Colloquium Mathematics - Prof. dr. T. Kalinowski University of New England

Title: Optimisation problems arising in operating a coal export supply chain

Abstract:

Over the last few years, I have worked on a range of optimisation problems arising in the context of operating railway networks feeding into the export terminals in New South Wales and Queensland. In the first part of the talk, I will give a high-level overview of some of the problems and the methods that were used to overcome the challenges in solving them. This includes system capacity estimation, maintenance planning, and efficient terminal operation.

I will then explain in a bit more detail some recent work (with Akshay Gupte, Fabian Rigterink and Hamish Waterer) on a new method to approximate the graphs of non-convex quadratic functions by convex polytopes. These functions appear in blending and pooling problems in various industries, and their convexification is an important ingredient in state-of-the-art methods for global optimisation. Due to the scale of the problems that need to be solved in practice, it is essential to work with relaxations that are as tight as possible. This is closely related to the Boolean Quadric Polytope (BQP), introduced in 1989 by Padberg in the context of 0-1-programming. For certain classes of functions, we use combinatorial methods to prove that using a small subset of the facets of BQP we can obtain an extended formulation for the convex hull of the graph of the function.

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