Authors: Audet, Charles
Brimberg, Jack
Hansen, Pierre
Le Digabel, Sébastien
Mladenović, Nenad 
Title: Pooling problem: Alternate formulations and solution methods
Journal: Management Science
Volume: 50
Issue: 6
First page: 761
Last page: 776
Issue Date: 1-Jun-2004
Rank: M21a
ISSN: 0025-1909
DOI: 10.1287/mnsc.1030.0207
Abstract: 
The pooling problem, which is fundamental to the petroleum industry, describes a situation in which products possessing different attribute qualities are mixed in a series of pools in such a way that the attribute qualities of the blended products of the end pools must satisfy given requirements. It is well known that the pooling problem can be modeled through bilinear and nonconvex quadratic programming. In this paper, we investigate how best to apply a new branch-and-cut quadratic programming algorithm to solve the pooling problem. To this effect, we consider two standard models: One is based primarily on flow variables, and the other relies on the proportion of flows entering pools. A hybrid of these two models is proposed for general pooling problems. Comparison of the computational properties of flow and proportion models is made on several problem instances taken from the literature. Moreover, a simple alternating procedure and a variable neighborhood search heuristic are developed to solve large instances and compared with the well-known method of successive linear programming. Solution of difficult test problems from the literature is substantially accelerated, and larger ones are solved exactly or approximately.
Keywords: Bilinear programming | Branch-and-cut | Heuristics | Pooling problem | Variable neighborhood search
Publisher: INFORMS

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