# Two tier integer programming using Benders style objective estimates

**Project level:** PhD, Masters, Honours

Benders Decomposition can be applied to problems with two tiers of decision variables, where the top tier are integer variables and the second tier are continuous variables.

This project would look at the application of similar approaches to problems where both tiers have integer variables. The top tier would typically be some form of binary facility selection/activation variables. Benders cuts using dual variables from the second tier would be replaced by numerically calculated partial derivatives.

The project could look to derive conditions under which the proposed approach guaranteed optimality or guaranteed a bound on the quality of the solution. It would also look at applying the proposed approach to a number of applications, to evaluate performance against competing approaches.