Start today in Kansas City … and drive over 18K miles over the next 35 days and you can see a baseball game in every major league ballpark. With no doubleheaders!
How does one figure this out? Linear programming — the old standard of management science.
This is an example of a network programming problem, as in Chapter 12 of the Powell and Baker MBA
text.
The decisions form an array: 30 ballparks against some number of days (larger than the likely minimum number).
The objective is probably to minimize the number of days (although it could be driving miles too).
The constraints are that 1) each park is visited one time, 2) there is a game at the park that day, 3) on each day there is at most one game to be seen, 4) drive time between games must be possible in 12 hour stints with 8 hours off in between (there’s no mention of the highway speed assumed).
The article from the June 3 issue of The Wall Street Journal says:
… Blatt plugged the schedule for each team into his model, while setting one key parameter: For every 12 hours of estimated driving between ballparks, the system must allow for eight hours of rest, ensuring that the road trip is, at least in theory, humanly possible.
If you think about it, there are probably a lot of ways to get to 30 parks in 30 days. But most of those would be pointless ones, involving trips from NYC to LA to Philly to Seattle on consecutive days, and so on.
That “key parameter” is what makes the trip “humanly possible” by car, because it gives you 45 hours to do the longest trip (1,530 miles) from Houston to LA, 39 hours to do the 1,330 from Seattle to Colorado, and 27 hours to do the 1,047 miles from Colorado to Milwaukee — and you only get one break on that last one. After that, the rest look ease.