Abstract
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, for both PCKP instances arising in real applications, and applications in which PCKP appears as an embedded structure.
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Boland, N., Bley, A., Fricke, C. et al. Clique-based facets for the precedence constrained knapsack problem. Math. Program. 133, 481–511 (2012). https://doi.org/10.1007/s10107-010-0438-7
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DOI: https://doi.org/10.1007/s10107-010-0438-7