Marmalade, seasonality, production planning

It's the middle of January, and this is the time of year to buy Seville oranges. And to make real "English" marmalade, you must have Seville oranges. However, these oranges are only available for a few weeks, from early January to early February. Commercial producers can preserve the fruit and spread the production over the rest of the year, but amateurs have a short window for home production. It is seasonality, but seasonality of supply of raw material, not seasonality of demand.

So yesterday and today we have been making marmalade. Just over 20 pounds of it. (This is one product in the kitchen which we measure in pounds, not in the metric way, because the glass jars we use are "one pound jars" or "12 ounce jars" even though they are labelled 454 grammes, or 340 grammes.) This was two batches in our large jam pan, and my forecast is that it will last us until early 2012. Forecasting demand for twelve months is not generally advisable in industry or commerce, but in our case we know that the rate we use it is about 20 to 24 pounds per year, and we buy a little each year to add variety to the diet, to support charities who sell home-made marmalade, to try other flavours, and because my family know that a jar of "interesting marmalade" will be a welcome present for birthday or Christmas. Given all this, our actual demand for our own marmalade is less than 20 pounds per year, so next year will probably be a "one batch" January. So here is a matter of "make-to-stock" production planning!

The basic recipe can be varied in many ways; extra fruit can be added, in which case the quantity of sugar needs to be increased. This year, for the first time, we have added some fresh pomelo.

Who would have thought that something so mundane could illustrate facets of operational research.

Here's the recipe for a basic batch, which we keep written in one of the cookbooks on an old 80 column punched card!

3lb Seville oranges
2 lemons
5.25 pints water
6lb sugar, which may be mixed granualted and demarara
0.5oz margarine or butter

1: peel the fruit and cut the peel into slivers of the size you like (ours are about 2cm by 2mm [it is easier to give small sizes in metric units])
2: put the peel into 2.25 pints of water and simmer gently for 90 to 120 minutes
3: chop the peeled fruit roughly (we either quarter the fruit or cut it into 4 or 5 slices) and put it all as pith in a large jam pan with 3 pints of water and simmer alongside the peel
4: Drain the pith into a bowl or pan through a colander, and scrape the pith through the colander as well, to give "body" to the marmalade.
5: unless you have two jam pans, now you need to wash the jam pan
6: add the drained liquid from the bowl to the jam pan, add the peel and its liquid, add the sugar and boil steadily ("rolling boil") until a test shows that it has reached setting temperature. (We take a small amount, put it on a saucer, cool it in the freezer for 30 seconds and then see if it wrinkles. Other methods exist.)
7: remove from heat, add the margarine/butter and stir to remove the scum on the liquid. Leave to cool for 6-10 minutes
8: meanwhile, wash your jars, and place in a cool oven to dry and sterilize at about 100 deg C,
9: Carefully fill each jar, and finish off as usual for home-made preserves.

The school which was too small

The current INFORMS blogging challenge/theme is about "O.R. and politics". It reminded me of a student project a great many years ago. It was never suitable for a research paper write-up, but a blog is an appropriate place to recount what happened.

The city had expanded, and a large housing estate had been built. Part of the development was a new primary school. However, before the estate was complete, the school became overcrowded. It was too small. Not much could be done to provide more space. The local politicians were embarrassed and the local media were not slow to blame them. The student (B) and I were asked to help the council officers make better decisions in the future.

So we interviewed people, read literature, and did our best to become familiar with aspects of planning. We quickly realised that the whole mess was multi-criteria, and many criteria were non-numerical. One of the attributes of O.R. should be the ability to cut through messes. For simplicity, here, we reduced the problem to a two way table. One dimension was the forecast demand, reduced to “Low”, “Medium”, “High” and the size of school “None”, “Small”, “Medium”, “Large”. In each of the twelve cells we wrote down aspects of the consequence of the two dimensions, and then iterated through meetings in which stake-holders could contribute their ideas. So the table of twelve cells became a tool for thinking with for planners and decision-makers. It could be – and was – used in other new developments in the city and region. Nothing high-tech, but we had helped to make the mess less messy. B went on to a career in O.R. and other messy problems.

Among the gems that we learnt along the way were the following:
(1) It takes about five years from initial ideas to opening a school, so the children who will use the school are being born at about the time of those initial ideas;
(2) Families with pre-school children are much more mobile than others, so it is not possible to forecast demand by local surveys of families;
(3) The forecasts made in the past had gone awry because of world-wide economic upheaval;

The abuse of forecasting

Mention the name "Gene Woolsey" to operational research scientists of the 1970s and 1980s, and you will probably get the reaction that he spoke and wrote great deal of common sense, mostly in "Interfaces". One of his stories is how he did a study in a particular factory, and a couple of years later returned on a visit. He said that he wanted to creep away quietly; the solution that he had proposed had been pinned on a board, and was being followed to the last detail. In the intervening years, the environment had changed, so all the external parameters of the model were different, making the solution totally inappropriate.

I thought of Gene last week, when our gas company sent us "Your Annual Gas Statement". It reads
"We've tried to make it as easy as possible to understand."

"Your usage: From 25 Aug 2009 to 24 Aug 2010, you used 15396.49 KWh of gas.
If you continue to use energy at the same rate over the next 12 months, we forecast your cost will be £568.21"

What wonderful precision! Especially as the power consumption is based on reading a meter which is accurate to +/-1 metric unit, and one of those is between 11 and 12 KWh. So, the meter can't determine whether we used 15390 or 15400 KWh, so the last three significant figures of their record are unnecessary. That translates to making the pence in the forecast unnecessary. But these errors are tiny in comparison with the assumptions that we will continue to use energy at the same rate.

It worries me that somebody has thought that this information is intended to be useful. If it was someone from the O.R. department, then I suggest that they creep away quietly now.

If you are from, or know someone from, the O.R. department of British Gas, do let them know of the abuse of forecasts.

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.

Google and influenza (flu)

One of my email signatures uses the following quotation:
In the information age, somebody has to specialize in the development and presentation of really useful information. Doing that for management and decision-making applications is the core role of Operational Research scientists. (Randy Robinson, the first executive director of INFORMS)
Throughout my working life, I have worked alongside some excellent statisticians, and been part of some wonderful data collection exercises. Randy R's comment sums up an important aspect of the work of O.R. people -- taking data which has been collected and making sense of that data for other people to use intelligently.
Over the past week, Google's work on modelling influenza epidemics has been made public. Essentially, the company is monitoring the fraction of search queries that they judge to be related to flu, week by week, and region by region in the USA. The results so far show that the fraction of queries that are related to flu increases during an epidemic, and the change can be seen more quickly than is possible by conventional means of epidemiological monitoring. So here is "really useful information" for "management and decision-making". Google's work can be read here.