Peter Grossman

Minimum Steiner trees on a set of concyclic points and their center

David Whittle, Marcus Brazil, Peter Alexander Grossman, Joachim Hyam Rubinstein, Doreen A Thomas

Journal article  |  2021  |  INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH

Consider a configuration of points comprising a point q and a set of concyclic points R that are all a given distance r from q in ..

Solving the prize-collecting Euclidean Steiner tree problem

David Whittle, Marcus Brazil, Peter A Grossman, J Hyam Rubinstein, Doreen A Thomas

Journal article  |  2020  |  INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH

The prize-collecting Euclidean Steiner tree (PCEST) problem is a generalization of the well-known Euclidean Steiner tree (EST) pro..

OPTIMAL LOCATION OF AN UNDERGROUND CONNECTOR USING DISCOUNTED STEINER TREE THEORY

KG Sirinanda, M Brazil, PA Grossman, JH Rubinstein, DA Thomas

Journal article  |  2020  |  ANZIAM JOURNAL

The objective of this paper is to demonstrate that the gradient-constrained discounted Steiner point algorithm (GCDSPA) described ..

Scheduling the construction of value and discount weighted trees for maximum net present value

PA Grossman, M Brazil, JH Rubinstein, DA Thomas

Journal article  |  2020  |  Computers and Operations Research

Given a binary rooted tree in which each edge has an associated value and an associated discount factor, the problem addressed her..

Minimal curvature-constrained networks

D Kirszenblat, KG Sirinanda, M Brazil, PA Grossman, JH Rubinstein, DA Thomas

Journal article  |  2018  |  JOURNAL OF GLOBAL OPTIMIZATION

This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given ..

Combined optimisation of an open-pit mine outline and the transition depth to underground mining

D Whittle, M Brazil, PA Grossman, JH Rubinstein, DA Thomas

Journal article  |  2018  |  EUROPEAN JOURNAL OF OPERATIONAL RESEARCH

Miners harvest minerals from ore-bodies in the ground by a variety of specialised mining methods, with most falling into the categ..

Strategic Underground Mine Access Design to Maximise the Net Present Value

M Brazil, K Sirinanda, P Grossman, J Rubinstein, D Thomas

Book Chapter  |  2018

To date, the scheduling and access design of an underground mine have only been considered as two separate optimisation problems. ..

Gradient-constrained discounted Steiner trees II: optimally locating a discounted Steiner point

KG Sirinanda, M Brazil, PA Grossman, JH Rubinstein, DA Thomas

Journal article  |  2016  |  JOURNAL OF GLOBAL OPTIMIZATION

A gradient-constrained discounted Steiner tree is a network interconnecting given set of nodes in Euclidean space where the gradie..

Determining the open pit to underground transition: A review of existing methods and a proposed new method

D Whittle, M Brazil, PA Grossman, JH Rubinstein, D THOMAS

Conference Proceedings  |  2016

Gradient-constrained discounted Steiner trees I: optimal tree configurations

KG Sirinanda, M Brazil, PA Grossman, JH Rubinstein, DA Thomas

Journal article  |  2016  |  Journal of Global Optimization

A gradient-constrained discounted Steiner treeT is a maximum Net Present Value (NPV) tree, spanning a given set N of nodes in spac..