A new cross decomposition method for stochastic mixed-integer linear programming

European Journal of Operational Research

Volumn 256, Issue 2, 2017, Pages 487-499

  Ogbe, Emmanuel ^a   Li, Xiang ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

Benders decomposition; Cross decomposition; Dantzig Wolfe decomposition; Mixed integer linear programming; Stochastic programming

Indexed keywords

CHAINS; STOCHASTIC PROGRAMMING; STOCHASTIC SYSTEMS; SUPPLY CHAINS;

BENDERS DECOMPOSITION; CHEMICAL SUPPLY CHAINS; COMPUTATIONAL ADVANTAGES; CROSS DECOMPOSITIONS; DANTZIG-WOLFE DECOMPOSITION; DESIGN AND OPERATIONS; LAGRANGIAN DECOMPOSITION; MIXED INTEGER LINEAR PROGRAMMING;

INTEGER PROGRAMMING;

EID: 85016478280     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2016.08.005     Document Type: Article

References (47)

1. Applegren, L.H., A column generation algorithm for a ship scheduling problem. Transportation Science 3 (1969), 53–68.
2. Balas, E., Bergthaller, C., Benders method revisited. Journal of Applied and Computational Mathematics 9 (1983), 3–12.
3. Barnhart, C., Johnson, E., Branch and price: Column generation for solving huge integer programs. Operations Research 46 (1998), 316–329.
4. Benders, J., Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4 (1962), 238–252.
5. Brook, A., Kendrick, D., Meeraus, A., GAMS, a user's guide. SIGNUM Newsletter 23:3–4 (1988), 10–11.
6. Bussieck, M.R., Ferris, M.C., Lohmann, T., Guss: Solving collections of data related models within gams. Kallrath, J., (eds.) Algebraic modeling systems: Modeling and solving real world optimization problems, 2012, Springer, Berlin, Heidelberg, 35–56.
7. Caroe, C., Schultz, R., Dual decomposition in stochastic integer programming. Operation Research Letters 24 (1999), 37–45.
8. Contreras, I., Cordeau, J., Laporte, G., Benders decomposition for large-scale uncapacited hub location. Operation Research 59 (2011), 1477–1490.
9. Coughlan, E., Lubbecke, M., Schulz, J., A branch-price-and-cut algorithm for multi-mode resource leveling. European Journal of Operational Research 245 (2015), 70–80.
10. CPLEX (2014). version 12.5. Armonk, New York: International Business Machines Corporation.
11. Čuček, L., Lam, H., Klemeš, J., Varbanov, P., Kravanja, Z., Synthesis of regional networks for the supply of energy and bioproducts. Clean Technologies and Environmental Policy 12 (2010), 635–645.
12. Dantzig, G., Wolfe, P., The decomposition principle for linear programs. Operations Research 8 (1960), 101–111.
13. Desaulniers, G., Desrosiers, J., Solomon, M., (eds.) (Trans.) A primer in column generation, 2005, Springer, US.
14. Desrosiers, J., Marco, E.L., A column generation approach to the urban transit crew scheduling problem. Transportation Science 23 (1989), 1–13.
15. Fisher, M., Lagrangian relaxation methods for solving integer programming problems. INFORMS 27 (1981), 1–18.
16. Fisher, M., An applications oriented guide to lagrangian relaxation. Interfaces 12 (1985), 10–21.
17. Florian, M., Guerin, G., Bushel, G., The engine scheduling problem in a railway network. INFORMS 14 (1976), 121–138.
18. Frangioni, A., About lagrangian methods in integer optimization. Annals of Operations Research 139 (2005), 163–193.
19. Garcia-Herreros, P., Wassick, J., Grossmann, I., Design of resilient supply chains with risk of facility disruptions. Industrial and Engineering Chemistry Research 53 (2014), 17240–17251.
20. Geoffrion, A.M., Generalized Benders decomposition. Journal of Optimization Theory and Applications 10:4 (1972), 237–260.
21. Geoffrion, A.M., Lagrangean relaxation for integer programming. Mathematical Programming Study 2 (1974), 82–114.
22. Guignard, M., Kim, S., Lagrangean decomposition: A model yielding stronger Lagrangean bounds. Mathematical Programming 39 (1987), 215–228.
23. Held, M., Wolfe, P., Crowder, H., Validation of subgradient optimization. Mathematical Programming 6 (1974), 62–88.
