## Finding an optimal seating chart for a wedding

### Finding an optimal seating chart

by Meghan L. Bellows (Department of Chemical and Biological Engineering, Princeton University) and J.D. Luc Peterson (Princeton Plasma Physics Laboratory, Princeton University)
EDITOR’S NOTE: The authors submitted this article long prior to the wedding. Somehow we managed to not see it until long after. The only benefit being that the article can and does include photographs taken at the wedding. We are delighted to publish it here, online.
Every year, millions of brides (not to mention their mothers, future mothers-in-law, and occasionally grooms) struggle with one of the most daunting tasks during the wedding-planning process: the seating chart. The guest responses are in, banquet hall is booked, menu choices have been made. You think the hard parts are over, but you have yet to embark upon the biggest headache of them all. In order to make this process easier, we present a mathematical formulation that models the seating chart problem. This model can be solved to find the optimal arrangement of guests at tables. At the very least, it can provide a starting point and hopefully minimize stress and arguments… [Read the entire article in PDF form]

### 8 Responses to “Finding an optimal seating chart for a wedding”

1. Teyster Says:

I was at this wedding, and I have to admit that my setting was most optimal.  The soup was really good too, though I don’t know how the model helps with that.

2. MHM Says:

Check out those incredible hand-calligraphied seating cards, purportedly done by a close member of the groom’s family.

3. A Mathematician’s Guide to Arranging a Seating Plan Says:

[…] our favourite has to be this mathematical optimization model created by Megan Bellows and Jean Luc Peterson, of Princeton University, for their wedding. They […]

4. Andy Brice Says:

Our PerfectTablePlan software also solves this problem. However we take a rather different approach, using a genetic algorithm instead of MINLP. This means that our answer is not guaranteed to be optimal, but we can usually get a pretty good solution in a very short time. Also we take account of whether guests are sitting next to each other or on the same table.

A 107 guest problem would probably take PerfectTablePlan < 1 minute on an up-to-date PC (as opposed to the 36 hours for a high spec compute node quoted in the paper). We have solved problems with thousands of guests on a standard PC.

As fans of the Ignoble Awards, we did offer Marc a free licence some time ago to help with seating the award ceremony, but we never heard back. Perhaps everyone likes everyone at the Ignoble Awards. ;0)

5. Andy Brice Says:

I think I spotted one mistake in the paper:

“So m = 17, n = 2, a = 10, and b = 1.

There are 2^17 = 131,702 possible combinations for seating these guests”

I believe 2^17 is the number of ways of sitting 17 guests on 2 tables
with 17 seats each (not 2 tables with 10 seats each). I believe the
correct answer can be computed using C(n,r) = n!/r!(n-r)! as:

2 x ( C(17,10) + C(17,9) + C(17,8) + C(17,7) )

=175,032

However I am not a mathematician, so I might be wrong!

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