O.R. on a trip to London

We went to London for a two-day break last week, and, inevitably, I looked at some of the experience with a pair of O.R.-problem-seeker's spectacles. Two of the things I saw are worth recording.

We went to the theatre (Phantom of the Opera); earlier in the year we had booked online and bought the cheapest tickets on sale ... even for a treat like this, we couldn't face paying some of the prices. The cheapest seats are £25; in Exeter and Taunton, where we generally go to the theatre, the most expensive seats are less than £20. When we got to the theatre, we discovered that the section in which our seats were located was closed for the evening, and we were bumped up to higher quality seats ... in fact the most expensive ones, at £59 each. At no charge, of course. So here is the cheapskate's optimal policy for theatre-going. Book well in advance, for a midweek (less popular) evening, in the cheapest section fof the theatre. Then wait and see what happens when you arrive. At worst, you have your seats. But you may get an upgrade instead. (Oh, and take your own chocolates ... theatre prices are high!)



We bought Oyster cards to pay for the trips around London on the bus and tube. The cost of fares is deducted from the balance on the card, up to a daily maximum, which depends on where you travel and when. So, off-peak, in zones 1-2, the cap is £5.60, which is also the price of a day card. We didn't save much except time with that. We did save when we used the tube in the morning rush-hour. Even then, the scheme has a cap on the day's deduction. Looking at the calculation of caps, we spotted an anomaly. For someone whose use of the system consists of one journay in the morning rush-hour and a number of journeys in the off-peak season, the cap may be more than the combined rush-hour fare and the cost of the day card. So it is better not to use the same Oyster card for the rush-hour and the rest of the day. So here's the optimal strategy for anyone doing this type of day's travelling very often. Have two cards. Use one for the rush-hour, and the other for the wandering about. It depends on what zones you are using, so I am not going to spell out what to do ... an exercise for the reader.

The best statistic I have heard for a long time

BBC Radio 4 has a flagship news and current affairs programme every weekday morning called "Today". Following one interviewer's comment, the presenter commented "The best statistic I have heard for a long time". He then paused and added words to the effect that the statistic was not good news, but had been presented in a clear way so that the meaning was easy to understand. It strikes me that those of us who work with mathematical models could learn from this example.

The interview had been about the social deprivation of parts of the east of London, and the comment was made: "for every tube stop on the Jubilee line [on London Underground] going east, from Westminster to Canning Town, life expectancy decreases by one year". It is not good news. But the information is conveyed in a way that is clear, simple and easy to assimilate. It is not cause and effect. Underground stations do not affect life expectancy. But one has a clear sense that the further you travel along the line, the more social deprivation, leading to lowered life expectancy, you will encounter. And the figure of "one year" is probably a rounded version of the data ... but for the purposes of this graphical illustration, it is precise enough. Someone has found a way to present information, which is of use to planners, in a way that is easy to take in. So we can learn from the example.

But, as usual, the story above is only part of the story. The statistic has been created by using limited information and extending it. The data which had been used said that the life expectancy for residents near Westminster station was seven years more than that for people living near Canning Town. They are eight stations apart. Nobody has written abot the life expectancy at those intermediate stations. All that has been done is to draw a straight line between the two extremes and assume linearity. Even though the method is not rigorous, it is still graphic. How can we learn to strike a balance between rigour and clarity?

Commuting Behaviour

A further observation from my trip to London is how there is a great difference between the social mix of commuters on public transport between Exeter and London. In Exeter, relatively few male executives use public transport. The rail lines are reasonably busy, but few males use the buses for commuting. But in London, it is quite normal and acceptable to use public transport. Of course, the infrastructure is better, but there is a difference in psychology as well. I wondered what research had appeared about the popularity of public transport commuting in cities of varying sizes.

It is relevant to O.R. because anyone working on transport models needs to remember the acceptability and feasibility of different modes of transport in different places. Behavioural psychology has its place in operational research.

Google turned up some figures for the United States. The comments are interesting. I wonder how much correlation there is between population and these percentages? And is there a similar set of data for other countries? And are there geographical effects to take into account?

RAW DATA: PUBLIC TRANSIT USE

Top 5 Cities for Public Transit Use

• 54.63% New York, NY
• 37.72% Washington, D.C.
• 32.66% San Francisco, CA
• 31.65% Boston, MA
• 25.92% Philadelphia, PA

With the exception of Washington , D.C. , every city here grew up in the horse and buggy days, with streetcar rail systems. The District of Columbia is part of the 1960-70s "graduating class" of newly subway-enabled cities, along with Atlanta (MARTA) and San Francisco Bay Area cities San Francisco and Oakland (BART). BART reaches regional airports, commuter rail systems CalTrain, ACE and Amtrak, and someday it may even roll down to suburban San Jose . Atlanta is planning to extend MARTA with its back-to-the-future PeachTree Street Trolley and improved bus service.

Bottom 5 Cities for Public Transit Use

• 1.07% Fort Worth, TX
• 1.03% Tulsa, OK
• 0.97% Oklahoma City, OK
• 0.54% Virginia Beach, VA
• 0.40% Arlington, TX

Surprise! These southern cities would benefit from re-installing light rail systems. Adding rail would provide residents relief from high gas prices -- and improve these cities' economic competitiveness. With air-conditioning thrown in, light rail would also provide relief from summer humidity.

When should one use O.R.?

Last week I had to go up to London (why is it always "up to London"?) for a meeting. Three and a half hours in a train to get there, three hours back, and two hours in the meeting. Every time I visit the capital, I am struck by the differences between Exeter (population 110,000) and London (population 7.5 million). This time my attention was caught by the advertisements on the London Underground (OK, I should get a life!). Several stations now have adverts projected across the tracks. But, the advert which caught my eye was on the walls of the escalators, where flat panel screens have replaced some of the static adverts. The advert was for T-mobile, and featured the company's recent TV advert, of a pre-arranged, choreographed flash-dance at Liverpool Station. "Life is for sharing" was the punch line.

Back home, I found the advert in full on Youtube, and also the director's background story behind an amusing and challenging project. Having enjoyed them both, I wondered whether there would be any place in the making of the advert for O.R.. How could "The Science of Better" make the production "Better"?

I suppose that the main traditional O.R. techniques that could have been used would be forecasting and scheduling. Forecasting to make sure that there were enough resources at the right time and the right place. Scheduling to make sure that resources were used as well as they could be. But there is actually little incentive to use O.R. in such a project. Either the people were ready for the advert on the morning of January 15th 2009, or they were not. There's no 95% confidence. It is a one-off event. And there is probably the answer. The director and his team worked to a deadline, made decisions as they were necessary and used a great deal of experience and common sense. And it worked.

Maybe if the director had to make such a film every two months for the next two or three years, then there would be a place for analysis and improvement, but that is not how the advertising world works. Perhaps an analyst can offer suggestions for improvements next time ....

And the other problem with the idea of scheduling is that you are dealing with people. It is often said that many O.R. techniques work better with machines and inanimate objects than when people interact!