We consider a knapsack problem with precedence constraints imposed on pairs of items, known as the precedence constrained knapsack problem (PCKP). This problem has applications in manufacturing and mining, and also appears as a subproblem in decomposition techniques for network design and related problems. We present a new approach for determining facets of the PCKP polyhedron based on clique inequalities. A comparison with existing techniques, that lift knapsack cover inequalities for the PCKP, is also presented. It is shown that the clique-based approach generates facets that cannot be found through the existing cover-based approaches, and that the addition of clique-based inequalities for the PCKP can be computationally beneficial.
|Publication status||Published - 2012|
Bley, A., Boland, N., Fricke, C., Froyland, G., & Sotirov, R. (2012). Clique-based facets for the precedence constrained knapsack problem. Mathematical Programming, 133(1), 481-511. http://www.optimization-online.org/DB_FILE/2009/10/2436.pdf