google Scholar
- (1966) On the probability distribution of the optimum of a random linear program. SIAM J. Control 21:211–222.Crossref, Google Scholar
- (1980) Network planning using two-stage programming under uncertainty. Recent Results in Stochastic Programming, Lecture Notes in Economics and Mathematical Systems, Vol. 179 (Springer, Berlin), 216–237.Crossref, Google Scholar
- (1990a) Dual method for the solution of a one-stage stochastic programming problem with random RHS obeying a discrete probability distribution. ZOR—Methods Models Oper. Res. 34:441–461.Crossref, Google Scholar
- (1990b) Totally positive linear programming problems. Leifman LJ eds. Functional Analysis, Optimization and Mathematical Economics. A Collection of Papers Dedicated to the Memory of L. V. Kantorovich (Oxford University Press, New York), 197–207.Google Scholar
- (1990c) The discrete moment problem and linear programming. Discrete Appl. Math. 27:235–254.Crossref, Google Scholar
- (1995) Stochastic Programming (Kluwer Scientific Publishers, Boston).Crossref, Google Scholar
- (1996) Brief introduction to linear programming. Math. Scientist 21(2):85–111.Google Scholar
- (2003) Probabilistic programming. Ruszczyński A, Shapiro A, eds. Stochastic Programming Handbooks in OR & MS, Vol. 10 (Elsevier, Amsterdam), 269–351.Crossref, Google Scholar
- (2007) On the relationship between probabilistic constrained, disjunctive and multiobjective programming. RUTCOR Research Report 07–2007.Google Scholar
- (2012) Multivariate value at risk and related topics. Ann. Oper. Res. 193:49–69.Crossref, Google Scholar
- (1991) On the existence of a feasible flow in a stochastic transportation network. Oper. Res. 39(1):119–129.Link, Google Scholar
- (1978) A new multivariate gamma distribution and its fitting to empirical streamflow data. Water Resources Res. 14: 19–24.Crossref, Google Scholar
- (1998) Programming under probabilistic constraint with discrete random variable. Giannessi F, Rapcsk T, eds. New Trends in Mathematical Programming (Kluwer Scientific Publishers, Boston), 235–255.Crossref, Google Scholar
- (2014) Scheduling of Power Generation (Springer, New York).Crossref, Google Scholar
- (1915) Uber positive Lösungen homogener linearer Gleichungen. Mathematische Annalen 76:340–342.Crossref, Google Scholar
- (2010) Single-commodity stochastic network design with multiple sources and sinks. Inform. Systems Oper. Res. 49(3):193–211.Crossref, Google Scholar
- (2010) Single source single-commodity stochastic network design. Computational Management Sci. 9(1):139–160.Google Scholar
- (2002) The integer programming background of a stochastic integer programming algorithm of Dentcheva-Prékopa-Ruszczyński. Optim. Methods Software 17:543–559.Crossref, Google Scholar
- (1993) The facets of the polyhedral set determined by the Gale- Hoffman inequalities. Math. Programming 62:215–222.Crossref, Google Scholar
- (2012) An improved cutting plane method for the solution of probabilistic constrained problem with discrete random variables. RUTCOR Research Report 12–2012.Google Scholar

