Monday, 25 June 2012

When the rains came

Tina and I got back from the Isle of Wight two days ago.  That may seem an odd way to start the blog, because it will not mean anything to many readers, so I must explain.  The Isle of Wight is a smallish island just off the south coast of England, famous for hosting sailing at the town of Cowes, and for the unspoilt countryside.  Over the last few days, it has been in the news headlines because of the Isle of Wight Music Festival.  This is an annual open-air festival, attracting 55,000 people for three days (Friday, Saturday and Sunday) to hear excellent music and join in the event in parks and fields just outside the main town of Newport.   Only this year, things went wrong.  The ground was wet, it rained very hard on Wednesday and Thursday and some of the campsite was flooded.

And the car parks were so wet that normal cars had difficulty manoeuvring (so many cars needed assistance from tow vehicles).  Because traffic was entering the festival site more slowly than expected, it started to back up onto the main highway, and it backed up more and more.  Before long, there was gridlock around the festival site.  Local people and businesses were affected as well.
As holidaymakers on the island, not there for the festival, we managed to keep away from the gridlock, but there were what the press call "horror stories" of people sleeping in their cars, and the ferries to the island could not dock because there was no way to clear the cargo of vehicles once they reached the island.  On Friday, various plans were implemented to clear the gridlock and sort out the worst of the problems, with considerable success.

Over the weekend, an emergency plan has been put into place to clear the site (here) and it seems to have worked.
As an observer, almost on the spot, I wondered what lessons could be drawn from the experience of the arrivals to the festival, who met the gridlock.  I imagine that one could devise an interesting case-study along the following lines, drawing on three strands of O.R. methodology.
  1. There was a queueing aspect.  How do you get vehicles off the highway and into the festival site?  Each one has to leave the traffic on the highway and enter one of the access gates.  The more gates, the more servers (in queue parlance).  However, the rate of service changed because of the state of the ground in the festival campsite and car parks.  Each service became several times as long as it would have been under "normal" conditions.  In consequence, the queues for service grew, because one of the first lessons that you learn in a course on queues is that the average service rate multiplied by the number of servers must exceed the average arrival rate, otherwise the queue for service grows and grows.
  2. There was a network aspect.  The highways of the Isle of Wight form a network.  Each arc of the network has a number of properties, including a capacity for vehicle flow.  In a course on networks, one could discuss the capacity of the network as a whole - assuming that there was free flow in those arcs and through the nodes.  Unfortunately, the principal highways close to the festival converged on one roundabout (at Wootton Common).  Traffic from one ferry came to the roundabout from the east, traffic from another ferry came from the north-west, and the road to the festival was the third arm of the roundabout, to the south-west.  Local traffic also needed to use these roads (including, sadly, traffic for services at the crematorium close to the roundabout).  The lesson one could draw for this is that network flow models are useful - up to a point, but do not work when the assumptions about them fall down.
  3. There could be a simulation aspect.  It would not be difficult to build a simulation model of the traffic on those three highways, and investigate what happens when the service rate at the festival site changes.  And that model would demonstrate how the congestion would spread around the vicinity of the event, and how gridlock would follow.  And such a model could be extended to test alternative strategies in case such weather-related problems happened again.

Wednesday, 13 June 2012

Rare events revisited

Last week I wrote about stock control of rarely used spare parts and the consequence of getting parameters wrong, and mentioned the example of a blast furnace which needed to be cooled and rebuilt.  Paul Rubin has commented that sometimes it is just bad luck for the organisation concerned.  I agree.  The stock control expressions for such a case are queue models, and there is always a finite chance that the demand for spare parts exceeds the number being stocked.

This evening we had a phone call about a furnace in Devon which needs to cool and be rebuilt,  You can search in vain for the steel industry of this county.  Iron and steel are not produced here.  Other minerals have been mined and traded in Devon over many years, notably tin for centuries, silver in places, gold in minute quantities, and copper in the nineteenth century.

