OR in Devon, UK

Thank you to South West Water (SWW) for the inspiration for this blog post.  Like many homes in the UK, we have a water meter and pay for our water usage by the cubic metre.  We pay quarterly, with a reading by SWW every six months and an estimated reading every three months.  Over the past year (October - September) the annual usage was about 55 cubic metres; the meter is read to whole numbers of cubic metres.  However, when I went to pay the latest bill, I was startled to see the graph below.  It claims to show our average daily usage of water month by month for the last two years.  How on earth can that be the case?

Let us leave aside the presence of 13 dots on the solid line, one of which claims to show the average consumption for the month (October 2024) which is only just starting.  Let us also lay aside the x-axis which is labelled with month and year and then there is a dotted line for a different year.  Let us lay aside the suppressed zero on the y-axis.  And what does the line between dots really mean?

No, think about how the company claims to know about daily consumption when the readings are taken at such large intervals.  How is it done? 

 Answer --- with great imagination.  They use averages and scaling.   Based on their supply data, they can assign fractions, f(1), f(2), ... f(12) to each month's demand for customers in my area of Devon.  then they take my 55 cubic metres, scale it by those fractions and scale it by the length of the month and ... HEY PRESTO! ... we have this graph.  I ran it through a spreadsheet and reverse engineered it to confirm that those dots do scale up to 55. 

So, this is imaginative.  Also wrong. Also pointless --- can it affect my behaviour?  As I have remarked elsewhere, numerical information should be communicated clearly and accurately.  Anything else is smoke and mirrors.

 Back in the days when I was a postgraduate student of Operational Research, one of the compulsory modules was about communication.  It was argued that people who do O.R. need to communicate their results with other people with clarity; that means explaining the results of O.R. studies to non-specialists.

Then, when I taught O.R. to undergraduates, we agreed to introduce a short "CommSkills" programme for the specialists in statistics and O.R..  There were lectures/presentations about written reports, interviewing techniques, making presentations (before Powerpoint, so it was with an overhead projector).  For practice small teams had to interview a staff member who was playing a role of a manager with a problem, come up with a solution, and make a presentation to their peers and the staff. I invented a queueing problem associated with a fictitious supermarket filling station --- how many pumps should there be?  Other colleagues were inventive with their "management" problems.  

(We had a slight tussle with university red tape; this programme could have no credits in the scheme of things, and therefore could not be made compulsory for the students.  We dealt with that with a very small stick and a bigger carrots.  The stick was: "If you don't take part, we will mention it when we write a job reference."  The carrots were a reward for the best final presentation, and the glowing reports from the previous cohort of students who had done the programme.  And after a few years, we had reports from our graduates that it was the most useful part of their course, and that graduates from other universities were envious of the skills that had been in our programme!)

Which brings this blog to lessons on conciseness.  Our programme emphasised that our students might be working with and for decision-makers who needed a clear, brief report.  We could point to words of Sir Winston Churchill, UK prime minister: "Report to me on one side of a sheet of paper ..."; the industrialist Sir John Harvey-Jones "I will not read a report that is longer than one side of A4"

So I loved this story: 

When most car companies come to replace a long-running and well-loved model they will create a lengthy and detailed brief setting out in many thousands of words what is required from the new model.  When in 1985, Lamborghini finally realised that it needed a new flagship  the brief from company president was as follows: 

"Create a Countach successor"

His engineers did as they were told, and all for a budget of just ten million pounds which included re-tooling the production line and extending the factory. Bargain.  (from "Boring Car Trivia volume 2)

And in my talk on the course, I produced some examples of poor communication in print.  What do you understand by a headline "Councillors probe flat flood"?  And I had a business graphic which had been produced for an internal readership and lifted without explanation into another document, intended for the shareholders of the company: lovely colour graphics, but what did they mean?

 My reading is often eclectic.  I recently found an unusual book called: "Boring Car Trivia volime 2" by Sniff Petrol --- a pseudonym!  This entry struck me:

In the early 2000s a Mercedes-Benz engineer spent a year scouring the world for the best button action.  The conclusion of his research was that the ideal button "throw" was 1.4mm and future Mercedes switches were designed accordingly.  All Benz button suppliers were issued with a finger pressure graph and soft-feel paint spec so that every single button felt the same no matter where it came from.

Let us assume that there is a bit of truth behind this.  And then, let us perform a cost-benefit analysis of this year-long project.  Cost: an employee's salary and travel expenses, then the engineering costs of producing the spec.  Benefit: any button in the customer's car feels the same, irrespective of whether it is on the dashboard, in-car entertainment, steering wheel, door.

The benefit is in the reputation of the company.  But why did it need a year's research?  If the engineers can produce a sample, then they must know how to control a button under pressure.  So why didn't they simply produce a variety of samples and make comparisons, possibly with a consumer panel?  In the process the company could have investigated what the consumer wanted, not what that travelling engineer thought was best.

