On solving discrete two-stage stochastic programs having mixed-integer first- and second-stage variables

Mathematical Programming

Volumn 108, Issue 2-3, 2006, Pages 597-616

  Sherali, Hanif D ^a   Zhu, Xiaomei ^a  

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

Author keywords

Benders' decomposition; Convexification; Reformulation Linearization Technique (RLT); Two stage stochastic mixed integer programs

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; FUNCTION EVALUATION; INTEGER PROGRAMMING; PROBLEM SOLVING;

BENDERS' DECOMPOSITION; CONVEXIFICATION; REFORMULATION-LINEARIZATION TECHNIQUE (RLT); TWO-STAGE STOCHASTIC MIXED-INTEGER PROGRAMS;

STOCHASTIC PROGRAMMING;

EID: 33745684007     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0724-6     Document Type: Article

References (24)

1. Ahmed, S.: Mean-risk objectives in stochastic programming. School of Industrial & Systems Engineering, Georgia Tech, Atlanta, GA (2004). Working Paper, available at http://www.optimizationonline.org/DB_HTML/2004/04/859.html
2. Ahmed, S., Tawarmalani, M., Sahinidis, N.V.: A finite branch and bound algorithm for two-stage stochastic integer programs. Mathematical Programming 100 (2), 355-377 (2004)
3. Balas, E., Ceria, S., Cornuéjols, G.: A lift-and-project cutting plane algorithm for mixed 0-1 programs. Mathematical Programming 58, 295-324 (1993)
4. Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238-252 (1962)
5. Blair, C., Jeroslow, R.: The value function of an integer program. Mathematical Programming 23, 237-273 (1982)
6. Carøe, C.C., Schultz, R.: Dual decomposition in stochastic integer programming. Operations Research Letters 24 (1-2), 37-45 (1999)
7. Carøe, C.C., Tind, J.: A cutting-plane approach to mixed 0-1 stochastic integer programs. European Journal of Operational Research 101 (2), 306-316 (1997)
8. Carøe, C.C., Tind, J.: L-shaped decomposition of two-stage stochastic programs with integer recourse. Mathematical Programming 83a (3), 451-464 (1998)
9. Jeroslow, R.G.: A cutting plane game for facial disjunctive programs. SIAM Journal of Control and Optimization 18, 264-280 (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 method for stochastic integer programs with complete recourse. Operations Research Letters 13 (3), 133-142 (1993)
12. Mulvey, J.M., Vanderbei, R.J., Zenios, S.A.: Robust optimization of large-scale systems. Operations Research 43 (2), 264-281 (1995)
13. Ntaimo, L., Sen, S.: The million-variable "march" for stochastic combinatorial optimization. Journal of Global Optimization 32 (3), 385-400 (2005)
14. Schultz, R.: On structure and stability in stochastic programs with random technology matrix and complete integer recourse. Mathematical Programming 70 (1), 73-89 (1995)
15. Schultz, R., Stougie, L., van der Vlerk, M.H.: Two-stage stochastic integer programming: a survey. Statistica Neerlandica 50 (3), 404-416 (1996). Also see http://mally.eco.rug.nl/index.html?biblio/SPlist.html
16. Schultz, R., Tiedemann, S.: Risk aversion via excess probabilities in stochastic programs with mixed-integer recourse. SIAM Journal on Optimization 14 (1), 115-138 (2003)
17. 2 algorithm for large scale stochastic mixed-integer programming: set convexification. Mathematical Programming 104 (1), 1-20 (2005)
18. Sen, S., Sherali, H.D.: Decomposition with branch-and-cut approaches for two stage stochastic mixed-integer programming. Mathematical Programming 106(2), 203-223 (2006)
19. Sherali, H.D.: A constructive proof of the representation theorem for polyhedral sets based on fundamental definitions. American Journal of Mathematical and Management Sciences 7 (3/4), 253-270 (1987)
20. Sherali, H.D., Adams, W.P.: A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Kluwer Academic Publishing, Boston, MA (1999)
21. Sherali, H.D., Fraticelli, B.M.P.: A modification of Benders' decomposition algorithm for discrete sub-problems: An approach for stochastic programs with integer recourse. Journal of Global Optimization 22, 319-342 (2002)
22. Stougie, L., van der Vlerk, M.H.: Stochastic integer programming. In: Dell'Amico, M., Maffioli, F., Martello, S., (eds.) Annotated Bibliographies in Combinatorial Optimization, Chapter 9:127-141 (1997)
23. Takriti, S., Ahmed, S.: On robust optimization of two-stage systems. Mathematical Programming 99a, 109-126 (2004)
24. van der Vlerk, M.H.: Convex approximations for complete integer recourse models. Mathematical Programming 99a, 297-310 (2004)