2018
DOI: 10.48550/arxiv.1803.02955
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Strong Convex Nonlinear Relaxations of the Pooling Problem

Abstract: We investigate new convex relaxations for the pooling problem, a classic nonconvex production planning problem in which input materials are mixed in intermediate pools, with the outputs of these pools further mixed to make output products meeting given attribute percentage requirements. Our relaxations are derived by considering a set which arises from the formulation by considering a single product, a single attibute, and a single pool. The convex hull of the resulting nonconvex set is not polyhedral. We deri… Show more

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Cited by 2 publications
(2 citation statements)
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“…While the standard pooling problem is NP-hard to solve [6,27], there are also some positive results. For instance, a polynomial-time n-approximation algorithm (n is the number of output nodes) is presented in [22], convex hull of special substructure (with one pool node) has been studied [34], and recently some very special cases of the pooling problem has been shown to be polynomially solvable [27,28,13,7]. However, none of these positive results apply for the generalized pooling problem in which the corresponding graph has arcs from the set (I × (I ∪ T )).…”
Section: Application Of Convex Hull Results To the Pooling Problemmentioning
confidence: 99%
“…While the standard pooling problem is NP-hard to solve [6,27], there are also some positive results. For instance, a polynomial-time n-approximation algorithm (n is the number of output nodes) is presented in [22], convex hull of special substructure (with one pool node) has been studied [34], and recently some very special cases of the pooling problem has been shown to be polynomially solvable [27,28,13,7]. However, none of these positive results apply for the generalized pooling problem in which the corresponding graph has arcs from the set (I × (I ∪ T )).…”
Section: Application Of Convex Hull Results To the Pooling Problemmentioning
confidence: 99%
“…These approaches are employed in state-of-theart mixed-integer nonlinear programming software where piecewise-linear relaxations may further improve solver performance on pooling problems (Gounaris et al, 2009;Hasan and Karimi, 2010;Kolodziej et al, 2013;Misener et al, 2011;Misener and Floudas, 2012;Wicaksono and Karimi, 2008). Further valid linear and convex inequalities are derived from nonconvex restrictions of the pooling problem (Luedtke et al, 2018).…”
Section: Brief Literature Overviewmentioning
confidence: 99%