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reference request – Textbook advice for linear programming decomposition fundamentals
I took the passage 42136 for Benders decomposition and Dantzig-Wolfe (DW) decomposition at Technical University of Denmark. Besides the textbook [conejo2006decomposition] (talked about by @A.Omidi as properly), following supplies are really helpful:
- [carøe1998l], chapter 5.1 in [birge2011introduction] for L-shaped Benders Decomposition, when it comes to two-stage (stochastic) MILP with first-stage integer variables
- [desrosiers2005primer] for fundamentals of DW
- [feillet2010tutorial] for car routing with DW
- [merle1999stabilized] and [rousseau2007interior] for stabilization in column technology in DW
- [lübbecke2005selected] for DW in depth
By the route, Benders’ decomposition is built-in in CPLEX Versions 12.7 and later. We obtained a visitor lecture from IBM that point. See How to utensil Benders’ decomposition utilizing CPLEX, IBM uphold. In explicit:
The Benders’ technique parameter controls how CPLEX does the decomposition. The best route to employ it consists of setting this parameter to three to instruct CPLEX to do the decomposition routinely, placing the constraints that intersect solely integer variables into the grasp downside.
- [conejo2006decomposition] Conejo, A. J., Castillo, E., Minguez, R., & Garcia-Bertrand, R. (2006). Decomposition methods in mathematical programming: engineering and science functions. Springer Science & Business Media.
- [carøe1998l] Carøe, C. C., & Tind, J. (1998). L-shaped decomposition of two-stage stochastic packages with integer recourse. Mathematical Programming, 83(1), 451-464.
- [birge2011introduction] Birge, J. R., & Louveaux, F. (2011). Introduction to stochastic programming. Springer Science & Business Media.
- [desrosiers2005primer] Desrosiers, J., & Lübbecke, M. E. (2005). A primer in column technology. In Column technology (pp. 1-32). Springer, Boston, MA.
- [lübbecke2005selected] Lübbecke, M. E., & Desrosiers, J. (2005). Selected subjects in column technology. Operations analysis, 53(6), 1007-1023.
- [rousseau2007interior] Rousseau, L. M., Gendreau, M., & Feillet, D. (2007). Interior level stabilization for column technology. Operations Research Letters, 35(5), 660-668.
- [merle1999stabilized] Du Merle, O., Villeneuve, D., Desrosiers, J., & Hansen, P. (1999). Stabilized column technology. Discrete Mathematics, 194(1-3), 229-237.
- [feillet2010tutorial] Feillet, D. (2010). A tutorial on column technology and branch-and-price for car routing issues. 4or, 8(4), 407-424.
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