Tuesday, 27 January 2009

Rabbit hole day, part 2

In one of our undergraduate modules we taught ideas of inventory control, both the theory and discussion of the practice. Naturally we looked at ABC analysis, the EOQ, Wagner-Whitin and problems with constraints. Then in exercises, we asked the students to think what practical obstacles there might be in applying the models. One question asked: "How may inventory models be used by small shop-keepers?", expecting a discussion about record keeping, the cost-benefit of having some kinds of records. Instead:

The first question to be answered is what we mean by "small". Given that the mean height of males in the UK is about 5ft 8in, with standard deviation 2.5in, "small" can be taken as males whose height is below 5ft 3in. Such people need assistance to reach high shelves, and Health and Safety legislation means that they must use ladders. Therefore we recommend that small shop-keepers arrange their shelving so that those items which are A or B are kept on low shelves, and C items are kept higher up.

And so it went on ....

Rabbit hole day

It is the fifth worldwide Rabbit Hole Day. So forget about normal blogs, and think laterally.

So, some levity. There is a famous paper on the mathematical theory of big game hunting, or how to catch a lion in Africa. As it was published in 1938, before O.R. existed as a discipline, other people have added their little bit to the original: so here are three ways that O.R. people and their allies catch lions.


Statisticians hunt the first animal they see N times and call it an lion.

Consultants don't hunt lions, and many have never hunted anything at all, but they can be hired by the hour to advise those people who do.

Operations research consultants can also measure the correlation of hat size and bullet color to efficiency of lion-hunting strategies, if someone else will only identify the lions.

A new page for IAOR

Yesterday I updated the webpage which advertises IAOR at the IFORS website, to reflect the change from "A printed journal with an electronic version" to "An electronic journal with a printed version". To my shame, the text that was there up until now had been written in 2002 and not brought up to date, but my excuse is that the responsibility for the web presence was not mine. But it is a reminder that webpages with dates or events need to be monitored.

The IAOR webpage will probably change again this week, as I have submitted a photograph for it.

Friday, 23 January 2009

Logistics in Ancient Egypt

A few years ago, I went to the inaugural address given by Exeter University's Professor of Archaeology, Professor Val Maxfield. (Her office was on the floor below mine, and I saw her several times a week as a result.) Before her lecture, I had little idea what her speciality in the subject was, and so her topic came as a surprise.

She spoke about excavations in the eastern mountains of Egypt, close to the Red Sea. There, the Romans quarried a stone called porphyry, and this was the only site in the world for this stone. (To find out more about it, go here.) But what fascinated me, as an O.R. person, was the logistics of moving the quarried stone from high in the mountains, to the Nile, and then by sea to Ostia (Rome's port) and overland from there to the city. The enterprise required extensive logistics. Engineers laid out a road that could be used to trundle the stone downhill and across the arid terrain. There were wells dug along the road. There had to be an infrastructure to house and feed the slaves who moved the stones, as well as the quarry-workers. These are skills which have been lost; today, if anyone needed to transport a ten tonne column a few hundred kilometres, then it would be done mechanically, and generally the logistics would have been simple.

I salute the logistics engineer(s) who were in charge of this enterprise.

When I discussed it with Val, she threw in two further aspects to think about. First, because sea travel was unreliable, "there are probably several shiploads of porphyry on the seabed of the Mediterranean". How disappointing for the engineers! Second, as the quarry was lost for centuries after the fall of the (western) Roman Empire, and the stone was prized in Byzantium/Constantinople/Istanbul, many of the monuments of Rome were looted and the stones taken to the capital of the Eastern Empire. Yet more logistics!

Sadly, the second century "Journal of Mining" and its published research paper: "The Logistics of Quarrying at Mons Porpyritis" is not available now.

Supply Chain management in Exodus

This year, Tina and I are reading the Bible together using a Chronological Bible, one which attempts to place the whole of the Old and New Testaments in their chronological order. Reading the whole Bible in one year is a challenge -- there are about four or five pages to read each day, and we read them aloud together after breakfast, before our family prayers.

Today we reached the account of the Children of Israel in Egypt, and Pharaoh's punishment that their slavery be made harder. They should continue making bricks for him, but they had to find their own straw (to bind the clay together). And, the word of God continues, this made their work much, much harder and their productivity fell.