 A couple of weeks ago, I spotted the book "Arriving Today" by Christopher Tims in our local library, and the blurb on the cover suggested that I might find it interesting to an O.R. reader.  Essentially, the book is about the journey of a small item from manufacturer to customer in the 2020s, where so much commerce is done online.  And in manufacturing, storage and transport, O.R. plays a part.  

Having finished the book, O.R. does get a mention, but not enough to merit a place in the extensive index.  As the UK O.R. Society repeatedly stresses, O.R. is "The Hidden Science".  The mention in the book comes alongside queueing theory, and attributes to the O.R. world the concept of a "buffer stock".  That said, buffer stocks are scarcely mentioned except at one stage in the supply chain.

So was it worth reading?  The first half of the book deals with the shipping of that small item from a factory in Vietnam, to a container port in that country, across the Pacific to California and thence through warehouses and trucks to the customer.  The research was done during the pandemic in 2020, which colours some of the text.  Interspersed with the description of the movement of the item, there are vignettes of the people involved (I especially enjoyed the navigation of the container ship from ocean to its berth.)  In the latter part of the book, a great deal of the text talks about the Amazon systems, their automation, and the pressure that the machinery and software puts on the employees.  Maybe this could have fitted into a second book?  The "last mile" of the shipping goes via UPS, and it is clear that the author prefers the management style of UPS to that of the aforementioned bigA.  But nobody told Tims that the routing system at UPS had won prizes for the OR team behind it!  

Would I recommend it to an OR readership?  Yes, because anyone interested in or involved with the world of online shopping is bound to find something new.  No, because there are no lessons on the process which leads to implementation of the work of OR people to the business practice here. 

 There have been numerous books and research papers on aspects of stock control, starting with the classical EOQ model (economic order quantity) and developing modifications to that and other models.  Stock control models have led to the concept of Just In Time production --- something which backfired during the COVID pandemic when supply chains were disrupted and demand for many items was more irregular than in less troubled times.  

Recently I went on a site visit which revealed an interesting variant on many of the usual introductory models.  Let me explain.  Here in Exeter, our domestic waste is collected by the local authority.  We sort it into four categories: 

(1) recyclables (paper, card, plastics), 

(2) garden waste 

(3) waste food

(4) non-recyclable stuff

Category (1) is sorted into its various categories, (2) is composted (in such quantities that harmful bacteria are killed by the heat), (3) goes to a digester system, (4) to the "energy from waste plant"

The site visit was to the energy from waste plant (EFWP), where the waste material is burnt in a very hot furnace to produce electricity.  Now the output from the EFWP needs to be relatively constant, but the input is variable.  So the stock control problem is concerned with the "stock" of stuff that is going to be burnt.  It isn't collected on Sundays (and not always on Saturdays)  so each week, the amount that is used has to be about 70% of what has come in, so that there is a supply at the end of deliveries on Friday evening to last to the following Monday.  Except that the daily supply is variable, and there are seasonal variations.  But on top of this, there are general holiday dates with no collections on one or more holiday dates.  Fortunately, these are known in advance.  So the basic amount of rubbish being held will follow a time line like this:

I didn't put a great deal of daily variation in that one.  With a more variable daily variation, we get:

and it is apparent that the amount available at the start of the weekend is also variable.  

But both clearly show that the storage space for "rubbish" has to be considerable.

The public holidays make things worse.  That is left to the reader as an exercise.  

How is the stock control managed?  By rules of thumb; the controller knows about the holidays, and the daily "demand" so works to ensure that there is stock to meet the demand.  And the controller does not have a degree in O.R.; I wonder what would ensue if an O.R. specialist tried to convince that team that a textbook formula would help!  

footnote: but of course!  This is a variant of the reservoir control problem!  We looked at that ages ago in http://orindevon.blogspot.com/2011/09/water-supply-and-environment.html.  There, each month had a target level for the water in the reservoir.  If the water was below that, then the reservoir was allowed to fill up, if above, more water was released.  Here, the problem is essentially the same, except that the target levels of waste in the incinerator are for each day, and those targets follow some kind of trend in the run-up to holidays. 

 I have been quiet on this blog for a while, not that I have gone away, but there have been so many other matters to deal with.  Hopefully I can get back to the coalface soon.  But today I was startled by this amazing statistic:

This company (a house agent) was so proud of their popularity that they could claim four-figure accuracy about their clients' delight.  As usual, stop and think.  The claim is that 98.96%, not 98.95%, nor 98.97% of clients were satisfied.  As I closed my eyes in the dentist's chair (the glossy brochure had been in the waiting room), I thought about the sample size to give such raw data, and obviously one sample would be of 1250 clients of whom 1237 were pleased.  Of course that would imply that the standard deviation would be quite large as well, and exactly 1250 clients being sampled seemed suspicious.  So, back home I ran through other sample sizes, and, lo and behold, 476 out of a sample of 481 also gives the same percentage to four significant figures.  

