# CARMA OR Seminar

## Wednesday, 10th Feb 2016

V205, Mathematics Building

# Dr Jason Matthews

(School of Mathematical and Physical Sciences, The University of Newcastle)

# SKU assignment in a multiple picking line order picking system

An order picking system in a distribution center (DC) owned by Pep Stores Ltd. (PEP) the largest single brand retailer in South Africa is investigated. Twelve independent unidirectional picking lines situated in the center of the DC are used to process all piece picking. Each picking line consists of a number of locations situated in a cyclical formation around a central conveyor belt and are serviced by multiple pickers walking in a clockwise direction.

On a daily planning level three sequential decisions tiers exist and are described as:

1. Assigning stock keeping units (SKUs) to available picking lines
2. Arranging the assigned SKUs on individual picking lines
3. Sequencing the resulting orders for pickers on individual picking lines Each decision tier defines a separate sub-problem which depends on the output of the preceding sub-problem.

These sub-problems are too complex to solve together and are addressed independently and in reverse sequence using mathematical programming and heuristic techniques. It is shown that the total walking distances of pickers may be significantly reduced when solving sub-problems 1 and 3 and that there is no significant impact when solving sub-problem 2. Moreover, by introducing additional work balance and small carton minimisation objectives into sub-problem 1 better trade-offs between objectives are achieved when compared to the current practice.

# CARMA Seminar

## Wednesday, 10th Feb 2016

V206, Mathematics Building

# Jim Cooper

(President & CEO, Maplesoft)

# The Future of Education

In this presentation we address the issues and challenges for Future of Education and how Maplesoft is committed to offers Tools such as Möbius™ to handle these challenges. Möbius is a comprehensive online courseware environment that focuses on science, technology, engineering, and mathematics (STEM). It is built on the notion that people learn by doing. With Möbius, your students can explore important concepts using engaging, interactive applications, visualize problems and solutions, and test their understanding by answering questions that are graded instantly. Throughout the entire lesson, students remain actively engaged with the material and receive constant feedback that solidifies their understanding.

When you use Möbiusto develop and deliver your online offerings, you remain in full control of your content and the learning experience.

• Bring your online vision to life, including online courses, open-access courses, formative testing, placement and remediation programs, independent learning, outreach programs, and flipped or blended classrooms.
• Provide exactly the content you want, from individual lessons and textbook supplements, to full courses, remedial materials, enrichment content, and more.
• Choose the learning experience by allowing students open access to your course material or guiding them along a specific learning path.
• Stay in control of your content, creating and customizing materials as you wish to suit your needs.
• Save your students money by dropping a traditional textbook, while simultaneously improving the learning experience.

# CARMA Discrete Mathematics Seminar

## Thursday, 11th Feb 2016

V205, Mathematics Building

# The Degree/Diameter Problem for Mixed Graphs

The Degree/Diameter Problem for graphs has its motivation in the efficient design of interconnection networks. It seeks to find the maximum possible order of a graph with a given (maximum) degree and diameter. It is known that graphs attaining the maximum possible value (the Moore bound) are extremely rare, but much activity is focussed on finding new examples of graphs or families of graph with orders approaching the bound as closely as possible. This problem was first mention in 1964 and has its motivation in the efficient design of interconnection networks. A lot of great mathematician studied this problem and obtained some results but there still remain a lot of unsolved problems about this subject. Our regretted professor Mirka Miller has given a great expansion to this problems and a lot of new results were given by her and her students. One of the problem she was recently interested in, was the Degree/Diameter problem for mixed graphs i.e. graphs in which we allow undirected edges and arcs (directed edges).

Some new result about the upper bound of this Moore mixed graph has been obtained in 2015. So this talk consists on giving the main known results about those graphs.

# 2016 Summer Student Presentations Part I

## Thursday, 11th Feb 2016

V205, Mathematics Building

Presentations will be held on Thursday afternoon and all day on Friday.

# 2016 Summer Student Presentations Part II

## Friday, 12th Feb 2016

V205, Mathematics Building

Presentations will be held on Thursday afternoon and all day on Friday.

# South Pacific Optimization Workshop SPOW 2016

## Tuesday, 16th Feb 2016 — Thursday, 18th Feb 2016

[Noumea]

For information, please visit the workshop website.

# CARMA Seminar

## Tuesday, 16th Feb 2016

V205, Mathematics Building

# Basic hypergeometric orthogonal polynomials

We will review the (now classical) scheme of basic ($q$-) hypergeometric orthogonal polynomials. It contains more than twenty families; for each family there exists at least one positive weight with respect to which the polynomials are orthogonal provided the parameter $q$ is real and lies between 0 and 1. In the talk we will describe how to reduce the scheme allowing the parameters in the families to be complex. The construction leads to new orthogonality properties or to generalization of known ones to the complex plane.

# CARMA Colloquium

## Thursday, 3rd Mar 2016

V205, Mathematics Building

# Andrew Rechnitzer

(University of British Colombia)

# Bounding the entropy of hard squares

Start labelling the vertices of the square grid with 0's and 1's with the condition that any pair of neighbouring vertices cannot both be labelled 1. If one considers the 1's to be the centres of small squares (rotated 45 degrees) then one has a picture of square-particles that cannot overlap.

This problem of "hard-squares" appears in different areas of mathematics - for example it has appeared separately as a lattice gas in statistical mechanics, as independent sets in combinatorics and as the golden-mean shift in symbolic dynamics. A core question in this model is to quantify the number of legal configurations - the entropy. In this talk I will discuss the what is known about the entropy and describe our recent work finding rigorous and precise bounds for hard-squares and related problems.

This is work together with Yao-ban Chan.

# Australasian Conference on Combinatorial Mathematics and Combinatorial Computing

## Monday, 12th Dec 2016 — Friday, 16th Dec 2016

University House

For details, please visit the conference web page.