Operational Research (O.R.) is the discipline of applying advanced analytical methods to help make better decisions. The O.R. approach often involves constructing and using mathematical models and problem structuring methods to represent the wide range of problems faced by organisations. The results of these models allow managers to make more informed decisions. The OR Society have developed ten problems for use in Decision mathematics lessons. Each problem consists of a PowerPoint presentation, a student worksheet and a suggested solution. The problems can be used as an introduction to a topic, part of the learning process or as a plenary exercise. The ten topics covered are: • Bin Packing • Critical Path Analysis • Dijkstra's Algorithm • Network Flow Problem • Linear Programming • Matching Problem • Minimum Spanning Tree • Planar Graphs • Route Inspection Problem • Travelling Salesperson Problem

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Matchings

A matching is a set of edges on a bipartite graph in which no two edges share a common vertex. A bipartite graph consists of two sets of vertices X and Y. The edges only join vertices in X to vertices in Y. A matching in a bipartite graph is the pairing of some or all of the vertices in X with some or all of the...

Minimum Spanning Tree

The aim of a minimum spanning tree is to connect every vertex of the network using the edges having the least possible total weight. The task requires students to analyse information about a town centre and suggest which roads should be pedestrianized. [

Minimum spanning tree: presentation...

Planarity

Many topological graphs have edges that cross. The aim is to re-draw the graph in such a way that none of the edges cross. The task informs students they are required to design a printed circuit board and since the wires are not insulated they must not cross.

Planarity: presentation - an...

Route Inspection

The aim of the route inspection problem is to find a route that is as short as possible yet goes down every road once and returns to the starting point. The task informs students that there has been a heavy snowfall overnight and that the students are required to clear the roads in the town centre as quickly as...

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