Tuesday, 31 January 2012

Distribution Centres - Algorithms and Consequences

I recently caught up with an OR-related video on TEDX by Mick Mountz "The hidden world of box-packing".  Operational Research is not mentioned by name -- typical of OR being "The hidden science".
How do you organise packing at a distribution centre?  Do the packers go and roam around the warehouse?  Or do you send things on a conveyor belt?  Mick Mountz' talk is all about creating a world for the packers, where the goods arrive automatically where the packer and their supply of boxes is to be found.  It works with robotic motors (coloured orange) which move the storage shelves (coloured blue) to the packing station. 
The talk has some good video material for teaching.  Beyond the illustration of a commercial site, there are some interesting comments about the consequences.  The system adapts to the speed at which a packer works; one person taking a bathroom break doesn't anyone else; and the underlying algorithms arrange the mobile shelves so that those with the most frequently wanted items are closest to the packing stations.  And that layout adapts with seasonality.  

There are numerous comments about the video, some for, some against.  Packing boxes is repetitive, but so are many jobs these days.  The packers do not get social interaction and it could be argued that the objective of creating a pleasant working environment has been ignored. 
There are further OR-related questions which could be considered.  How big does the distribution centre have to be to make it worthwhile for the proprietor?  Could such a system be used for packing where a customer walks into the store, or is it solely for online retail? 

Tuesday, 24 January 2012

Where do buses go?

We took the bus to the coast the other day; using public transport means that we can walk from A to B without needing to walk back from B to A.  (For the record, A was Dawlish Warren, B was Dawlish, and we walked along the sea-wall.)  Part way there, the bus deviated from the main road.  "I wonder", asked Tina, "why the bus goes this way in this village, and usually stays on the main road?"
We thought about it.  The village of Starcross is beside the Exe estuary.  The main road runs between the houses and the railway and river, so is wholly on the west side of the main road.  So taking a deviation through back streets means that more people are closer to the bus route than if the bus stayed on the main road.  For the price of a slight increase of journey time, the average distance travelled by passengers was much reduced.
And we thought about other bus routes we know.  Some do deviate off the main road to go through, or closer to housing.  Does anyone do cost-benefit analysis about it?  Or are such bus routes determined heuristicly?  The research papers that I have seen about bus operations are all concerned with scheduling the vehicles and their crews, not determining the routes.
The next step in our pondering about O.R. and buses was to wonder about when the company judges it worthwhile altering a bus route to serve new housing.  There's a new housing estate on the edge of Exeter, which is not served by any public transport, but we frequently see people struggling the quarter mile or more from the nearest bus stop with their shopping bags.  But to bring an existing bus service into that estate would mean rescheduling that service and have implications for the staff rotas as well.  So it may be some time until that estate gets a regular service.
Any research on these topics out there?

SX9781 : Starcross; war memorial and railway station by David Smith
Starcross, the main road and railway

Saturday, 14 January 2012

More on unnecessary meetings and optimisation

Having written about meetings yesterday, I remembered this article, which combines the O.R. ideas of optimisation with a discussion about meetings.  As will be apparent, it is not my own work, and I am not sure about copyright ...