It struck me that here is one of the earliest recorded instances of a supply chain and how bad management made it go wrong. Up till then, there was a supply chain of Egyptians providing straw for the Hebrews making bricks. Pharaoh's orders broke that. And it went wrong. The Bible tells the story from the production end. What happened, one wonders, about the upstream end? What happened to those whose livelihood had been based on supplying straw?

Amazingly, there are many hits when you Google with the keywords "supply chain" + exodus + straw, and one which comes up high is a Christian sermon about modern slavery ... not quite what I was thinking about, but fascinating that someone else has linked the ideas in a church. Here is that link.

The Italian Job -- a solution

The British papers this week are finding space for a few stories other than the inauguration of Barack Obama and the current credit crunch. One such is the outcome of a competition to solve the forty-year old problem of the end of the film, The Italian Job. The competition was organised by the British Royal Society of Chemistry (why not a mathematical society?). It is good to see mathematical modelling, problem solving and decision making in the news media. So here is the story, courtesy of Britain's Daily Telegraph.


As cliffhanger endings go, there are few more famous than that of The Italian Job. With their coach dangling precariously over an Alpine ravine, a gang of plucky British robbers – led by Michael Caine's Charlie Croker – face the choice of saving themselves or risking all to retrieve the stash of gold they have stolen from Turin. However, each move they make towards the rear of the coach to reach their haul results in the vehicle inching further over the abyss.

The film ends with the famous words from Croker: "Hang on a minute, lads – I've got a great idea." But what was the idea – and would it have worked?

=== The winning solution -- for which the prize is a holiday in Turin, but no gold.

This IT expert's solution starts with Croker and his gang smashing most of the windows of the coach, using a hard object like a shoe. The windows to the rear, which hang over the cliff, would break outwards, removing their weight. The gang would reach round and smash the windows at the front inwards, to retain their weight. One of the gang should then be lowered by their feet to let the air out of the front tyres, making the coach settle on the ground. Finally, the pipe to the fuel tank, which Godwin estimated would have 36 gallons of diesel left, would be slashed. As the fuel poured away, it would remove 130kg (286lb) from the back of the coach – more than enough for a 90kg man to start removing the gold bars.
===And for those who like puns ...
"Keep singing The Self Preservation Society," he tells the gang. The chorus starts up again until they all get frogs in their throats. The frogs start to jump up and down, which rocks the bus.

They use the rocks to weigh the end of the bus. "Keep singing, lads."

They sing louder, but now the frogs have gone, their throats get sore. They use the saw to cut the gold bars in half. Two halves make a whole. They pass the gold out through the hole, and jump out.

Still singing, they've now all gone hoarse. They load the gold on to the horses and ride off into the sunset.


Tuesday, 20 January 2009

The paradox of optimal location

Yesterday I was talking with a former student, whose company provides statistical advice to clients in the service industry. He mentioned an interesting paradox about optimal location, in this case of ambulances. The UK government has various standards or targets to be achieved by public sector bodies, and one of these is about how quickly ambulances can reach an emergency. It's of the form: "In X% of calls, the ambulance must reach the emergency within Y minutes".

He said that in urban areas, it is relatively easy to deploy vehicles to achieve this, because of the short distances involved. And it is also reasonably easy in regions where there are several medium to large towns and cities and a scattered rural population, because the response to the cities dominates the statistics. But the targets are hard to achieve where there are many small to medium sized towns, none of which have sufficient demand to require a vehicle of their own. Then the solution leads to an excess of vehicles.

You can test this for yourself. Suppose that the district is an equilateral triangle, and the demand is such that one vehicle is needed. If the population is spread uniformly across it, then you place your vehicle at the centre of the triangle. If the population is concentrated and divided equally at the three corners, then the best place would still be the centre, but nobody lives there, and so the vehicle should be located at one of the corners. But that means that in two cases out of three, the vehicle must travel to one of the other settlements, and potentially violate the service standard.

I haven't seen this paradox mentioned anywhere in the literature, so you may have read it here first!

