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Introduction

This unit is intended to be the third unit of the course and will introduce several topics that will be new to most students. The topics covered are Bin Packing, Networks, Linear Programming and Critical Path Analysis. These topics have a common theme in that they have all been developed over the last 70 years as useful techniques for solving decision-making problems. This unit is intended to be an introduction to these topics as they will be revisited later in the course.

Each topic is introduced though a specific real world problem rather than by direct teaching. These problems being intentionally “thought provoking”, should stimulate plenty of discussion and argument as to the best approach. It is our belief that the traditional algorithms can emerge through these discussions as the students continually reassess their own thinking as new ideas emerge. As requested I have added some exercises to each section.

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Networks Overview

In this section, the word network is given a mathematical meaning. We say that a network is a graph in which each arc (or edge) is assigned a number called its weight. The problem generally is to maximize or minimize the sum of these weights subject to certain conditions. Typical examples include route finding algorithms and minimum connector problems. Harder problems such as the Travelling Salesman problem and the Chinese Postman problem will feature in a later Pathway.

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Documents included

Network.notebook - Notebook file containing four initial problems for use with a Smartboard.

Network.pptx - PowerPoint file containing four initial problems.

Network Teachers Guide.notebook - Notebook file giving examples of well known algorithms for use with a Smartboard.

Network Teachers Guide.pptx - A PowerPoint file giving examples of well known algorithms.

Examples_networks.notebook Examples of networks that can be used for further discussion and practice (notebook file).

Examples_networks.pptx Examples of networks that can be used for further discussion and practice (PowerPoint).

Examples_networks.docx - A student handout.