I don't know which is most impressive: the statistic, the ignorance of the company doing the survey for the client, or the folly of  the copywriter for the house agent.  What do you think?

 When I studied Operational Research, one of the two professors in the O.R. Department at the University of Lancaster was Professor Alan Mercer.  Anyone who knew Alan will know that he was in amazing character, and I am delighted that I co-authored one paper with him.  [https://doi.org/10.1057/jors.1978.188] (He wasn't my academic supervisor; I collaborated with him and his research associate Malcolm King on a project about the Church of England.)  

Alan had a fund of stories; someone had once asked him why there was still the need for O.R. scientists; if O.R. was such a powerful tool, why were there still unsolved problems?  His answer was that there will always be the need for O.R. in business, commerce, education and all areas of management, because new problems arise as a result of technological change, as a result of new industries, and as a result of twists to old problems, and (possibly most important of all) O.R. is needed to remind managers of techniques and results discovered years before.

Worldwide concern about Covid-19 has illustrated Alan's answer; there have been new problems identified across many sectors.  Stock control, disease modelling and monitoring, ward scheduling, supply chain analysis, distribution and queue models, and much else.  

Alan contributed work on location modelling, and distribution planning.  More than once, he lamented that his paper "The Churching of Urban England" (which explored models for location of facilities, in this case, churches, and which was published in the proceedings of the IFORS conference in 1969) was overlooked because other researchers didn't spot the relevance of such models to other location problems.

A recent paper in the Journal of the O.R. Society illustrates Alan's point about technological change and new industries.  Chunkmok Lee published "An exact algorithm for the electric-vehicle routing problem with nonlinear charge time"  [https://doi.org/10.1080/01605682.2020.1730250] .  New technology: electric vehicles.  New industry: home deliveries.  Twist to an old problem: location modelling of charging stations.  

That same issue of JORS (JORS 2021, vol 72, no 7 (July)) had other papers which illustrate the ongoing need for Operational Research.  Giuseppe Bruno and others look at the problem of collecting mail at a time when demand for postal services is declining[https://doi.org/10.1080/01605682.2020.1736446].  A.H. Kelte and others tackle the allocation of kindergarten spaces in Norway as the education system develops new constraints.[https://doi.org/10.1080/01605682.2020.1727786]   Both are old problems; both have new twists.  

So, O.R. Scientists - you will always be needed!

 There was a day, in my teenage years, when my parents bought a second car.  I don't know whether they analysed that decision.  It was probably prompted by the fact that my mother had passed her driving test (in the UK, in the fifties and sixties, not all married women could drive; driving cars was still a male preserve, and my mother, like so many others did not work after she was married).  But their decision to increase the domestic resources of cars is an example of decisions which occur in many situations.  Cars do not come in fractional parts; you either have one or you do not.  And the jump from having one resource to having two is a big one.

Why?

In many situations for management, the demand for a single resource increases steadily.  Suppose that a resource is being used 80% of the time now, and the demand increases to 90%.  Forecasting suggests that the demand will continue to  rise.  So, sooner or later, the use of the resource will exceed its capacity.  So a second resource will be needed.  However, as soon as the second resource is available, the average demand for each one will fall to (say) 50% of capacity.  And to an outside observer, that suggests inefficiency; there is unused capacity.  So, in a sense, the decision maker who obtains the second resource is "damned if (s)he does, damned if (s)he doesn't".  It is similar to Catch-22.  

(note that with more resources, the drop in average resource usage going from N resources to (N+1) is much less; naively, if N resources are all being used 100% of the time, then N+1 will be used (100N/(N+1))% of the time.)

Vehicles are an obvious example of a discrete resource.  But public facilities also fall into this problem of discreteness.  When should a new surgery be opened?  When should a new school be built?  And on a personal level, during lockdown, when should a family buy a second computer?

The vehicle problem struck me in the city earlier.  We have one council vehicle to empty the bottle-banks around us.  It is well-used; we are rather good at recycling glass.  And we don't have kerbside collection of glass in the city, yet.  The vehicle is also used to empty the recycling bins for drinks cartons (tetrapaks).  The city has chosen to stress the glass recycling over cartons, so there are many more places with glass recycling containers than carton recycling containers.  Cartons can be all dealt with in one run around the bins; glass necessitates many runs around the many sites of the glass-bins.  

So, should the city expand the number of bins for cartons?  If so, then it will need a second council vehicle to empty those bins and some of the glass-bins.  But, that's a capital cost or a vehicle, a capital cost for more carton-bins, plus wages, plus running cost, for a very small increase in the income from recycling material.  What's to be done?  At present, nothing.  The status quo remains.  But the problem will not go away.  The population of the city is growing, so demand for all kinds of recycling facilities and equipment will grow.

