Two-Stage Stochastic Mixed-Integer Programming

In many optimisation problems arising in real life, some of the parameters are not known precisely at the point at which one must make a decision.  (For example, one might wish to design a telecommunications network, while having only estimates of the likely amount of traffic that users will wish to send through it.) 

Not only that, but it is frequently the case in which some or all of the decision variables have to take integer (whole-number) values.  (For example, it may be that the fiber-optic cables only come in particular sizes, and one must decide how many of each size to install between each pair of points in the network.)

The above considerations have led researchers to define a class of optimisation problems called two-stage stochastic mixed-integer programs.  In these problems, one seeks to minimise the cost of the decisions taken immediately, plus the expected cost of any decisions which may need to be taken later on, once the values of the parameters become known.  Unfortunately, these problems are extremely difficult to solve, even approximately.

This project would be concerned with the development of new techniques for solving two-stage stochastic mixed-integer programs (either exactly or approximately), implementing the methods in computer software, and evaluating their performance on a suitable collection of test instances.

Applicants for this research project need to have good qualifications in mathematics or a related discipline, and have experience with computer programming.  Experience with the LaTeX type-setting package would also be desirable, but is not essential as training can be given.

For further information contact Adam Letchford or Konstantinos Kaparis.

Return to the Optimisation Research Group page.