Abstract
The paper deals with the Knapsack Problem with conflicts, also known as the Disjunctively Constrained Knapsack Problem (DCKP). The conflicts are represented by a graph whose vertices are the items such that adjacent items cannot be packed in the knapsack simultaneously. We consider a classical formulation for the DCKP, study the polytope associated with this formulation and investigate the facial aspect of its basic constraints. We then present some valid inequalities. Based on this study, we discuss separation routines of the valid inequalities and devise a Branch-and-Cut algorithm. Preliminary results on a set of problem instances are also given.
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