Short Course on Multistage Optimization

This is a short course that introduces the basic theory and methodology of multistage optimization presented first at IIT Bombay in December, 2015. It was updated and presented again at Zuse Institute Berlin in December, 2016. It was presented last at Friedrich-Alexander-Universität Erlangen-NürnbergErlangen in March, 2017. However, the slides are being continuously updated to incorporate recent work. The course is now in five parts.

Lecture slides (last updated March 26, 2017)


  • M. Güzelsoy and T. K. Ralphs, “Duality for Mixed-Integer Linear Programs,” International Journal of Operations Research, vol. 4, pp. 118-137, 2007. [PDF]
  • A. Hassanzadeh and T. K. Ralphs, “A Generalized Benders’ Algorithm for Two-Stage Stochastic Program with Mixed Integer Recourse,” COR@L Laboratory Report 14T-005, Lehigh University 2014. [PDF]
  • A. Hassanzadeh and T. K. Ralphs, “On the Value Function of a Mixed Integer Linear Optimization Problem and an Algorithm for Its Construction,” COR@L Laboratory Report 14T-004, Lehigh University 2014. [PDF]
  • S. DeNegre and T. K. Ralphs, “A Branch-and-Cut Algorithm for Bilevel Integer Programming,” in Proceedings of the Eleventh INFORMS Computing Society Meeting, 2009, pp. 65-78. [PDF]
  • S. A. Tahernejad, S. T. DeNegre, and T. K. Ralphs, “A Branch-and-Cut Algorithm for Mixed Integer Bilevel Linear Optimization Problems and Its Implementation,” COR@L Technical Report 16T-015 2016. [PDF]


  • MibS (Mixed Integer Bilevel Solver)

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