Friday, 3 December 2010

OR and the holidays

This blog post contributes to the INFORMS monthly blogging theme. Look for the INFORMS blog to summarize the blogs at the end of the month.

I have two younger brothers, and we all have families. Choosing where to meet, when to meet and what to do for a Christmas family get-together is a multi-criteria decision problem, and our conclusions demonstrate that solutions to a repeated problem change with time as circumstances alter.

One brother (Michael) lives near Leicester, one (Andrew) near Gatwick, and we live in Exeter. For simplicity, these may be regarded as the vertices of a triangle, sides 4 hours, 5 hours and 3 to 4 hours (depending on the traffic around London).

In the old days it was easy. We all met at my parents' home, which was reasonably central. All that was needed was to schedule who travelled when, and help mum with the catering, cleaning and beds. It wasn't too hard to plan what to do.

Even when mum died, we continued to gather at the same place, but we needed to plan a great deal more for the catering.

Then dad came and lived with us, and people came here; with a smaller house than the parents' home, we needed to arrange that Andrew and Michael would overlap for lunch on the day that one arrived and the other departed.

But when dad died, we all felt that there were better times of the year to visit one another. Tourist attractions are generally closed in December, and that limits the scope for days out. So the problem became more interesting. Meanwhile, the next generation was growing up, which brought other people's criteria into the decision process.

We reached a conclusion that we did not need to meet in December, and for several years got together for a Saturday in January, when it was cheaper to travel by public transport, and there were places we could visit together or things we could do together. So that gave a feasible solution, which ticked several boxes for all of us: ease of travel (we each made a train journey with at most one change of trains), a warm place to meet with space for presents to be exchanged, an activity which was pleasant. There was one surprising downside; the presents that we gave had to be compact and portable as we would be carrying them all day.

Then there was a birth and activities which involved theatre or shows in London became infeasible. One year we strolled in London with a toddler, and fortunately the weather wsa good. We all saw parts of the capital which were new, so it was a memorable meeting.

Another birth meant a baby and toddler to be entertained, along with two twenty-somethings who might or might not be around in January, but were more likely to be available in the week between Christmas Day and the New Year. So the weight attached to different criteria changed. We fed our locations into a website (rendeznew) which told us that the meeting point in the centre of the three homes was near Swindon. So we searched for a suitable place to meet and eat there, hopefully with space for the restless children.

And that is the solution at present. Soon after Christmas, three cars (loaded with people and presents) will congregate on a gastropub near Swindon. Each of us will have a two to three hour drive each way, and we have told the staff that it is a family gathering. We are trying out a third pub, for variety.

Could all this be automated? As I have explained, there have been changes in our needs and hence on the emphasis on different criteria. The web site wasn't really needed, as we could see from a map that Swindon was reasonably central, and we had the knowledge of the UK road system to guide us. Once we had found the right locale, we could have searched for places to eat, by specifying criteria (must have car park, serve vegetarian food, be child friendly) but these would be binary constraints (yes/no) and we might want to treat them as slightly soft constraints.

Sometime, I may return to the algorithm used in rendeznew, which has interetsing O.R. aspects.

An astute reader may spot that there is one constraint which we have implicitly included. Nobody wants to stay in a hotel for the family get together.

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