Monday, 19 January 2009

Marketing Crisps and Operational Research

Having mentioned crisps, my mind wandered to a recent news story about marketing with an O.R. twist. The UK crisp brand Walkers called on consumers to come up with new ideas for flavours of crisps, with the slogan "Do us a flavour". Six were identified as potentially usable: chilli and chocolate, onion bhaji, Cajun squirrel, fish and chips, crispy duck and hoi sin, and builder's breakfast. There is a public vote to determine the winning flavour which will then remain on sale.

The competition has generated a considerable amount of public interest. Walkers had originally expected about 250,000 entries into the competition, however, it actually received about 1.2m flavour suggestions.

And there is the O.R. twist. Who made the forecast? Has anyone stood up, put their hand on their heart, and admitted "Our forecast model was wrong. We were 80% below."? In the circumstances, I suspect that the forecast was more of a guess than a mathematical model, and the success, both in consumer response and free publicity, will mean that the forecasters will live to forecast for another campaign.

Marketing and Operational Research

My impressions are that in the United Kingdom, surprisingly few O.R. scientists have published papers relating to marketing. The U.S. O.R. society, INFORMS, publishes a journal devoted to quantitative marketing, but there is no comparable interest in the U.K.. Over the years, I have had one or two encounters with projects relating to some aspect of marketing, but have never got a sense that marketing departments use O.R. advice very much. Some of the projects have started with the adage "Half the money spent on advertising is wasted -- but nobody knows which half; if you knew which half, you would make a fortune."

In my postgraduate course we came across a problem which I have never seen written up, perhaps because the problem was trying to build a model to explain some anomalous data and the parameters would have been a commercial secret. So here, nearly forty years after it happened, is a summary.

For many years, the dominant company in the U.K. market for potato crisps was "Smith's". They held over half the market. Then a new brand was launched, called Golden Wonder. Over the subsequent few months, surveys were carried out to try to measure brand awareness. The problem was that the percentage answering the question "What was the brand of crisps that you last bought?" with "GW" was far lower than the percentage market share for GW. Why?

The answer was inertia and lack of awareness of the brand. Purchasers would ask for a "packet of crisps" and since most shops (and especially bars) only stocked one brand of an item that occupied a lot of storage space, the purchasers accepted what they were given and did not associate their purchase with a brand -- and Smith's had been the leading brand for so long that the association was "Smithscrisps" as one word.

So, as students, we were asked to re-work what the consultants had done, and build a model to link the growth over time of the sales and the growth over time of the awareness. It taught us about building and fitting nonlinear models, and a little about the vagaries of our fellow humans. But it could never have been written up as a paper!

Wednesday, 14 January 2009

The psychology of implementation of O.R.

It has been generally acknowledged in the O.R. that I have studied that implementing O.R. needs to recognise the psychology of the eventual user. There are numerous anecdotes and O.R. legends about this. The problem of elevators in the New York skyscraper is one of the oldest.
Office workers complained about the time they had to wait for elevators, so an O.R. team was asked to try and find an appropriate solution.
Various models were built in the investigation. These considered having more elevators, faster elevators, elevators that only stopped at particular floors. All were deemed insufficient.
Then the psychologist on the team proposed that there be full-length mirrors in the lobbies between the doors of the elevators. His argument was that these mirrors would reduce the perceived time of waiting; some people could arrange their clothing and check their hair; others could surreptitiously watch their fellow workers in the mirror. (The original story was sexist; this is the PC version.)
Result: no more complaints. The solution cost very little.
The same solution approach explains why you have magazines in waiting rooms, and automated advertising screens in bank and other queues. (Does anyone know of an airport where the queues are entertained by such screens? In those that I have visited, the queues have to watch endless reminders about what cannot be taken through security, or how to prepare for security.) And it also partly explains the popularity of glass-walled lifts, where there is something to watch while you are travelling.
(By the way, some statistics show that elevators are the safest form of transport in terms of deaths per passenger mile.)

Many years later, I came across a note about differing national psychologies. We were discussing the optimal timing of the red phase on traffic lights at a junction such as a cross roads. In heavy traffic, the throughput is maximised by having very long phases. The constraint is psychological; if the lights do not turn from red to green, those waiting at the red light start to become impatient. My informant suggested that two minutes was the limit in the UK, nearly three in the USA, and in Japan, the patient Japanese motorist only started to fret after four minutes. I'd be interested in knowing the basis for this.

