The topics on partitioning problems will be investigated from the polyhedral point of view. This approach consists in associating a polytope defined as the convex hull of the feasible solutions of the problem, and to study the facial structure of this polytope. We are interested in finding large classes of facets of the polytope under investigation in order to obtain good partial description of this polytope. Then we have to investigate the separation problems for the classes of facets that have been determined and using these results we plan to implement a Branch and Cut algorithm for the problem.
The packing problems will be investigated using two different approaches. One of them is a more combinatorial approach to design polynomial approximation algorithms for which we can prove some asymptotic performance ([17, 18, 19, 20, 21, 22]).The other approach consists in modelling the problem as an integer linear programming problem and uses columm generation techniques to solve it approximately ([11, 12]).