24. Holloway, C.A., A generalized approach to Dantzig–Wolfe decomposition for concave programs. Operations Research 21:1 (1973), 210–220.
25. Holmberg, K., On the convergence of cross decomposition. Mathematical Programming 47 (1990), 269–296.
26. Holmberg, K., Mean value cross decomposition applied to integer programming problems. European Journal of Operational Research 97 (1997), 124–138.
27. Iyer, R., Grossmann, I., Optimal planning and scheduling of offshore oil field infrastructure investment and operations. Industrial and Engineering Chemistry Research 37 (1998), 1380–1397.
28. Lasdon, L., Optimization theory for large systems. first ed., 1970, Macmillian, Toronto, Canada.
29. Li, J., Karimi, I., Scrinivasan, R., Recipe determination and scheduling of gasoline blending operations. AICHE 56 (2010), 441–465.
30. Li, X., Tomasgard, A., Barton, P.I., Nonconvex generalized Benders decomposition for stochastic separable mixed-integer nonlinear programs. Journal of Optimization Theory and Applications 151 (2011), 425–454.
31. Lubbecke, M.E., Desrosiers, J., Selected topics in column generation. Operation Research 53 (2005), 1007–1023.
32. Magnanti, R.T., Wong, T.L., Accelerating Benders decomposition: Algorithmic enhancement and model selection criteria. Operation Research 29 (1981), 464–484.
33. McClean, K., Li, X., Robust scenario formulations for strategic supply chain optimization under uncertainty. Industrial and Engineering Chemistry Research 52 (2013), 5721–5734.
34. McClean, K., Ogbe, E., Li, X., Novel formulation and efficient solution strategy for strategic optimization of an industrial chemical supply chain under demand uncertainty. The Canadian Journal of Chemical Engineering 93 (2015), 971–985.
35. Mitra, S., Garcia-Herreros, P., Grossmann, I., A novel cross-decomposition multi-cut scheme for two-stage stochastic programming. Computer Aided Chemical Engineering 33 (2014), 241–246.
36. Mitra, S., Garcia-Herreros, P., Grossmann, I.E., A cross-decomposition scheme with integrated primal–dual multi-cuts for two-stage stochastic programming investment planning problems. Mathematical Programming 157:1 (2016), 95–119.
37. Oukil, A., Amor, H., Desrosiers, J., Gueddari, H., Stabilized column generation for highly degenerate multiple-depot vehicle scheduling problems. Computers and Operations Research 34 (2007), 817–834.
38. Papageorgiou, L., Supply chain optimization for the process industries: Advances and opportunities. Computers and Chemical Engineering 33:12 (2009), 1931–1938.
39. Sahinidis, N., Grossman, I., Reformulation of the multiperiod MILP model for capacity expansion of chemical processes. Operations Research 40 (1992), S127–S144.
40. Slyke, R.M.V., Wets, R., L-shaped linear programs with applications to optimal control and stochastic programming. SIAM Journal on Applied Mathematics 17 (1969), 638–663.
41. Snyder, L., Daskin, M., Reliable models for facility: The expected failure cost case. Transportation Science 39 (2005), 400–416.
42. Van Roy, T.J., Cross decomposition for mixed integer programming. Mathematical programming 25:1 (1983), 46–63.
43. Van Roy, T.J., A cross decomposition algorithm for capacitated facility location. Operations Research 34 (1986), 145–163.
44. Vance, P.A., Barnhart, C., Johnson, E.L., Nemhauser, G.L., Solving binary cutting stock problems by column generation and branch-and-bound. Computational Optimization and Applications 3 (1994), 111–130.
45. Vanderbeck, F., On Dantzig/Wolfe decomposition for integer programming and ways to perform branching in the branch-and-price algorithm. Operations Research 48 (2000), 111–128.
46. Vanderbeck, F., A generic view of Dantzig/Wolfe decomposition for mixed integer programming. Operation Research Letters 23 (2006), 296–306.
47. Vanderbeck, F., Branching in branch-and-price: A generic scheme. Mathematical Programming 130 (2011), 249–294.