Title: Pooling Problems: Advances in Theory and Applications
Speaker: Fabian Rigterink
Affiliation: School of Mathematical and Physical Sciences – The University of Newcastle Australia
Location: Room 554 Huxley Building
Time: 3:00pm

Abstract. The pooling problem is a nonconvex nonlinear programming problem with important applications. The nonlinearities of the problem arise from bilinear constraints that capture the blending of raw materials. In this talk, we summarise our recent contributions to the problem, which fall into the following categories:
Formulations: we propose new multi-commodity flow formulations based on output, input and output and (input, output) commodities, and evaluate their performance computationally.
Complexity: we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time.
Bounding the gap between the McCormick relaxation and the convex hull: we show that the so-called McCormick relaxation can be arbitrarily worse than the convex hull.
Convex hulls of bilinear functions: Padberg introduced new classes of inequalities that can significantly strengthen the McCormick relaxation. We study classes of bilinear functions where some of the Padberg inequalities characterise the convex hull, and evaluate computationally which of the inequalities are strongest.
We conclude the talk by studying an application of particular interest to Novocastrians: optimising coal blending operations at the port of Newcastle; the world’s largest coal export port. This is joint work with my PhD supervisors, Dr Thomas Kalinowski, Prof Natashia Boland, and Prof Martin Savelsbergh.

About the speaker. Fabian Rigterink is a PhD candidate at the University of Newcastle, Australia. He is supervised by Dr Thomas Kalinowski, Prof Natashia Boland, and Prof Martin Savelsbergh. Prior to commencing his PhD, Fabian received his BSc and MSc in Industrial Engineering and Management from Karlsruhe Institute of Technology, Germany.