Dealing with seasonal telephone calls

Please note that this post is extremely frivolous.

Just before Christmas 2018, Nav, one of the few other operational research scientists in Devon, posted in Facebook that he had spent over five hours in a telephone call.  It was about his research, but I commented, tongue in cheek, that such a long wait on the telephone at that time of year meant that Santa Claus needed more elves to be call handlers.  Nav replied that this was clearly an O.R. problem, determining the staffing of a call centre.  Could this blog examine the problem? he asked.

The literature on call centres is extensive; much of it starts from queue theory models.  The literature on Santa Claus is extensive as well, and there is a recent mathematical monograph which has some related material.  "The Indisputable Existence of Santa Claus" is subtitled "The Mathematics of Christmas".  (Fry, H and Evans, T.O., 2016, ISBN 978-1-784-16274-0)  However, there is no discussion of how Santa Claus's call centres operate.  Even worse, the authors do not acknowledge the long-standing problem which has faced the Claus Team of managing postal enquiries within a limited turnaround time.  Since these postal enquiries generally follow standard form letters "Dear Santa, I have been/have not been a very good child all year.  I would like you to bring me .......  My address is .... There will be mince pies and a drink when you come. Love ....." the handling of them is quite mechanical.  So the "service time" for the queue of postal requests is close to constant and this makes the queue models easier than those for stochastic service times.  It is not surprising that the Claus Team solved this staffing problem long ago.

However, it is well known that telephone messages do not have constant service time, but their duration is a random variable.  Thus, my suggestion that more elves are needed seemed to acknowledge limited analysis by the Claus Team.  As the only data on hand was the queueing time of one call (Nav's "over five hours"), I found it rather hard to reach any well-defined conclusion about how the system could be improved, and so I mulled over the problem over some mulled wine.  

In due course, my glass was empty. I did a little more research and discovered that the Claus Team had progressed from having a call centre, which is why that long queueing time had happened - the call centre is old technology.  As is well known in O.R., one should not automatically solve the problem that is presented; it may be superficial, and there will be a deeper problem behind that which is presented.  Here the deeper problem is how to satisfy enquiries to the Claus Team; the superficial problem was the size of the call centre. 

Although I could not find definite evidence, it appears that the elves are being retrained.  Why?  The Claus Team has developed a suite of apps for tablets and smart phones which allow children to submit their requests without needing to contact an elf operator.  All that is needed is to activate the app and follow the recorded instructions.  On a smart phone, the app will simulate the experience of making a call, but it is the app that provides a spoken response, not an operator.

A further development has been trialled in several hundred thousand homes in 2018, and that is to use smart speakers.  A child turns to a smart speaker and says "Alexa, I want to send a message to Santa Claus."  This instigates a programmed response which is indistinguishable from a direct message to Lapland.

With these developments, it is likely that postal requests to the Claus Team will be reduced, and - in the not too distant future - the elf call centre will be closed down, and become a historical relic.  Millions of children will miss it.  But progress is progress. 

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