Solving mixed-integer robust optimization problems with interval uncertainty using Benders decomposition

Journal of the Operational Research Society

Volumn 66, Issue 4, 2015, Pages 664-673

  Siddiqui, Sauleh ^a   Gabriel, Steven A ^b   Azarm, Shapour ^b  

^a JOHNS HOPKINS UNIVERSITY   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

Benders decomposition; interval uncertainty; mixed integer; quasiconvex function; robust optimization

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; STOCHASTIC PROGRAMMING;

BENDERS DECOMPOSITION; INTERVAL UNCERTAINTY; MIXED INTEGER; QUASICONVEX FUNCTIONS; ROBUST OPTIMIZATION;

INTEGER PROGRAMMING;

EID: 84924588341     PISSN: 01605682     EISSN: 14769360     Source Type: Journal    
DOI: 10.1057/jors.2014.41     Document Type: Article

References (26)

1. Atamturk A. (2006). Strong formulations of robust mixed 0-1 programming. Mathematical Programming 108(2-3): 235-250
2. Balling R, Free J and Parkinson A. (1986). Consideration of worst-case manufacturing tolerances in design optimization. Journal of Mechanisms, Transmissions, Automation in Design 108(4): 438-441
3. Beale E. (1965). Survey of integer programming. Journal of the Operational Research Society 16(2): 219-228
4. Ben-Tal A and Nemirovski A. (2002). Robust optimization-methodology and applications. Mathematical Programming, Series B 92(3): 453-480
5. Benders J. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerishe Mathematik 4(1): 238-252
6. Bertsimas D and Sim M (2004a). The price of robustness. Operations Research 52(1): 35-33
7. Bertsimas D and Sim M (2004b). Robust discrete optimization under ellipsoidal uncertainty sets, http://web.mit.edu/dbertsim/www/papers.html, accessed 3 April 2014
8. Conejo AJ, Castillo E, Minguez R and Garcia-Bertrand R. (2006). Decomposition Techniques in Mathematical Programming. Springer: New York, NY.
9. Floudas CA et al. (1999). Handbook of Test Problems in Local and Global Optimization. Springer: New York, NY.
10. Gabriel S, Shim Y, Conejo A, De la Torre S and Garcia-Bertrand R. (2009). A Benders decomposition method for discretely-constrained mathematical programs with equilibrium constraints. Journal of the Operational Research Society 61(9): 1-16
11. GAMS. 2009). General Algebraic Modeling System, GAMS Version 22.9 www.gams.com
12. Ganzerli S and Pantelides CP. (1999). Load and resistance convex models for optimum design. Structural Optimization 17(4): 259-268
13. Hock W and Schittkowski K. (1980). Test Examples for Nonlinear Programming Codes. Springer-Verlag: New York, NY.
14. Li M, Azarm S and Boyars A. (2006). A new deterministic approach using sensitivity region measures for multi-objective robust and feasibility robust design optimization. Journal of Mechanical Design 128(4): 874-883
15. Li M, Gabriel S, Shim Y and Azarm S. (2011). Interval uncertainty-based robust optimization for convex and non-convex quadratic programs with applications in network infrastructure planning. Networks and Spatial Economics 11(1): 159-191
16. Magrab E, Azarm S, Balachandran B, Duncan J, Herold K and Walsh G. (2004). An Engineer's Guide to Matlab. Prentice-Hall: New York, NY.
17. Montemanni R. (2006). A Benders decomposition approach for the robust spanning tree problem with interval data. Discrete Optimization 174(3): 1479-1490
18. Ng TS, Sun. Y and Fowler J. (2010). Semiconductor lot allocation using robust optimization. European Journal of Operational Research 205(3): 557-570
19. Poojari C, Lucas C and Mitra G. (2008). Robust solutions and risk measures for a supply chain planning problem under uncertainty. Journal of the Operational Research Society 59(1): 2-12
20. Saito H and Murota K. (2007). Benders decomposition approach to robust mixed integer programming. Pacific Journal of Optimization 3(1): 99-112
21. Siddiqui S. (2011). Solving two-level optimization problems with application to robust design and energy markets. Doctoral Dissertation, University of Maryland, College Park, MD.
22. Siddiqui S, Azarm S and Gabriel S. (2011). A modified Benders decomposition method for efficient robust optimization under interval uncertainty. Structural and Multidisciplinary Optimization 44(2): 259-275
23. Soyster AL. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research 21(5): 1154-1157
24. Wu Y. (2011). Modeling of containerized air cargo forwarding problems under uncertainty. Journal of the Operational Research Society 62(7): 1211-1226
25. Zeghal F, Haouari M, Sherali H and Aissaoui N. (2011). Flexible aircraft fleeting and routing at TunisAir. Journal of the Operational Research Society 62(2): 368-380
26. Zhu X and Sherali H. (2009). Two-stage workforce planning under demand fluctuations and uncertainty. Journal of the Operational Research Society 60(1): 94-103