The precedence constrained knapsack problem: Separating maximally violated inequalities

We consider the problem of separating maximally violated inequalities for the precedence constrained knapsack problem. Though we consider maximally violated constraints in general, special emphasis is placed on induced cover inequalities and induced clique inequalities. Our contributions include a new partial characterization of maximally violated inequalities, a new safe shrinking technique, and new insights on strengthening and lifting. This work follows on the work of Boyd (1993), Park and Park (1997), van de Leesel et al (1999) and Boland et al (2011).