Monday, 24 August 2009

How many items make a pack?

From time to time, I observe a package or a product in a shop or elsewhere, and wonder why the manufacturers have selected a particular size or number of items.

On my website, there are pictures from the ROCARO conference in Niamey in 2004, including a picture of a beer bottle holding 48cc. Why 48?

The paper towels in the washroom here come in packs of 180 towels. Why 180?

British food packaging is plagued with anomalous sizes. Jam, marmalade and numerous other items are sold in packs weighing 454gm or 340gm (equivalent to 1 pound, or 12 ounces). Flour is sold in bags weighing 1.5kg -- a reminder that it was formerly sold in bags weighing 3 pounds (why 3?)

For the final consumer, these assorted sizes are little more than an irritant; but within a supply chain, they can be more serious.

Now I shall start to collect and report odd-sized packs.

More about psychology

It is salutary to remember that the second world war, which had such an influence on my childhood, is now studied as "history" at schools. Although I was born several years afterwards, the war was sufficiently recent to affect me in various ways. Added to the change in "distance" is the change in technology and communication.

It was natural for my training in O.R. to begin with a little of the background to O.R. from WW2; we were all peers, in the sense that we had grown up with family experiences from parents and relatives of the horrors of that conflict. And our lecturers on the postgraduate O.R. programme had either experienced the pioneering wartime years of O.R., or had been mentored by those who had been involved. One of the first case-studies we heard about was the classic of "O.R. against the U-boat".

(The O.R. pioneers had been asked to try an improve the success of depth charges used against enemy submarines. The main numerical control in a depth charge is the depth at which the explosive is triggered, by the pressure of water. Until O.R. was brought in, the calculations assumed that a submarine dived immediately at the time it was sighted by the approaching aircraft. Therefore the depth was set at about 150 feet. The O.R. team convinced the military that the deth should be set much less, since submarines did not dive as quickly as had been assumed, and the accuracy of the aircraft was greater for a submarine that remained visible for longer. Suffice it to say that the "success" rate increased. This is pictured on the cover of an out-of-print book.)

I was reminded of this story last week when I noticed a copy of a book about the WW2 battle against U-boats for sale as an unwanted book in the city library. It was written from the point of view of a naval historian, and I spent a few minutes looking to see whether there was any mention of O.R. and its place. Yes, O.R. was mentioned in two places. The first retold the story of the depth charges. The second was non-mathematical. It was the psychology of spotting an aircraft. And the O.R. group were credited with the idea that the underside of the attacking aircraft should be painted white, which would camouflage them against the sky. The O.R. people analysed the results afterwards and demonstrated that this simple measure increased the success rate by a further 30%.

Reflecting on these stories over the last few days, I wondered about two aspects of these stories.

First, how much do we encourage our fellow O.R. scientists to think about psychology and human behaviour?

Second, what are the stories of O.R. success that we can use to enthuse the next generation of O.R. people?

(In the latter context, I have used the success of airline O.R. groups in rescheduling U.S. flights after the atrocities of 9/11, and the role of O.R. in scheduling public transport for the Olympic Games in Beijing.)

Monday, 17 August 2009

Football Statistics

I confess that I do not follow fotball particularly closely, but a column in the Independent on Saturday 15th August caught my eye. It was headed "The Statistics" and below were two bar charts that showed: (1) Points won by champions; (2) Points required to stay up. The two recorded time series are for the last 17 seasons.

I have just run regressions on these (sad, but there seemed to be a time trend) and discovered that the number of points needed to stay up is getting smaller at a statistically significant rate. Now this is curious, as there would seem to be no real reason for such a trend. It cannot continue for ever. But, of course, there is a simple trap that the data led into. The reason that there appeared to be a time trend was that the first three years were all high, and of course, they influenced the regression line. Remove those three outliers and then there is no trend. A caveat for the careless analyst.

OR Insight

I have just received the latest (September 2009, 22:3) issue of the journal OR Insight, one of the OR Society's regular publications. I'm interested because it has an article that I wrote, the first which has appeared in this journal.

OR Insight aims to promote Operational Research in action, with a serious emphasis on the application area. Since the start of the year, a new editorial team has been in charge and they have been determined to get good quality reports of the nature of modelling and tackling problems with OR. (So why did my paper get in!)

My paper discusses the phenomenon of "Open Studios" as a means of promoting the creative arts in the UK and elsewhere. I tackled it from an OR perspective, and as such I think it is the first paper in the area. I wrote for OR Insight because I wanted to tell a story, and this seemed the best journal for that type of paper.

But there are three other excellent papers, each telling a story of a study and the modelling which went with it.

The first considers one of the difficulties of modern life - home deliveries from mail order companies and similar. If you are out when the delivery van arrives, what happens to your package? Fraser McLeod and Tom Cherrett model one option, that customers should go to a central collection point; they look at the environmental impact of that scenario.

The second looks at health care provision of transport. The perspective is focussed on the patient (in contrast to the the apparent manager-centred perspctive often met in OR studies). The authors (David Bamford, Helen Thornton and James Bamford) conclude with two penetrating questions: "What went well?"; "What could we have done better?" Maybe those should be asked at the end of more OR studies!

And the third, by Gary Graham and John Hill, looks at the regional newspaper industry in the 21st century, and the relationship between print and electronic media. The internet is creating value for the newspaper industry, even though sales of regional newspapers are falling slowly in the UK.

Go get a copy!