### 5 responses to “Choosing Summer Camps for Your Kids”

1. Laura McLay

This is great! I love your detailed model and analysis. How you enforce the preference rules seems to have a large impact on the results. All of the kids go to math, tennis, and fishing. This is largely because math and fishing have “champions” who prefer these activities to all the rest. So the math-hating children are forced to go to math camp to save a few bucks.

I’m not sure why soccer isn’t selected. I’m dissecting your preference constraints. It seems like if a child goes to one of his least preferred choices (Earl goes to fishing because David loves to fish), then Tennis is a good choice *relative to* the other activities selected for the kids. I don’t have enough time to give you my best answer. Hopefully, some of your other readers can comment on this.

2. orbythebeach

Thanks, Laura! Indeed, the list of preferences and the preference enforcement rules make a big difference. In fact, they explain the counter-intuitive answer. You’re “warm” but not quite there yet :-) If nobody gets it right, I’ll write another post with the explanation.

3. Tallys,

Nice post! Did you use this model to solve an actual problem?

In the solution returned by the solver, it seems we can’t simply exchange Tennis by Soccer because of David. He was the only one who did not take Tennis. But since he took Cook, which is his number 6 preference, nobody can’t take Soccer because it is his 4 preference.

Have you tested which would be the result if you added an additional constraint requiring at least one child to take soccer?

4. orbythebeach

Guilherme: you’re correct about David. If anyone were sent to soccer camp, David would have to go to soccer camp as well (because of the preference rules). As a consequence, the savings obtained from changing the tennis camps of the other kids to soccer camps would be more than offset by the extra expense of sending David to soccer camp. I didn’t run the test you propose, though. I haven’t used this model on an actual problem either, but it would be nice if someone did! Thank you for your comment and feliz natal!