Wednesday, 18 April 2012

A real-life bottleneck

At the weekend, Tina and I went to the Exeter Festival of South-West Food and Drink which is held in the courtyard of Exeter Castle (Rougemont Castle - it is mentioned in Shakespeare's Richard III) and the adjacent park (Northernhay Gardens). 

It is a splendid event, and we came away with a few purchases (duck sausages, anyone?), the taste of locally made ice-cream and samples of several chutneys and preserves, and a cookery book for me.  As usual, there was the need for a little bit of operational research in the organisation.  How big should the pavilion for the demonstration kitchen be?  How long should each celebrity chef be given for their presentation, and how can you manage the queues for samples of their cooking? 

At the centre of the show there was a bottleneck for the flow of pedestrians.  The only path from the castle to the park was through a narrow doorway, at the end of a path on one side and at the head of steps on the other.  It was not safe for people to wait on the latter side unless they were at the foot of the steps.  So a control was needed.  The organisers enlisted members of the Exeter Sea Cadets to control flow.  One at the doorway, the other at the foot of the steps, allowing batches of pedestrians through alternately.  It worked, sort of, but the teenagers were dealing with people who didn't expect to be controlled, so at times there were glitches in the smooth running.  Fortunately, most of those attending only needed to go through the doorway once in each direction during their visit, but it struck us that this doorway, and its capacity for flow, would be an unexpected factor in determining the capacity of the festival. 

There are obvious parallels with controls for traffic around road-works and other road hazards. 

When forecasts go wrong

In 1987, the south-east of Britain was hit by some very strong winds.  The BBC weatherman, Michael Fish, has had to live with the broadcast that he made the night before.  The piece that everyone remembers is taken out of context, when he said there wasn't a hurricane on the way.  He went on to say that people in the south-east should batten down the hatches because there would be some very strong winds, but most people forget this and remember the words about the non-existent hurricane.  Even so, it is admitted that the forecast that night was not accurate, because the path of the strong winds was not predicted correctly.

Mistakes in forecasting in operational research are usually much less serious, but this week, Marks and Spencer (M&S) shares dropped 3% in one day as a result of the admission of some poor forecasting, coupled with poor supply chain management.  In February this year, there was a spell of very cold weather in the U.K., which drove customers to M&S to stock up with warm clothing.  Sadly, the shops ran out of several lines of womenswear and the sales of the chain (Britain's largest clothing retailer) suffered.  Newspaper reports and the company's spokesmen have concentrated on this mistake, while ignoring the fact that the forecasts for menswear and clothes for children were satisfactory.  A lesson for practitioners -- you are remembered for mistakes, like Michael Fish, and not for your successes, even if the latter outnumber the former! 

Forecasting fashion is traditionally very difficult, leaving aside the effects of the British weather.  In the same reports of the shortages of warm clothes, there was a note about how demand outstripped supply for ballet shoes in M&S.  The demand for these was only vaguely connected to the weather, and much more about fashion.  M&S say that they could have sold twice the number of pairs than they did.  (As an aside, how do they know that?  How can you record lost demand very accurately in a store where customers serve themselves?  Mind you "twice" sounds a good number, implying that they have measured it and they accept that their estimate is not precise.) 

The company commented on the problem of supply chain management in two ways.  First, there was some unspecified bottleneck which had affected the supply in advance of the demand (so the forecasts must have been closer to demand, and the errors in the forecasts would have been smaller if this glitch had not happened), and second, the lag in the "warm womenswear supply chain" was about four to six weeks.  The delay because goods come from the Far East.

As usual, the media reports gloss over the "hidden science" of operational research which helped manage the forecasts and the supply chain planning.

Monday, 9 April 2012

Forecasts for a one-off event

It was time to give blood today, and as usual, it was interesting to observe the way that the staff manage a set of queues in series.  Queue 1 -- single server -- registration; queue 2 -- several servers -- test blood for iron, and administer donor questionnaire; queue 3 -- several servers -- give blood; queue 4 -- single server today, usually two servers -- refreshment (and today there were Easter eggs!).  queue 3 was the critical one, and today there was a bottleneck there because of staff being off for the Easter holiday.   I was asked if I minded being attended to by a trainee "donor care attendant" who was starting a second career after having been made redundant from the police force.

However, more interesting for O.R. than the queues was the discussion of forecasting blood stocks for the start of the Olympics.  I have mentioned this before (here).  Anyhow, numbers have now been put to the target inventory.  Based on the normal daily requirements for blood, the amount normally held in stock, and the amount used in the last big emergency in the UK (the 7/7 bombing in London) a target has been set of about 50% more than the normal stock level.  I am not sure whether the actual figures are in the public domain, so I won't quote them.  Actually, the target level is quoted to one significant digit, so I suspect that the people who came up with it are going to be happy if the actual number in stock is within 10% of their target. 

So the donor service is gradually building up stocks, and developing additional plans in case there is a situation which requires extra donations.  I have been able to book my next donation for a few days before the Olympics start, so there may be a pouch of my blood in that enhanced stock.  Do I get a gold medal for that?

Friday, 6 April 2012

A bizarre crime statistic

Last week, statistics of pickpocket crimes in the UK were published.  The newspaper seized on one aspect of these, which was the age of the victim.  The headline was that there had been one victim aged 110 years, and two babies of under 12 months.  And, further down the story, was the assertion: "The most likely age to be a victim is 23 years old".

Clearly, the reporter had confused the statistics.  The crime report may have observed that the most frequent age of a pickpocket victim was 23, but that is not the same as being the most likely.  First, pickpockets do not (I guess) ask their victim their age before carrying out the crime.  There is no specific age-dependence on being a victim.  Second, the chance of being a victim depends on one's lifestyle.  People aged 23 are quite likely to have a lifestyle that places them in locations and at times where they may have their pockets picked, compared with older people.  People aged 23 are more likely to carry items attractive to pickpockets than retired people.  So really the data about age is misleading ... and one wonders what response the journalist expected his/her readers to make to the story.

I guess many O.R. practitioners have seen similar cases of statistics being misused; the lesson is to take statistics with a pinch of salt.

"The probability increased steadily until it reached boiling point" one (non-mathematician) lecturer announced.