The article below appeared in the journal "Eureka", issue 33, October 1970.  As is clear from the introduction, it is reproduced from another source, which is unnamed.
The Optimum Size for an Establishment
by H. W. O. Petard
(The Editor would like to thank Professor M. V. Wilkes who discovered this paper quite recently and very kindly passed it on to Eureka. As older readers will know the author was famed in mathematical circles for his incredible article on the Mathematical Theory of Big Game Hunting which appeared in the American Mathematical Monthly during 1938 and later in Eureka no. 16. The article below was probably written some time during the war)
1. Introduction
It is a commonplace that the amount of work done by an Establishment of Civil Servants is not directly proportional to its size; indeed, cases may readily be quoted in which an increase in staff has impeded rather than furthered the objects for which an establishment exists. In the present paper I shall examine the problem analytically; and derive formulae by means of which the optimum size for an establishment may be determined. I shall make use for this purpose of the Kinetic Theory of Civil Servant Swarms which has been developed by Ponticelli. As this theory is not as well known as it deserves, I propose in the next section to give a brief summary of the most important results.
2. The Kinetic Theory of Civil Servant Swarms
The fundamental concept in this theory is 'pressure', which may be defined as the force that the establishment as a whole can bring to bear in order to achieve its objects, for example, to overcome the obstruction of other establishments or departments, or itself to obstruct some design originating from without. At first sight it might be thought that a Civil Service establishment, by virtue of the random motions of its members, would exert a pressure of precisely zero; a moment's consideration of the analogous case of a gas consisting of molecules moving with random velocities, will, however, show that this is not the case, and that in fact a finite pressure is always exerted. This pressure is, of course, less than the pressure of a hypothetical pseudo-establishment in which the energies of the staff are all oriented in the same direction.
I will not here enunciate all the results of the Kinetic Theory, for which reference should be made to the original sources; two results, however, are of particular importance:
(a) In order to do work an establishment must continually expand.
(b) The larger the establishment becomes the less is the pressure it exerts
3. The Optimum Size for an establishment.
We shall suppose that the establishment consists of n members; this number is only to include those members of staff in positions of responsibility, as it is not my intention in this paper to examine in detail the relations existing, for example, between an officer and his secretary. Let a fraction k of each officer's time (office hours only being considered) be devoted to the work of the establishment, and let a fraction m be devoted to productive work; the difference, namely (k-m), will then be devoted to internal liaison with other members of the establishment. We will suppose for simplicity that the quantities k and m are the same for all members. Normally, k2 and higher powers may be neglected. In what follows it will be convenient to take the working day as the unit of time.
Since each officer has to liaise with each of his (n-1) colleagues, we have, assuming he spends the same amount of time with each,
k - m = a(n - 1)
where a is a constant.
The total time spent on liaison by all the officers taken together is then
a n (n - 1)
while the total time spent on useful work is
It will thus be seen that as n increases, the time spent on liaison increases much more rapidly than the time spent on useful work.
If we assume that the size of the establishment is optimum when these two quantities are equal, we have
a n (n - 1) = n m
or n =1+ m/a
Since exactly half the time k is spent on useful work, we must have
so that the above equation for n becomes
n =1+ k/(2a)
4. A Numerical Example
To illustrate the foregoing results in a practical case, let us suppose that the daily liaison between officers is limited to the writing of one short minute, or the making of one short telephone call, the total duration being on the average 3 minutes. If the length of the working day is five hours, we have
a = 3/(5 x 60) = 0. 01
If we now take for k the value 0.5, we get for n
n =1 + 0.5/(2 x 0. 01)= 26
Thus the optimum size for an establishment under these conditions is 26.

Friday, 13 January 2012

Is your meeting really necessary?

Thanks to http://analyticzen.wordpress.com/2011/12/23/work-moments/ I listened to Jason Fried on the subject of meetings.  When we taught undergraduate students about communications skills, we sometimes used a film called "Meetings, Bl***y Meetings" which satirised the management culture which arranged a meeting at fixed time intervals, irrespective of whether or not there was anything to discuss.
Now I know that sometimes, we in O.R. need meetings, but do we need every one of them?  I wonder.

Absurd precision

Our local swimming pool, like other public buildings, has to display an energy efficiency certificate.  While waiting for Tina to finish changing, I started to read this (OK, I should get a life!) and was amazed that the total usable floor area in square metres (about 2500) was quoted to two decimal places.  (So there were six significant digits in the printed record.)  It may be that the company was simply converting dimensions in imperial units (the building dates from the 1930s, before metrication in the UK) but I wondered whether anyone providing the dimension had the common sense to think that 0.01 square metres is a little smaller than the area of a postcard.
But how many OR studies have been guilty of the same absurd precision?  Papers that came to me to be refereed often had similarly absurdly precise data, based on parameters that were quoted to one or two significant figures.  It must be accurate -- the computer says so!
Oh dear!  I had posed the above two paragraphs, and opened the latest issue of the Journal of the O.R. Society.   It included several atrocities. 
One row of a table told me that the four parts of an algorithm took:
0.54 secs, 0.22 secs, 10.76 secs and 7620.64 secs, with a total of these and other parts, of 7633.53 secs.  The fourth component used 99.8% of the time, so the algorithm's efficiency depends on that.
Another table had a column of figures: 6349.09, 6244.68, 4103.79 etc, for the time taken to find a solution to a problem where the data was measured in metres and the total of all measurements was about 3000 metres -- so the problem solution was correct to something greater than 1 in 3000 (let's be generous, and say 0.1%) but the time in the first row was correct to 0.01 in 6000.

