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# Decision Mathematics

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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### Bin Packing

The purpose of bin packing is to pack a collection of objects into containers called bins. The bins are all the same size and the objects to be packed are different sizes. The aim is to pack the objects into the bins using the fewest possible bins. In this example students are asked to save computer files onto a CD...

### Dijkstra's Algorithm

Dijkstra's algorithm finds the shortest path for a given problem. Dijkstra's algorithm can be used to find the shortest route between two cities. This algorithm is so powerful that it not only finds the shortest path from a chosen source to a given destination, it also finds all of the shortest paths from the...

### Flows

The network flow problem involves finding the optimum route through a flow network; a directed graph where each arc has a capacity and each arc receives a flow. Typical examples include: evacuation plans and delivery services. The problem involves students analysing the plan of a school canteen and deciding whether...

### Linear Programming

Linear Programming involves creating a function that represents a real life problem. The aim is to optimise this function given certain constraints. Simple examples of linear programming will have few variables and constraints, however, real life situations will have many more variables and constraints that will...