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Clique-based facets for the precedence constrained knapsack problem

Natashia Boland(Natashia.Boland***at***newcastle.edu.au)
Andreas Bley(bley***at***math.tu-berlin.de)
Christopher Fricke(chris.fricke***at***tsgconsulting.com.au)
Gary Froyland(g.froyland***at***unsw.edu.au)
Renata Sotirov(r.sotirov***at***uvt.nl)

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.

Keywords: Precedence constrained knapsack problem, Clique inequalities, Integer programming

Category 1: Integer Programming (Cutting Plane Approaches )

Citation: School of Mathematical and Physical Sciences, The University of Newcastle, NSW, 2308, Australia, October 2009

Download: [PDF]

Entry Submitted: 10/26/2009
Entry Accepted: 10/26/2009
Entry Last Modified: 10/26/2009

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