O.R. in developing countries

Following on from the comments about Eritrea, my mind wandered to ask which countries have not been linked to a published O.R. paper.
According to the Traveler's Century Club there are 319 countries in the world (I'm not a member as you have to have visited one hundred or more from their list, and my tally is about sixty). The United Nations has 192 members. The International Federation of Operational Research Societies (IFORS) has "over forty five" members (it was 48 when the roll was called at the last IFORS conference, but there are a few national societies whose current existence is uncertain. So we can reckon that there is work on O.R. in those countries.
But which countries are missing?
My quick check found no O.R. papers from:

Burma (Myanmar)
North Korea
from my knowledge of Africa and Asia. I would be interested if anyone can correct this list. I need to look at South America.
(My "rules" are that a paper should be about an application in the country, or which has been developed with enough data from the country to claim relevance. The "rules" do not say that the work should have been implemented.)

Tuesday, 13 January 2009

O.R. in Eritrea

When IAOR prints an abstract relating to O.R. in a developing country, it is usually cross-indexed with the name of that country. So the latest "OR in a DC" abstract marks a rare event -- it is the first that has been included (as far as my records go) about O.R. in Eritrea.

The paper is:
Cost analysis of an integrated disease surveillance and response system: case of Burkina Faso, Eritrea, and Mali
Zana C Somda, Martin I Meltzerl, Helen N Perryl, Nancy E Messonnier, Usman Abdulmumini, Goitom Mebrahtu, Massambou Sacko, Kandioura Toure, Salimnta Ouedraogo Ki, Tuoyo Okorosobo, Wondimagegnehu Alemu and Idrissa Sow
published in:
Cost Effectiveness and Resource Allocation 2009, 7:1doi:10.1186/1478-7547-7-1

Papers with so many authors/co-authors are also rare events.

By the way, if you don't know where Eritrea is, the map shows it in the north-east corner of Africa, bordering on the Red Sea.

Wednesday, 7 January 2009


There is currently an advert on UK commercial radio which trades on people's innumeracy.
Switch from sugar to a sugar substitute and "you will save about 7000 Calories per year".
It sounds a lot, but that is les sthan 20 per day, i.e. less than 1% of the daily recommended intake.
But "Seven thousand" sounds a lot, doesn't it!

Think of the user!

Good O.R. has to be implemented. Period. Full stop.
So, at some stage, someone needs to think of the person who will use the results. The problem may have been presented by management, and the person who pays for the work is in the management hierarchy, but the person who actually uses the results is probably not in management. Which is why implementation is important.
I have linked implementation and design before, but over the Christmas holiday we had experience of both good design (implementation) and bad.
Let's start with the bad news. We bought a new set of Christmas lights to make an arch around the front door. They came with an integral control box which had one button only. Repeated pressing of the button cycled through several patterns of flashing lights, with one where all bulbs stayed on all the time. So we put the string of lights up, switched on and discovered that the default was a pattern which faded and flashed -- too garish for us. So we cycled and selected the constant selection. Then we switched off, to put the string onto a time switch. When it came on, we were back to the default. As a result, at some stage every evening, yours truly had to press the button to select our favoured setting. With a little forethought, the designer could have ensured that the setting that had been selected became the default one for the next off--on sequence ... because that is what the user had expressed a wish to show what was wanted.
The good news was that Tina was given a DAB radio. Plug it in, switch it on, and set up the controls. It was extremely easy, with clear instructions, designed with the user in mind. Full marks for those at "Pure" for thinking of the user.

Monday, 5 January 2009

O.R. and waste management2

Another slant on a topic which I referred to in August 2008
One of the responsibilities of editing the International Abstracts in Operations Research is to have an awareness of the areas of application of O.R., and especially those which lead to publications in the academic literature. Someone has said that applications of O.R. should be so good that they can be published in the literature of the application area. And that imposes a high standard for the O.R. scientist, having an ability to work within another discipline to such a high standard that ones work stands up against the peers in that discipline.

So it is interesting to notice that more and more O.R. work is being reported relating to waste management. An IAOR search in the online version produced over 240 hits for "waste AND management", running across many aspects of the subject: location of facilities, vehicle routing and scheduling, capacity planning, multicriteria models for planning a waste management programme, etc. etc.

But comparatively little of this work has appeared in the O.R. literature. It is mostly in the application area. I wonder why?