Chance-Constrained Binary Packing Problems

Published Online:https://doi.org/10.1287/ijoc.2014.0595

References

  • Andreello G, Caprara A, Fischetti M (2007) Embedding {0, 1/2}cuts in a branch-and-cut framework: A computational study. INFORMS J. Comput. 19(2):229–238.LinkGoogle Scholar
  • Applegate DL, Bixby RE, Chvátal V, Cook WJ (2006) The Traveling Salesman Problem (Princeton University Press, Princeton, NJ).Google Scholar
  • Atamtürk A (2004) Sequence independent lifting for mixed-integer programming. Oper. Res. 52(3):487–490.LinkGoogle Scholar
  • Atamtürk A, Narayanan V (2009) The submodular 0-1 knapsack polytope. Discrete Optim. 6(4):333–344.CrossrefGoogle Scholar
  • Balas E, Zemel E (1978) Facets of the knapsack polytope from minimal covers. SIAM J. Appl. Math. 34(1):119–148.CrossrefGoogle Scholar
  • Beasley JE (1990) OR-library: Distributing test problems by electronic mail. J. Oper. Res. Soc. 41(1):1069–1072.CrossrefGoogle Scholar
  • Ben-Tal A, Ghaoui LE, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Beraldi P, Bruni ME (2010) An exact approach for solving integer problems under probabilistic constraints with random technology matrix. Ann. Oper. Res. 177(1):127–137.CrossrefGoogle Scholar
  • Beraldi P, Ruszczyński A (2002) The probabilistic set-covering problem. Oper. Res. 50(6):956–967.LinkGoogle Scholar
  • Beraldi P, Bruni ME, Violi A (2012) Capital rationing problems under uncertainty and risk. Comp. Optim. Appl. 51(3):1375–1396.CrossrefGoogle Scholar
  • Calafiore GC, Campi MC (2005) Uncertain convex programs: Randomized solutions and confidence levels. Math. Programming 102(1):25–46.CrossrefGoogle Scholar
  • Calafiore GC, Campi MC (2006) The scenario approach to robust control design. IEEE Trans. Automat. Control 51(5):742–753.CrossrefGoogle Scholar
  • Campi MC, Garatti S (2011) A sampling-and-discarding approach to chance-constrained optimization: Feasibility and optimality. J. Optim. Theory Appl. 148(2):257–280.CrossrefGoogle Scholar
  • Charnes A, Cooper WW (1963) Deterministic equivalents for optimizing and satisficing under chance constraints. Oper. Res. 11(1):18–39.LinkGoogle Scholar
  • Chvátal V, Cook W, Espinoza D (2013) Local cuts for mixed-integer programming. Math. Programming Comput. 5(2):171–200.CrossrefGoogle Scholar
  • Dentcheva D, Martinez G (2012) Regularization methods for optimization problems with probabilistic constraints. Math. Programming 138(1–2):223–251.CrossrefGoogle Scholar
  • Dentcheva D, Prékopa A, Ruszczyński A (2000) Concavity and efficient points of discrete distributions in probabilistic programming. Math. Programming 89(1):55–77.CrossrefGoogle Scholar
  • Gu Z, Nemhauser GL, Savelsbergh MWP (1998) Lifted cover inequalities for 0-1 integer programs: Computation. INFORMS J. Comput. 10(4):427–437.LinkGoogle Scholar
  • Gu Z, Nemhauser GL, Savelsbergh MWP (1999) Lifted cover inequalities for 0-1 integer programs: Complexity. INFORMS J. Comput. 11(1):117–123.LinkGoogle Scholar
  • Gu Z, Nemhauser GL, Savelsbergh MWP (2000) Sequence independent lifting in mixed integer programming. J. Comb. Optim. 4(1):109–129.CrossrefGoogle Scholar
  • Kaparis K, Letchford AN (2008) Local and global lifted cover inequalities for the multidimensional knapsack problem. Eur. J. Oper. Res. 186(1):91–103.CrossrefGoogle Scholar
  • Kaparis K, Letchford AN (2010) Separation algorithms for 0-1 knapsack polytopes. Math. Programming 124(1–2):69–91.CrossrefGoogle Scholar
  • Küçükyavuz S (2012) On mixing sets arising in chance-constrained programming. Math. Programming 132(1–2):31–56.CrossrefGoogle Scholar
  • Lejeune MA (2012) Pattern-based modeling and solution of probabilistically constrained optimization problems. Oper. Res. 60(6):1356–1372.LinkGoogle Scholar
  • Luedtke J (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.CrossrefGoogle Scholar
  • Luedtke J (2014) A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support. Math. Programming 146(1–2):219–244CrossrefGoogle Scholar
  • Luedtke J, Ahmed S (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19(2):674–699.CrossrefGoogle Scholar
  • Luedtke J, Ahmed S, Nemhauser GL (2010) An integer programming approach for linear programs with probabilistic constraints. Math. Programming 12(2):247–272.CrossrefGoogle Scholar
  • Nemhauser GL, Wolsey LA (1988) Integer and Combinatorial Optimization, Wiley-Interscience Series in Discrete Mathematics and Optimization (John Wiley & Sons, New York).CrossrefGoogle Scholar
  • Nemirovski A, Shapiro A (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
  • Nemirovski A, Shapiro A (2006) Convex approximations of chance constrained programs. SIAM J. Optim. 17(4):969–996.CrossrefGoogle Scholar
  • Padberg MW (1973) On the facial structure of set packing polyhedra. Math. Programming 5(1):198–216.CrossrefGoogle Scholar
  • Padberg MW (1975) Technical note—A note on zero-one programming. Oper. Res. 23(4):833–837.LinkGoogle Scholar
  • Pagnoncelli B, Ahmed S, Shapiro A (2009) The sample average approximation method for chance constrained programming: Theory and applications. J. Optim. Theory Appl. 142(2):399–416.CrossrefGoogle Scholar
  • Qiu F, Ahmed S, Dey SS, Wolsey LA (2014) Covering linear programming with violations. INFORMS J. Comput. 26(3):531–546.LinkGoogle Scholar
  • Ruszczyński A (2002) Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra. Math. Programming 93(2):195–215.CrossrefGoogle Scholar
  • Saxena A, Goyal V, Lejeune M (2009) MIP reformulations of the probabilistic set covering problem. Math. Programming 121(1):1–31.CrossrefGoogle Scholar
  • Song Y (2013) Structure-exploiting algorithms for chance-constrained and integer stochastic programs. Ph.D. thesis, University of Wisconsin–Madison.Google Scholar
  • Tanner MW, Ntaimo L (2010) IIS branch-and-cut for joint chance-constrained programs and application to optimal vaccine allocation. Eur. J. Oper. Res. 207(1):290–296.CrossrefGoogle Scholar
  • Zemel E (1989) Easily computable facets of the knapsack polytope. Math. Oper. Res. 14(4):760–764.LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.