Friday, 28 October 2011

Looking for examples of O.R.

Recently, Laura McLay posted an article about the queues at her local pumpkin patch.  (  I commented that her observation was typical of many situations in life, where experience of O.R. means that one observes a situation and realises that there is scope for improvement. 

I think that those of us who have been, or are, involved with teaching the practice of Operational Research to students, are likely to collect examples from everyday life where O.R. is appropriate.  We collect them, think about them, and use them in teaching.  And a further common feature is that we often observe situations where it would be infeasible for the decision-maker to use O.R..  Not all decision-makers have heard of the subject, and so do not realise that a specialist in the subject could help, and not all organisations could afford O.R. consultancy.  Throughout my career, I have taken telephone calls from a number of organisations, describing problems, and I have often spent a short time in conversation and suggesting how to solve those problems ... at no charge ... are these successful consultancies?  (I think so.) 

Two more examples of situations where O.R. could be useful have struck me in the last couple of days. 

First, I had to take my car to be serviced.  The mechanics do not know in advance how long it will take to trace and correct the fault.  The same is true for many of the other cars that have been booked in.  So, the managers have to decide how many cars to be booked in, and (a common problem) the sequence of starting on each car.  The problem at my mechanic is the limited parking space, to add to the complications.  Obviously, experience of mechanical work means that the business can set heuristic limits and a heuristic schedule, but it would be interesting to have a student project looking at the business.

Second, Tina and I went for a walk with some old friends, near their home in St Alban's.  They took us to Heartwood Forest, where a large new woodland is being created.  (  As we looked round, we noted that some saplings were protected individually using treeguards (for example and others were in a field with secure fencing all round, and no individual protection.  Here's the problem; when does it become more cost-effective to use secure fencing rather than individual protections?  There are several aspects to the problem.  Let's take a simple case: You are planting N saplings in a field.  When N is small, individual protection must be better.  As N increase, does it ever become better to protect them all together?  You can cost the capital expense of protection.  Then you must think about how frequently can the field be inspected?  What will maintenance cost?  What fraction of loss of trees to rabbits and other mammals is acceptable?   I look forward to hearing some answers from foresters!

Thursday, 6 October 2011

Supermarket wars

Today Waitrose opened their supermarket in Exeter. This means that Exeter has the following supermarkets with carparks:
Tesco 3 (one large, two small)
Aldi 2
Lidl 2
Sainsbury 2
Morrisons 1
Waitrose 1
Cooperative 2

along with city centre stores which rely on city council or private car parks (Tesco, Sainsbury, Cooperative)

Now, if you are marketing one of these, the coming of a new one will have some effect on your sales. So what do you do? Encourage customers to stick with your business. The simplest way is to offer discounts. O.R. might be useful in suggesting how large the discounts should be. What have we received?

(1) £5 voucher for Waitrose if you spend £25 (in the local paper)
(2) £3 voucher at Sainsbury if you spend £15 (given when I spent £3 in the store; usually the offer is much less generous)
(3) four £5 vouchers at Tesco if we spend £20 (each voucher valid for a week)

So, the offers are all for a discount of 20 to 25%. I will not be surprised if we are given further vouchers in the next few weeks.

The next O.R. problem is to plan our shopping to take advantage of these offers! That looks like an allocation problem.