The furnace concerned is a glass furnace.  Tina was planning to have a one-day course in glass-blowing, and the call was to postpone the course.  The excellent glass artist Siddy Langley lives about ten miles from here, and last weekend she discovered that the glass pot in her furnace had cracked.  There are pictures of the spectacular consequences in her blog.  This is one of Paul's cases of bad luck.  As Siddy says in the blog, the only thing to do is to let the furnace cool, chip out the glass which has gone solid and rebuild the furnace.  There is no way that a broken pot can be replaced while the furnace is at 1200degrees C.  We are sorry for Siddy, who makes beautiful glass items.  No inventory control policies are appropriate for an item like this.

Tuesday, 12 June 2012

What price a season ticket?

Although it is only June, the football clubs of the U.K. are already selling their season tickets for the next season, which starts in August/September -- in fact, the lowest prices were available in a time window that closed two or three months ago.  Seeing the adverts, I wondered whether anyone had done research about the pricing of season tickets for sports teams, and multi-entry prices for clubs and facilities. 

So let's ask the question for a football team?
If the ticket to one match cost X, and there are N matches, what discount should there be for a season ticket holder?  Obviously, the season ticket should cost less than NX, but how much less?  For Exeter City, N is 23, and the cheapest season ticket is £343 (£326 if you buy it this week)

It isn't as simple as this, of course, because there are perks for having a season ticket. So the supporter needs to factor these into account when deciding whether a season ticket is a good buy or not.

Now, let's think about other kinds of season ticket. 

It costs me £2.50 for a swim in the city pool.  How much should I pay for a three-month pass?  Here, the number of times that I swim is the defining variable, and my regular use of the pool means that a pass costing £31.80 (less than 13 times the single ticket) is a bargain.  How did the pool management reach that figure?  It is priced low so as to be an incentive to people to buy a season ticket, while, on the other hand the single visit cost is perhaps high to cover the costs of administration. 

And then there are tickets like the British National Trust, where a season ticket costs about the same as entrance fees to six of their properties around the country.  Season ticket holders also receive a magazine three times a year, and a handbook, so there are incentives for loyalty.  How did the National Trust reach a conclusion about the relative costs of single entry and season tickets.  (Incidentally, visitors to Britain who plan to visit several National Trust properties could save by joining the organisation.)

And another example which I met recently is a season ticket for one tourist attraction.  In this case it was a public garden, which local people might want to return to several times in a year.  Here the season ticket was priced at just less than four times the entrance fee, and again there was a magazine and special events available to season ticket holders. 

But has anyone actually researched this topic?

Friday, 8 June 2012

Slow moving parts; stock control

I only taught inventory management (stock control) for a couple of years, and then the university appointed a specialist who taught most of the material.  From time to time after that I was asked to contribute to lectures and co-wrote a few academic papers about inventories in particular circumstances. 

One story which sticks in my mind came from one of the text books and it cited the experience of an American iron and steel maker from the 1960s.  Maybe a reader can identify the case?  There was one essential component for the blast furnace which cost about 250 dollars.  Based on someone's calculation of the frequency of needing this item, the company had determined that it was a slow-moving item, and the appropriate model for replenishment was to hold two spares, and as soon as one was used, to order another.  There was a lead time of a few weeks, between placing the order and receiving the item.  Such a model is common for slow-moving items; the key variable is the number to have in-stock-plus-on-order.  The model depends on the cost of storage, the cost of a failure if no items are in stock, the lead time for delivery and the lifetime distribution for the item.  If calculated properly, there will be a minute chance of not having a spare when one is needed.

One day the inevitable happened.  The component failed, there were two items on-order and none in-stock.  And the consequence was: the furnace had to be closed down, and then fired up again when the component had been replaced.  Total cost; about half a million dollars.

I used this example to emphasise the importance of getting correct values for all the costs involved.  In this case, I suspected that the someone seriously underestimated the cost of having no items in stock when there was a need, or, miscalculated the lifetime distribution for the component.

Why did I remember this story?  Today, our local news includes an item about the failure of a large windfarm in Devon.  According to the story, one component has failed.  I wonder who miscalculated the stock control policy for spares for this component?

