Cutting Planes for Multistage Stochastic Integer Programs

References

• Ahmed S., King A. J., Parija G. A multi-stage stochastic integer programming approach for capacity expansion under uncertainty. J. Global Optim. (2003) 26:3–24Crossref, Google Scholar
• Barany I., van Roy T., Wolsey L. A. Uncapacitated lot-sizing: The convex hull of solutions. Math. Programming Stud. (1984) 22:32–43Crossref, Google Scholar
• Carøe C. C., Schultz R. Dual decomposition in stochastic integer programming. Oper. Res. Lett. (1999) 24:37–45Crossref, Google Scholar
• Cook W., Kannan R., Schrijver A. J. Chvátal closures for mixed integer programming problems. Math. Programming (1990) 47:155–174Crossref, Google Scholar
• Di Summa M., Wolsey L. A. Lot-sizing on a tree. Oper. Res. Lett. (2008) 36(1):7–13Crossref, Google Scholar
• Guan Y. Pairing inequalities and stochastic lot-sizing problems: A study in integer programming. (2005) . Ph.D. thesis, Georgia Institute of Technology, AtlantaGoogle Scholar
• Guan Y., Ahmed S., Nemhauser G. L. Sequential pairing of mixed integer inequalities. Discrete Optim. (2007) 4:21–39Crossref, Google Scholar
• Guan Y., Ahmed S., Nemhauser G. L., Miller A. J. A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem. Math. Programming (2006) 105:55–84Crossref, Google Scholar
• Günlük O., Pochet Y. Mixing MIR inequalities for mixed integer programs. Math. Programming (2001) 90:429–457Crossref, Google Scholar
• Loparic M., Marchand H., Wolsey L. A. Dynamic knapsack sets and capacitated lot-sizing. Math. Programming (2003) 95:53–69Crossref, Google Scholar
• Lulli G., Sen S. A branch and price algorithm for multi-stage stochastic integer programming with application to stochastic batch-sizing problems. Management Sci. (2004) 50:786–796Link, Google Scholar
• Miller A. J., Wolsey L. A. Tight formulations for some simple mixed integer programs and convex objective integer programs. Math. Programming (2003) 78:73–88Crossref, Google Scholar
• Nemhauser G. L., Wolsey L. A.Integer and Combinatorial Optimization (1988) (Wiley, New York) Crossref, Google Scholar
• Nemhauser G. L., Wolsey L. A. A recursive procedure for generating all cuts for 0–1 mixed integer programs. Math. Programming (1990) 46:379–390Crossref, Google Scholar
• Nowak M. P., Römisch W. Stochastic Lagrangian relaxation applied to power scheduling in a hydro-thermal system under uncertainty. Ann. Oper. Res. (2000) 100:251–272Crossref, Google Scholar
• Römisch W., Schultz R., Grötschel M., Krumke S. O., Rambau J. Multistage stochastic integer programs: An introduction. Online Optimization of Large Scale Systems (2001) (Springer-Verlag, Berlin-Dahlem) 579–598Crossref, Google Scholar
• Sen S., Aardal K., Nemhauser G. L., Weismantel R. Algorithms for stochastic mixed-integer programming models. Handbook of Discrete Optimization (2005) (North-Holland Publishing Co., Amsterdam) 515–558Crossref, Google Scholar
• Singh K., Philpott A. B., Wood K. Dantzig-Wolfe decomposition for solving multi-stage stochastic capacity planning problems. (2008) . Under reviewGoogle Scholar
• Takriti S., Birge J. R., Long E. A stochastic model for the unit commitment problem. IEEE Trans. Power Systems (1996) 11:1497–1508Crossref, Google Scholar