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A special case of the generalized pooling problem arising in the mining industry

Natashia Boland (natashia.boland***at***isye.gatech.edu)
Thomas Kalinowski (thomas.kalinowski***at***newcastle.edu.au)
Fabian Rigterink (fabian.rigterink***at***uon.edu.au)
Martin Savelsbergh (martin.savelsbergh***at***isye.gatech.edu)

Abstract: Iron ore and coal are substantial contributors to Australia's export economy. Both are blended products that are made-to-order according to customers' desired product qualities. Mining companies have a great interest in meeting these target qualities since deviations generally result in contractually agreed penalties. This paper studies a variation of the generalized pooling problem (GPP) arising in this context. The GPP is a minimum cost network flow problem with additional bilinear constraints to capture the blending of raw materials. In the variation we study, costs are not associated with network flows but with deviations from target qualities. We propose a bilinear program (BLP) that we solve locally using nonlinear programming solvers to obtain upper bounds. We linearly relax the BLP using McCormick relaxations and solve the resulting linear program (LP) to obtain lower bounds. A computational study on 26 instances, representing a real-life industry setting and having quarterly, half-yearly, annual and triannual planning horizons, shows that even for large-scale BLPs, these bounds can be calculated efficiently.

Keywords: blending; generalized pooling problem; bilinear programming; nonlinear programming

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Global Optimization (Applications )

Citation:

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Entry Submitted: 07/22/2015
Entry Accepted: 07/22/2015
Entry Last Modified: 04/25/2016

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