Clique-based facets for the precedence constrained knapsack problem

A. Bley, N. Boland, C. Fricke, G. Froyland, R. Sotirov

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)481-511
JournalMathematical Programming
Issue number1
Publication statusPublished - 2012


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