On a Level-Set Characterization of the Value Function of an Integer Program and Its Application to Stochastic Programming

Published Online:https://doi.org/10.1287/opre.1120.1156

References

  • Ahmed S, Tawarmalani M, Sahinidis N. A finite branch and bound algorithm for two-stage stochastic integer programs. Math. Programming (2004) 100(2):355–377CrossrefGoogle Scholar
  • Alonso-Ayuso A, Escudero LF, Ortuño MT. BFC, a branch-and-fix coordination algorithmic framework for solving some types of stochastic pure and mixed 0–1 programs. Eur. J. Oper. Res. (2003) 151(3):503–519CrossrefGoogle Scholar
  • Alonso-Ayuso A, Escudero LF, Guignard M, Quinteros M, Weintraub A. Forestry management under uncertainty. Ann. Oper. Res. (2011) 190(1):17–39CrossrefGoogle Scholar
  • Birge JR, Louveaux F. Introduction to Stochastic Programming (2011) (Springer, New York) CrossrefGoogle Scholar
  • Blair CE, Jeroslow RG. The value function of an integer program. Math. Programming (1982) 23(1):237–273CrossrefGoogle Scholar
  • Carøe CC, Tind J. L-shaped decomposition of two-stage stochastic programs with integer recourse. Math. Programming (1998) 83(3):451–464CrossrefGoogle Scholar
  • Gassmann HI. MSLiP: A computer code for the multistage stochastic linear programming problem. Math. Programming (1990) 47(1):407–423CrossrefGoogle Scholar
  • Gassmann HI. The SMPS format for stochastic linear programs. (2005) . Accessed March 1, 2013, http://myweb.dal.ca/gassmann/smps2.htmGoogle Scholar
  • Gordan P. Über die auflösung linearer gleichungen mit reellen coeffizienten. Mathematische Annalen (1873) 6(1):23–28CrossrefGoogle Scholar
  • Guan Y. Pairing inequalities and stochastic lot-sizing problems: A study in integer programming. (2005) . Ph.D. thesis, Georgia Institute of Technology, AtlantaGoogle Scholar
  • Güzelsoy M, Ralphs TK. Duality for mixed-integer linear programs. Internat. J. Oper. Res. (2007) 4(3):118–137Google Scholar
  • Hemmecke R, Schultz R. Decomposition of test sets in stochastic integer programming. Math. Programming (2003) 94(2):323–341CrossrefGoogle Scholar
  • Horst R, Tuy H. Global Optimization: Deterministic Approaches (1996) (Springer, Berlin) CrossrefGoogle Scholar
  • ILOGIBM ILOG CPLEX 11.0 User's Manual (2007) (ILOG CPLEX Division, Incline Village, NV) Google Scholar
  • Jeroslow R. Some basis theorems for integral monoids. Math. Oper. Res. (1978) 3(2):145–154LinkGoogle Scholar
  • Klabjan D. A practical algorithm for computing a subadditive dual function for set partitioning. Comput. Optim. Appl. (2004) 29(3):347–368CrossrefGoogle Scholar
  • Klabjan D. Subadditive approaches in integer programming. Eur. J. Oper. Res. (2007) 183(2):525–545CrossrefGoogle Scholar
  • Kong N, Schaefer AJ, Hunsaker B. Two-stage integer programs with stochastic right-hand sides: A superadditive dual approach. Math. Programming (2006) 108(2):275–296CrossrefGoogle Scholar
  • Nemhauser GL, Wolsey LA. Integer and Combinatorial Optimization (1988) (John Wiley & Sons, Inc., New York) CrossrefGoogle Scholar
  • Ntaimo L. Disjunctive decomposition for two-stage stochastic mixed-binary programs with random recourse. Oper. Res. (2010) 58(1):229–243LinkGoogle Scholar
  • Ntaimo L, Sen S. A comparative study of decomposition algorithms for stochastic combinatorial optimization. Comput. Optim. Appl. (2008) 40(3):299–319CrossrefGoogle Scholar
  • Özaltın OY, Prokopyev OA, Schaefer AJ. Two-stage quadratic integer programs with stochastic right-hand sides. Math. Programming (2012) 131(1):121–158CrossrefGoogle Scholar
  • Papadimitriou CH, Steiglitz K. Combinatorial Optimization: Procedures and Complexity (1998) (Dover Publications, Mineola, NY) Google Scholar
  • Ruszczyński A, Shapiro A. Stochastic Programming (2003) (Elsevier, Amsterdam) Handbooks in Operations Research and Management ScienceCrossrefGoogle Scholar
  • Schultz R. On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Math. Programming (1995) 70(1):73–90Google Scholar
  • Schultz R, Stougie L, van der Vlerk MH. Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis reductions. Math. Programming (1998) 83(1):229–252Google Scholar
  • Sen S, Higle JL. The C3 theorem and a D2 algorithm for large scale stochastic mixed-integer programming: Set convexification. Math. Programming (2005) 104(1):1–20CrossrefGoogle Scholar
  • Sen S, Sherali HD. Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming. Math. Programming (2006) 106(2):203–223CrossrefGoogle Scholar
  • Shapiro A, Dentcheva D, Ruszczyński A. Lectures on Stochastic Programming: Modeling and Theory (2009) (Society for Industrial and Applied Mathematics, Philadelphia) CrossrefGoogle Scholar
  • Sherali HD, Fraticelli BMP. A modification of Benders' decomposition algorithm for discrete subproblems: An approach for stochastic programs with integer recourse. J. Global Optim. (2002) 22(1):319–342CrossrefGoogle Scholar
  • Sherali HD, Smith JC. Two-stage stochastic hierarchical multiple risk problems: Models and algorithms. Math. Programming (2009) 120(2):403–427CrossrefGoogle Scholar
  • Sherali HD, Zhu X. On solving discrete two-stage stochastic programs having mixed-integer first- and second-stage variables. Math. Programming (2006) 108(2):597–616CrossrefGoogle Scholar
  • Stougie L. Design and analysis of algorithms for stochastic integer programming. (1987) . Ph.D. thesis, Center for Mathematics and Computer Science, AmsterdamGoogle Scholar
  • Toriello A, Nemhauser G. The value function of an infinite-horizon single-item lot-sizing problem. Oper. Res. Lett. (2012) 40(1):12–14CrossrefGoogle Scholar
  • Trapp A. RANDOMRHS 2013: Test instances for stochastic integer programming. (2013) . Accessed March 1, 2013, http://users.wpi.edu/~atrapp/randomrhs_2013.htmGoogle Scholar
  • Wolsey LA. Integer programming duality: Price functions and sensitivity analysis. Math. Programming (1981) 20(2):173–195CrossrefGoogle Scholar
  • Yuan Y, Sen S. Enhanced cut generation methods for decomposition-based branch and cut for two-stage stochastic mixed-integer programs. INFORMS J. Comput. (2009) 21(3):480–487LinkGoogle 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.