Saturday, 7 January 2012

Four lessons about resolutions for 2012 (and O.R.)

Until INFORMS suggested that we bloggers on O.R. should write about the relationship of our discipline and the making of New Year resolutions, I had not considered that the two could be interrelated.  But, reflecting on the INFORMS challenge over the holiday, I realise that there are several similarities.  (Yes, I do have a life, and I did enjoy the holiday period, and I didn't spend every waking moment thinking about O.R.)

Lesson number 1: philosophy.  New Year resolutions are based on observing the past, learning from the past, and selecting ways to improve the future for a person, family or even business.  O.R. models are based on observing the past, learning from the past, and selecting ways to improve the future for a business, family or even person.

Lesson number 2: forecasting.  The Roman deity Janus was famous for having two faces, one to look back to the "old year", one to look forward to the "new year".   (Did you know that the word "janitor" is related to Janus?  Janus is the deity in charge of gates and doors.)  When one makes resolutions, one looks back (see lesson 1) and makes a forecast for the future.  Usually, in personal circumstances, one uses what O.R. people know as "A naive forecast" that the future will be very similar to the past.  Makers of New Year resolutions do not (generally) use exponential smoothing, seasonally adjusted models, or Box-Jenkins time series models to forecast for the coming year.  But experienced O.R. professionals know that there are numerous situations where that naive forecast is as good a method as possible, even if it may get dressed up in detail to justify the consultancy fee to the client.

Lesson number 3: developing the New Year resolutions.  Lifestyle coaches recommend that any change in personal habits should have five characteristics, referred to as "SMART".  This is an acronym well-known in O.R. circles, for "Specific, Measured, Attainable, Relevant, Timed", and these five words are often used implicitly or explicitly in O.R. studies.
Specific means that the resolution specifies in detail the change that is expected: "I will lose seven pounds by June 30th", just as an O.R. study may specify that the cost of distributing widgets will be reduced by 2% during the coming financial year.  In both resolutions and O.R. studies, being specific leads to a plan of action, identifying matters that need to be changed, when and how.
Measured relates to the above, as both the examples include numerical measures.  It is not enough to resolve "I will lose weight by June 30th" or build models which aim to "reduce the cost of distributing widgets"
Attainable means that the resolution or O.R. proposal is feasible.  It may not be possible to lose seventeen pounds by June 30th (unless you are dieting under medical supervision); it may not be possible to reduce distribution costs by 10%.
Relevant means that the resolution is an important one; anyone can suggest a resolution that is trivial, and O.R. analysis of irrelevant parts of an organisation may be interesting but unproductive.  (cf "rearranging the deck-chairs on the Titanic")
Timed is part of being specific giving a timetable for change in personal habits or business parameters.

Lesson number 4: implementation.  It is often noted by O.R. scientists that one must identify the person or persons in an organisation who will own the solution to the O.R. problem and ensure that it is implemented.  The journal "Interfaces" used to insist on supporting letters from an individual in a client organisation assuring the readers that the proposal in a practical paper had been implemented and achieved the benefits that had been claimed.  For New Year resolutions, the person making the resolution has the responsibility of implementing the plan to achieve the desired result.  However, there is much evidence that successful New Year resolutions are associated with an outsider whose responsibility it is to monitor progress, and help keep the plan on course.  Allied with this is the common suggestion that resolutions should be written down and placed prominently as a reminder.  In other words, implement the resolution into the regular routine, just as implementation of an O.R. study should be done consistently.

And one more parallel.  For both resolutions and O.R. implementation, go forward with determination and persistence.