Chance-Constrained Binary Packing Problems
Published Online:19 May 2014https://doi.org/10.1287/ijoc.2014.0595
References
- (2007) Embedding {0, 1/2}cuts in a branch-and-cut framework: A computational study. INFORMS J. Comput. 19(2):229–238.Link, Google Scholar
- (2006) The Traveling Salesman Problem (Princeton University Press, Princeton, NJ).Google Scholar
- (2004) Sequence independent lifting for mixed-integer programming. Oper. Res. 52(3):487–490.Link, Google Scholar
- (2009) The submodular 0-1 knapsack polytope. Discrete Optim. 6(4):333–344.Crossref, Google Scholar
- (1978) Facets of the knapsack polytope from minimal covers. SIAM J. Appl. Math. 34(1):119–148.Crossref, Google Scholar
- (1990) OR-library: Distributing test problems by electronic mail. J. Oper. Res. Soc. 41(1):1069–1072.Crossref, Google Scholar
- (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
- (2010) An exact approach for solving integer problems under probabilistic constraints with random technology matrix. Ann. Oper. Res. 177(1):127–137.Crossref, Google Scholar
- (2002) The probabilistic set-covering problem. Oper. Res. 50(6):956–967.Link, Google Scholar
- (2012) Capital rationing problems under uncertainty and risk. Comp. Optim. Appl. 51(3):1375–1396.Crossref, Google Scholar
- (2005) Uncertain convex programs: Randomized solutions and confidence levels. Math. Programming 102(1):25–46.Crossref, Google Scholar
- (2006) The scenario approach to robust control design. IEEE Trans. Automat. Control 51(5):742–753.Crossref, Google Scholar
- (2011) A sampling-and-discarding approach to chance-constrained optimization: Feasibility and optimality. J. Optim. Theory Appl. 148(2):257–280.Crossref, Google Scholar
- (1963) Deterministic equivalents for optimizing and satisficing under chance constraints. Oper. Res. 11(1):18–39.Link, Google Scholar
- (2013) Local cuts for mixed-integer programming. Math. Programming Comput. 5(2):171–200.Crossref, Google Scholar
- (2012) Regularization methods for optimization problems with probabilistic constraints. Math. Programming 138(1–2):223–251.Crossref, Google Scholar
- (2000) Concavity and efficient points of discrete distributions in probabilistic programming. Math. Programming 89(1):55–77.Crossref, Google Scholar
- (1998) Lifted cover inequalities for 0-1 integer programs: Computation. INFORMS J. Comput. 10(4):427–437.Link, Google Scholar
- (1999) Lifted cover inequalities for 0-1 integer programs: Complexity. INFORMS J. Comput. 11(1):117–123.Link, Google Scholar
- (2000) Sequence independent lifting in mixed integer programming. J. Comb. Optim. 4(1):109–129.Crossref, Google Scholar
- (2008) Local and global lifted cover inequalities for the multidimensional knapsack problem. Eur. J. Oper. Res. 186(1):91–103.Crossref, Google Scholar
- (2010) Separation algorithms for 0-1 knapsack polytopes. Math. Programming 124(1–2):69–91.Crossref, Google Scholar
- (2012) On mixing sets arising in chance-constrained programming. Math. Programming 132(1–2):31–56.Crossref, Google Scholar
- (2012) Pattern-based modeling and solution of probabilistically constrained optimization problems. Oper. Res. 60(6):1356–1372.Link, Google Scholar
- (2010) An integer programming and decomposition approach to general chance-constrained mathematical programs. Eisenbrand F, Shepherd FB, eds. IPCO 2010, Lecture Notes in Computer Science (Springer-Verlag, Berlin), 271–284.Crossref, Google Scholar
- (2014) A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support. Math. Programming 146(1–2):219–244Crossref, 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 programs with probabilistic constraints. Math. Programming 12(2):247–272.Crossref, Google Scholar
- (1988) Integer and Combinatorial Optimization, Wiley-Interscience Series in Discrete Mathematics and Optimization (John Wiley & Sons, New York).Crossref, Google Scholar
- (2005) Scenario approximation of chance constraints. Calafiore G, Dabbene F, eds. Probabilistic and Randomized Methods for Design Under Uncertainty (Springer, London), 3–48.Google Scholar
- (2006) Convex approximations of chance constrained programs. SIAM J. Optim. 17(4):969–996.Crossref, Google Scholar
- (1973) On the facial structure of set packing polyhedra. Math. Programming 5(1):198–216.Crossref, Google Scholar
- (1975) Technical note—A note on zero-one programming. Oper. Res. 23(4):833–837.Link, Google Scholar
- (2009) The sample average approximation method for chance constrained programming: Theory and applications. J. Optim. Theory Appl. 142(2):399–416.Crossref, Google Scholar
- (2014) Covering linear programming with violations. INFORMS J. Comput. 26(3):531–546.Link, Google Scholar
- (2002) Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra. Math. Programming 93(2):195–215.Crossref, Google Scholar
- (2009) MIP reformulations of the probabilistic set covering problem. Math. Programming 121(1):1–31.Crossref, Google Scholar
- (2013) Structure-exploiting algorithms for chance-constrained and integer stochastic programs. Ph.D. thesis, University of Wisconsin–Madison.Google Scholar
- (2010) IIS branch-and-cut for joint chance-constrained programs and application to optimal vaccine allocation. Eur. J. Oper. Res. 207(1):290–296.Crossref, Google Scholar
- (1989) Easily computable facets of the knapsack polytope. Math. Oper. Res. 14(4):760–764.Link, Google Scholar

