In this study, I focus on the derivation and use of cutting planes to solve general mixed integer problems, and in particular inventory problems combined with other problems such as distribution, supplier selection, vehicle routing, etc (called complex inventory problems). In order to achieve this goal, I first consider substructures (relaxations) of such problems which are obtained by the coherent loss of information. The polyhedral structure of those simpler mixed integer sets is studied to derive strong valid inequalities. Finally those strong inequalities are included in the cutting planes algorithm to solve the general mixed integer problems.
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