Riley Cooper is an undergraduate student in the School of Mathematical and Physical Sciences at the University of Newcastle, studying a Bachelor of Mathematics degree with specialisation in Applied Mathematics and Statistics. He is interested in Applied Mathematics with focuses on Optimisation, Programming and Computation and Statistics with focuses on Bayesian Analysis, Markov Chains and Data Science. Flexibility of the Bachelor of Mathematics degree has allowed Riley to study a range of topics in Pure Mathematics on top of the Applied Mathematics and Statistics Majors. Riley has also established programming skills in different languages in relation to his university study. By being placed on the Faculty of Science and Information Technology Commendation List for every year of tertiary study to date, Riley has proven strong academic results. Riley was granted the Faculty of Science and Information Technology Summer Vacation Scholarship in 2016 and was able to pursue his interest in Mathematical Research. Under the supervision of Dr Thomas Kalinowski, Riley completed a research project titled “Allocation of Indivisible Goods”. Studying abroad at the University of Leeds in 2017 gave Riley the opportunity to experience university life in a different country, travel, and build many personal skills. Riley intends to complete an Honours degree in Applied Mathematics or Statistics and to then to pursue work and/or graduate study.
Lot Sizing on a Cycle
Production planning and scheduling problems are a key component in many supply chains. A recurring model in these problems is the multi-item lot sizing model in which a schedule of production is determined for each item being produced so that the demand for each item is satisfied subject to constraints on production, inventory and the operation of the machinery. In this project we will investigate a variant of the classical deterministic single-item lot sizing problem in which the underlying network is a cycle. Such a variant is motivated by strategic production planning and scheduling problems in which it is often convenient to assume that the planning horizon wraps around on itself, thereby eliminating the need to specify boundary conditions and avoiding possible end effects. Such an approach can be viewed as a form of steady state model.
In this project we will introduce the single-item lot sizing problem on a cycle. We will propose a mixed-integer programming formulation for the problem, explore the structural properties of the optimal solutions, and use them to establish the computational complexity of the problem and develop efficient algorithms for its solution. Finally we will investigate the polyhedral structure of the convex hull of the set of feasible solutions to the problem and propose extended formulations and strong reformulations for the problem.