Thursday, 17 March 2011

Why OR in sports? Some reflections

Why is OR applicable to sports?

Many sports have a score, a number, to be maximised or optimised - hence there is a link to OR

Most sports have limited resources, to be used optimally - hence OR, The resources may be the team, or time, or money

Many sports operate sequentially, with decisions being made in order - just like in dynamic programming

Sports events require transport and supply chains - areas where OR has expertise

In a separate blog, I have mentioned the range of sports which have provided abstracts in IAOR. Most of those links are to strategy in the sport itself. My other blog on the subject considers the problems of scheduling transport.

Transport to sports events

When I studied OR as a postgraduate, we were presented with several scenarios to reflect on their logistical problems. One was related to sports transport.

An event is scheduled at time T1 and finishes at time T2. Spectators arrive by public transport in advance of time T1. Their arrivals are spread over a considerable period, as their plans vary. Some may want to be very early, others arrive in the last few minutes. But the general distribution of their arrivals is widely spread. So the transport provision has to reflect this ... with vehicles scheduled over a wide range of times before T1.

On the other hand, at time T2, all those who arrived by public transport are ready to depart at the same time. So the public transport has to be concentrated into a much smaller time window.

These are the same sorts of problem that one meets in other circumstances, but the size of the crowds at some sports events make the contrasting problems particularly difficult.

OR has been used by the organisers of the recent Olympics to cope with this scheduling problem. And already, the London Underground OR team is planning how to cope with the 2012 Games.

OR in Sport - the index

This month's suggestion from INFORMS is that bloggers should write about OR in Sport.
The problem that I have about this is knowing where to start. When I edited IAOR, there were numerous research papers that were included in IAOR, and I cross referenced them by sport. So my records show that there were abstracts relating to the following sports:
horse racing
So, this is my first contribution - an index!

Tuesday, 15 March 2011

Reducing wood waste

It is interesting to see how technology can be used to create something which is ethically and aesthetically pleasing. I have been pointed to the website of a company called Bolefloor who make wooden floorboards. But these are not rectangular boards, they follow the natural curves of the wood, so that there is less waste in shaping the boards.

So, here is their process:
1) take a tree
2) saw it and plane it into planks of uniform thickness (21mm)
3) scan the shape of the edges
4) now optimise -- how can the floor of a room be made of these planks, like a jigsaw, with plain or tongue-and-groove edges, to minimise the waste? Here is the O.R. content, though it looks as if it was people who come from the computer science academic regime who did it.
5) shape the edges and ship to the customer.

Result - a beautiful, unique floor.

Tuesday, 1 March 2011

Puzzles and logic

My father had a selection of books of mathematical puzzles, and as a youngster I used to enjoy trying to solve them. Later, we subscribed to a Sunday newspaper, the Sunday Times, which had a weekly "Brainteaser". These were problems of logic and mathematics which we enjoyed solving together. Much to my mother's dismay, some Sunday lunchtime meals were disturbed as he and I debated how to solve the problem.

These were puzzles where the first stage was to sort out the logic needed to solve them. Recently, a number of puzzles have become popular, such as Sudoku. These need logic (and minimal mathematical skill) but the logic is more or less the same each time. I am interested in the reasoning behind the setting of such problems; how can you guarantee that the puzzle can be solved and has a a unique solution?

The Independent newspaper has carried Sudoku puzzles for several years; recently, it has carried a range of puzzles. We have been looking at the ones that are called "Maths Puzzle". These are based around the nine digits 1-9, arranged in a square, with two mathematical operators between the three digits in each row, and between the three digits in each column. Then, at the three row ends and three column feet, are the results of the "sum". The challenge is to work out where the nine digits are placed, given the six results and the twelve operators. See "Maths Puzzle" for an example.

So, I wonder how such problems are set. With nine digits, the checking could be done by brute force very quickly, and that is how I suspect it is verified. The newspaper's problems have an easy puzzle, with two digits entered, and a hard one with one digit entered. Tina and I tackle the problems ignoring those digits. Much more need for logic.

And the O.R. link? The solution is a problem of combinatorial optimisation.