### Mixed Integer Programming

### Mixed Integer Programming

*OPL User Guide: modelling integer/boolean variables***Skills Modelling**

Know the main combinatorial optimization problems and model them as an integer linear program: knapsack, bin packing, set covering, set partitionning, minimum cost flow, shortest path

*Self training**OPL User Guide:*using .dat files with OPL and the Caseine editor**Skills Solving**

Know the definition of a linear relaxation

Know the relation between the value of an optimal solution of the MIP and of the linear relaxation

Be able to explain the principle of the Branch and Bound algorithm graphically (2 variables)

Know which variable can be branched on and the branching conditions

Know how to calculate the lower and upper bound during the execution of the algorithm

Know the conditions that allow to cut a branch

*Self training*