Thursday, 7 June 2012

Entrepreneurs and Operational Research part 2

 Last month I raised the question of whether Entrepreneurship relates to the Operational Research mentality.  Since then, a few people have suggested that there have been a number of consultancies created by entrepreneurs in the O.R. world devoted to consulting with specific tools.  I opened my monthly newsletter from the (UK) O.R.Society to find that there had been a presentation at the Student Conference on O.R. in April.  Here is what was written:

Entrepreneurship in Operational Research - Essential bedfellows? by David Buxton

David Buxton has had a varied career history. Starting out as a Geographer before moving into Analytical roles and then into senior positions in general management. Recently, David move into academia, before taking the risky step to strike out and founded dseConsulting. Enjoying commercial success and a reputation as a simulation expert, last year he joined forces to also launch decisionLab, styled as the modern approach to OR consultancy.

These business ventures and the previous experiences have each given different insights into the role of OR in business, and had led David to believe that an entrepreneurial spirit in Operational Research is an essential component.  Looking at the definition of an entrepreneur: “someone who identifies an opportunity and organises, operates and assumes the risk for a business venture to exploit that opportunity“, it is easy to see that this should be the very essence of OR. However, in practice, we frequently see OR as a ’behind the scenes’ or supporting function? As evidence of this - given the difference our work can make, and the decisions we work on - wouldn’t we expect to see some of the high flyers of the business and political worlds coming from an OR background?

So why is it that we don’t? Perhaps we should focus more on risk taking?

And what about those characteristics associated with the most successful entrepreneurs: interpersonal skills, the ability to persuade, the ability to lead and motivate, charisma? Are those skills traditionally valued and developed in OR?

In the end, does it really matter? Perhaps other disciplines are better suited to the cut and thrust of a commercially-driven world - we can let them take the plaudits whilst we continue with the decision support. But does this threaten to marginalise OR? And in a competitive job-market what can an OR graduate do stand out?

Using examples from his own experience, David will highlight the importance of the inner entrepreneur. It hasn’t all been plain sailing and in this talk David will share his mistakes as well as successes to provide you with insight to help you prepare for your own career and recognise the skills you’ll need to move seamlessly from academic to commercial to consultancy environments.

The science of better hotel breakfasts

I have just returned from a short holiday which meant that Tina and I stayed in seven different hotels (in Germany and Austria, thank you for asking).  Since new experiences often lead to questions about the efficiency of the system that one observes, I have come back with a few ideas.

In each hotel, we had a breakfast buffet.  Provision of food like this raises several questions that  Operational Research can contribute to, but -- as is often the case -- the users are too small to consider analytic methods.  So they use heuristics, which are successful in most cases.

So, here are three problems for the hotel manager:
(1) Inventory control
(2) Scheduling of replenishment of food
(3) Layout of the items on display

(1) is concerned with ensuring that the supplies on the sideboard are sufficient, and therefore you need staff to monitor the levels of each item.  They staff can use rules of thumb to judge when the bowl of yogurt, jug of milk, or tray of cold meat needs to be replenished.  But there are hidden inventory problems, such as stock rotation.  Some items on the sideboard are emptied from the top, and refilled at the top, which may mean that the material at the bottom of the container is not touched during the day.  Care therefore is needed to ensure some rotation of such items.  One hotel had a very neat silo for cereals, with the cereal being removed from close to the bottom, and the container refilled from the top.  But we wondered how they staff managed the rotation of jam.

(2) is particularly concerned with replenishing hot food -- on the sideboard it is kept in bain maries or chafing dishes, and again there need to be heuristics that the kitchen can follow, knowing that cooking some items takes a non-negligible amount of time.  One hotel had a large tank of boiling water for those of us who wanted to drink tea, and we were horrified to see it being refilled by a waitress who had to raise a10 litre pot of boiling water to the top of the tank (her eye level) and pour it in.  Alternatively, in smaller places, food can be cooked to order, which reduces the problem of scheduling.

(3) means understanding the flow of the guests past the sideboard, and the amount of time that is spent at each station.  There are lessons from planning production lines which might be brought to help, but the psychology of different guests would need to be studied.  What I eat for breakfast will be different from what Tina eats, and from practically every other guest.  And -- even when you think that all guests are catered for -- someone will prove exceptional.  On successive days I watched people mixing jam and plain yogurt; one filled the bowl with yogurt and added jam, the other put the jam in first. 

We observed two neat solutions to everyday problems: provide a small rubbish bin on the breakfast table for waste butter wrappers and the like, so waste doesn't get into the dishwasher; provide very small bowls for jam and honey, to be filled from the large containers on the sideboard.