And an added problem about this sort of possible expansion.  There is a problem of recruitment of drivers qualified to handle heavy goods vehicles.  According to one statistic earlier this month, in the UK there are 100,000 vacancies for HGV drivers.  So even if we could justify a second vehicle, it might be hard to recruit a new driver.  

Meanwhile, I will walk to the nearest glass bin, and occasionally cycle the 4 kilometres to the most convenient carton-bin, combining such a journey with a pleasure ride.  

And I will never know how my parents justified the second car, because --- just like many two-car households --- the cars were only used for a fraction of the time.  But back then, there were no car-sharing schemes, and our home in the village didn't have a very good public transport system.

 Early in the Covid-19 pandemic, the British government encouraged local authorities to develop traffic management schemes which would encourage "greener" transport.  This led to several cities rapidly creating "low traffic networks" (described here), sometimes with minimal public consultation.

Here in Exeter, the response was to prioritise cycling over motorised transport, and several roads were closed to all traffic except cycles and (sometimes) buses.  Because the response had been partly to help those who needed to travel to keep physically distant from others, this aspect was highlighted. 

One of the closures is very near our home.  I have refrained from writing about it until some of the dust of controversy has settled, and because I was one of many letterwriters to the council about it.  I also lampooned the person who had authorised the advance signage as it reminded me of the children's book character who was told "You ain't got the sense you were born with".

(To deal with the signage; the advance signs read "New road layout to assist social distancing".  This may be a good reason, but is no help to a motorist who encounters it.  That motorist wants to know what to do; the reason is not directly explained.  If traffic is reduced in this road, it encourages walkers and cyclists to use it, and then they will be kept away from congested roads, so it will be easier for that sort of traveller to be 2 metres (or 6 feet) from others.)

Back to my local road closure.  The road has been closed to all but buses and cycles.  Before this, it was used as a rat-run by a small number of drivers, and by locals going to the local hospital, schools and shops.  

 Who benefits from the closure?  Walkers and cyclists can use a quieter road without traffic (which often broke the speed limit).  Local people who now have less noise from traffic and less pollution.  Bus passengers gain from a route which has better time-keeping.  Many motorists, since they are redirected to roads where there is automatic traffic control.

Who suffers?  Local people who cannot use the road as a driving route from their homes to some businesses.  Tradesmen and delivery drivers, who must now follow different (longer) routes.  

And intangibles?  Some people may change their behaviour.  Will the changed traffic pattern mean more contributions to global warming or less?  How is the closure to be monitored for violators?

And those are just the start of the conflicting objectives, just as in much of Operational Research.  What makes this interesting is that the benefits are extremely small for each individual, and there are a lot of people who benefit, but most will not realise that they are benefitting.  However for a few local people, the suffering seems big.  Small gains for the many; large losses for the few.  How do you balance these?  

The council has made its decision, which has accepted the benefits, but has made a few small changes for the benefit of the few. 

One of the recurrent problems of managing queues is randomness. And when human beings are involved, there is nearly always some randomness. And that's why queues involving machines are easier to deal with; machines are more predictable! Until the problem is scheduling emergency maintenance, due to a particular kind of randomness called failure.

Many analyses of control of human queues advise that to be efficient, the randomness must be reduced.

So, my day of second vaccination was an especially interesting experience for being in a queue which was very controlled for efficiency. I was there for my vaccination against Covid-19. The appointment was at 9:40am, along with about a dozen other people. But of course, we arrived at random times. We joined a single line to be checked in, one by one. Once past that point, control to deal with randomness started. Each patient was sent to a numbered chair, so there were ten of us, all ready to be called for a numbered "server'' (or vaccination nurse) That smoothed out the arrival process, by ensuring there was always a reservoir of people in the waiting area. Then our chair number was called, and we proceeded to a numbered room, where another chair awaited us outside.

So each nurse, in their room, always had a "customer'' being served and another waiting to be served. In queue parlance, the servers were working at 100% capacity. But of course, there was scope for each one to take a break.

All excellent control of a system, smoothing the arrival process at the servers so carefully. Well done, whoever devised this scheme!

All was well until Tina and I compared notes about our experiences, and it transpired that the "system'' found it hard to cope with people in wheelchairs and buggies, who couldn't use the numbered chairs. And the process of "serving'' for Tina and I was slightly different; she was asked different questions from me, and was given more documentation than I got. So, not quite full marks for planning, but still very good. 

I know that there has been a great deal of modelling in the health service in the United Kingdom to streamline the vaccination process.  The pandemic will provide plenty of case studies for O.R. researchers in that sector.  But, I wonder, will there be any rivalry between the designers of different queue management systems?