Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming

Mathematical Programming

Volumn 106, Issue 2, 2006, Pages 203-223

  Sen, Suvrajeet ^a   Sherali, Hanif D ^b  

^a University of Arizona   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Branch and Cut; Decomposition; Mixed Integer Programming; Stochastic Programming

Indexed keywords

FUNCTIONS; INTEGER PROGRAMMING; LINEAR PROGRAMMING; PROBLEM SOLVING; STOCHASTIC PROGRAMMING;

BENDERS' DECOMPOSITION; BRANCH-AND-CUT; MIXED-INTEGER PROGRAMMING; SECOND-STAGE SUBPROBLEM(S);

DECOMPOSITION;

EID: 31744441041     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-005-0592-5     Document Type: Article

References (25)

1. Ahmed, S., Tawarmalani, M., Sahinidis, N.V.: A finite branch and bound algorithm for two-stage stochastic integer programs. Math. Prog. 100, 355-377 (2004)
2. Balas, E.: Disjunctive programming. Annals of Discrete Mathematics 5, 3-51 (1979)
3. Balas, E., Ceria, S., Cornuéjols, G.: A lift-and-project cutting plane algorithm for mixed 0-1 programs. Math. Prog. 58, 295-324 (1993)
4. Blair, C.: A closed-form representation of mixed-integer program value functions. Math. Prog. 71, 127-136 (1995)
5. Blair, C., Jeroslow, R.: The value function of an integer program. Math. Prog. 23, 237-273 (1982)
6. Birge, J.R., Louveaux, E: Introduction to Stochastic Programming. Springer, Berlin, Germany, 1997
7. Caroe, C.C.: Decomposition in Stochastic Integer Programming. Ph.D. thesis, Institute of Mathematical Sciences, Dept. of Operations Research, University of Copenhagen, Denmark, 1998
8. Caroe, C.C., Schultz, R. : Dual decomposition in stochastic integer programming. Operations Research Letters 24, 37-45 (1999)
9. Jeroslow, R.: A cutting plane game for facial disjunctive programs. SIAM Journal on Control and Optimization 18, 264-281 (1980)
10. Klein Haneveld, W.K., van der Vlerk, M.H.: Stochastic integer programming: general models and algorithms. Annals of Operations Research 85, 39-57 (1999)
11. Laporte, G., Louveaux, F.V.: The integer L-shaped methods for stochastic integer programs with complete recourse. Operations Research Letters 13, 133-142 (1993)
12. Lovász, L., Schrijver, A.: Cones of matrices and set functions and 0-1 optimization. SIAM J. on Optimization 1, 166-190 (1991)
13. Lulli, G., Sen, S.: A branch and price algorithm for multi-stage stochastic integer programs with applications to stochastic lot sizing problems. Management Science 50, 786-796 (2004)
14. Ntaimo, L., Sen, S.: The million variable "march" for stochastic combinatorial optimization. To appear in Journal of Global Optimization 2003
15. Ruszczyński, A.: Decomposition methods in stochastic programming. Mathematical Programming B (Liebling and de Werra (eds.)), 79, 333-353 (1997)
16. Schultz, R. : On the structure and stability in stochastic programs with random technology matrix and complete integer recourse. Mathematical Programming 70, 73-89 (1995)
17. Schultz, R.: Stochastic programming with integer variables. Mathematical Programming Series B 97, 285-309 (2003)
18. Sen, S.: Decomposition algorithms for stochastic mixed-integer programming models. To appear in Handbook of Discrete Optimization. (K. Aardal, G. Nemhauser, R. Weismental, eds.), Elsevier Publishers, 2003
19. 2 algorithm for large scale stochastic optimization: set convexification. To appear in Mathematical Programming, 2004
20. Sen, S., Higle, J.L., Ntaimo, L.: A summary and illustration of disjunctive decomposition with set convexification. Stochastic Integer Programming and Network Interdiction Models. (D.L. Woodruff ed.), Kluwer Academic Press, Dordrecht, The Netherlands, 2002, pp. 105-125
21. Sen, S., Sherali, H.D.: A branch and bound algorithm for extreme point mathematical programming. Discrete Applied Mathematics 11, 265-280 (1985)
22. Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM Journal on Discrete Mathematics 3, 411-430 (1990)
23. Sherali, H.D., Adams, W.P.: A hierarchy of relaxations and convex hull characterizations for mixed integer zero-one programming problems. Discrete Applied Mathematics 52, 83-106 (1994)
24. Sherali, H.D., Adams, W.P.: A Reformulation-Lizearization Technique for Solving Discrete and Continuous Nonconvex problems. Kluwer Academic Publishers, Boston, MA, 1999
25. Sherali, H.D., Fraticelli, B.M.P: A modification of Benders' decomposition algorithm for discrete subproblems: an approach for stochastic programs with integer recourse. Journal of Global Optimization 22, 319-342 (2002)