1. Operational Research (O.R.) case studies

2. What’s the problem? www.LearnAboutOR.com

3. You are an electronic engineer… www.LearnAboutOR.com

4. You are designing a Printed Circuit Board (PCB) PCBs are used in electronics to connect electrical components using conductive pathways Since the wires are not insulated, they must not cross www.LearnAboutOR.com

5. You have designed the circuit that you want, but some of the wires cross www.LearnAboutOR.com

6. Is it possible to redraw your circuit in such a way that no wires cross? www.LearnAboutOR.com

7. Let’s summarise the problem We have a graph with some edges which cross We want to know if it is possible to re-draw it in such a way that none of the edges cross www.LearnAboutOR.com

8. This is an example of a Planarity Problem www.LearnAboutOR.com

9. Planarity Problems A graph is planar if it can be drawn in a plane so that no two edges meet (except at a vertex to which they are both incident) www.LearnAboutOR.com

10. Another example where this is used Utilities (gas, water, electricity) companies trying to lay pipes that do not cross each other… www.LearnAboutOR.com

11. Over the next few lessons, we will look at ways of approaching problems of this type… What next? www.LearnAboutOR.com