A hierarchy of bounds for stochastic mixed-integer programs

Mathematical Programming

Volumn 138, Issue 1-2, 2013, Pages 253-272

  Sandikçi, Burhaneddin ^a   Kong, Nan ^b   Schaefer, Andrew J ^c  

^a UNIVERSITY OF CHICAGO   (United States)

^b PURDUE UNIVERSITY   (United States)

^c University of Pittsburgh   (United States)

Author keywords

Bounding; Mixed integer programs; Stochastic programming

Indexed keywords

BOUNDING; BOUNDING TECHNIQUES; COMPLEMENTARY TOOLS; FORMULATED PROBLEMS; LINEAR RELAXATIONS; LOWER AND UPPER BOUNDS; MIXED-INTEGER PROGRAMS; OBJECTIVE FUNCTIONS;

INTEGER PROGRAMMING; STOCHASTIC PROGRAMMING;

MATRIX ALGEBRA;

EID: 84875459846     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-012-0526-y     Document Type: Article

References (20)

1. Ahmed S.; Garcia R.: Dynamic capacity acquisition and assignment under uncertainty. Ann. Oper. Res. 124, 267-283 (2003)
2. Birge J.R.: The value of the stochastic solution in stochastic linear programs with fixed recourse. Math. Program. 24, 314-325 (1982)
3. Birge J.R.: Aggregation bounds in stochastic linear programming. Math. Program. 31, 25-41 (1985)
4. Birge J.R.; Louveaux F.: Introduction to Stochastic Programming. Springer, NewYork (1997)
5. Edmundson, H.P.: Bounds on the Expectation of a Convex Function of a Random Variable. Tech. rep. RAND Corporation, Santa Monica (1956)
6. Frauendorfer K.: Solving SLP recourse problems with binary multivariate distributions - the dependent case. Math. Oper. Res. 13(3), 377-394 (1988)
7. Huang C.C.; Vertinsky I.; Ziemba W.T.: Sharp bounds on the value of perfect information. Oper. Res. 25(1), 128-139 (1977)
8. Huang C.C.; Ziemba W.T.; Ben-Tal A.: Bounds on the expectation of a convex function of a random variable: with applications to stochastic programming. Oper. Res. 25(2), 315-325 (1977)
9. Jensen J.L.: Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica 30(1), 175-193 (1906)
10. Jorjani S.; Scott C.H.; Woodruff D.L.: Optimal selection of subsets of sizes for production. Int. J. Prod. Res. 37(16), 3697-3710 (1999)
11. Kall P.; Mayer J.: Stochastic Linear Programming: Models, Theory, and Computation. Springer, Berlin (2005)
12. Kall P.; Stoyan D.: Solving stochastic programming problems with recourse including error bounds. Mathematische Operationsforschung und Statistik, Ser. Optimization 13, 431-447 (1982)
13. Klaassen, P.: Critical review paper submitted as part of the requirements for the General Examination in Operations Research. MIT, Boston (1991)
14. Madansky A.: Bounds on the expectation of a convex function of a multivariate random variable. Ann. Math. Stat. 30(3), 743-746 (1959)
15. Madansky A.: Inequalities for stochastic linear programming problems. Manag. Sci. 6(2), 197-204 (1960)
16. Ntaimo L.; Sen S.: The million-variable 'march' for stochastic combinatorial optimization. J. Global Optimi. 32(3), 385-400 (2005)
17. Rosa C.H.; Takriti S.: Improving aggregation bounds for two-stage stochastic programs. Oper. Res. Lett. 24(3), 127-137 (1999)
18. Ruszczyński, A.; Shapiro, A. (eds.): Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10. Elsevier, Amsterdam (2003)
19. Zipkin P.H.: Bounds for row-aggregation in linear programming. Oper. Res. 28(4), 903-916 (1980)
20. Zipkin P.H.: Bounds on the effect of aggregating variables in linear programming. Oper. Res. 28(2), 403-418 (1980)