Josh Robbins attempts to see a baseball game in all thirty major league baseball parks in 26 days.
Yes, you read that right.
And Major League Baseball doesn't make that easy. As you can guess, he has to see two games in one day four times -- but in markets with two teams (New York, Chicago, San Francisco/Oakland, Los Angeles) they try to schedule the two teams to be on the home at opposite times. That makes sense, because that way if you think "I want to see a baseball game today" you've got a good chance.
In fact, his four doubleheaders are Dodgers-Padres (which apparently was a bit of a tight squeeze, since the Dodgers went into extra innings), Yankees-Mets (that one should be easy; every few years the Mets and the Yankees play a game at one park in the afternoon and at the other park the same night; they're doing it today); Phillies-Nationals (which will be tight even if the games go the ordinary length; they start six hours apart, average game length is three hours or so, and the cities are two and a half hours apart with no traffic -- oh, and he's doing it on a Thursday); Cubs-Brewers.
My point is that 25 days might be possible -- but probably not. Most baseball games are scheduled for around 1 PM or around 7 PM, and games last three hours, to see two in one day requires the sites to be no more than three hours apart. The pairs that are doable in one day are probably:
Mets-Yankees, Mets-Phillies, Yankees-Phillies
Phillies-Orioles, Phillies-Nationals, Orioles-Nationals
Dodgers-Padres, Padres-Angels, Angels-Dodgers
White Sox-Cubs, White Sox-Brewers, Cubs-Brewers
Giants-A's
but of course one can do only one from each row, so it's only possible to double up on five days. Basically, this is the problem of looking for the largest matching in the graph that I defined above, where the edges are teams within about three hours' driving distance of each other.
(Oddly enough, each two-team market (and yes, I know, Baltimore and Washington may or may not be the same market) seems to have another team a couple hours away. In two cases that team is the Phillies. As you may know, this blog likes the Phillies.)
So 25 is theoretically possible, if the Scheduling Gods worked in one's favor -- but I'd be scared to even look at the schedules to try and figure it out. And what happens if there's a rainout?
As a problem in actually scheduling things, the other tricky part is that Denver really isn't near any other team. And Robbins' schedule had him at a 7:05 game in San Diego, followed by a 1:05 game in Denver the next day -- but Denver's a time zone to the east of San Diego, so that's seventeen hours between starts. Fourteen hours driving time. For 1,078 miles.
For some other variants of the traveling salesman problem which involve the road network, see Barry Stiefel's 50 states in a week's vacation (driving, with flights to Alaska and Hawaii) and 21 states in one day. The last one cheats a bit -- it's a 26-hour day, since he started in the Eastern time zone during daylight savings time (GMT-4), and did the trip on a day when we went back to standard time (GMT-5) and then crossed into the Central time zone (GMT-6). The difference here is that you only have to enter each state instead of reaching a point.
Oh, and I feel obliged to point out that I find the meme of going on a long road trip this summer because "this is the last summer it'll ever be possible" kind of stupid. (Not that anybody here brought it up.)
Edited (Saturday morning): Google Maps says Cleveland to Detroit can be driven in 2:46. I didn't realize they were that close together. They'd be even closer if someone built a bridge across Lake Erie.
(Saturday afternoon): Cleveland to Pittsburgh in 2:18. I'll admit the reason I forgot this one is that mentally I think of Pittsburgh as being in the same state as me and Cleveland as not being in it, so they must be far apart. This is despite the fact that I live about five miles from New Jersey.
Anyway, you could shave off yet another day by combining the Indians with either the Pirates or the Tigers.
Showing posts with label optimization. Show all posts
Showing posts with label optimization. Show all posts
27 June 2008
07 February 2008
How to load airplanes faster
Optimal boarding method for airline passengers (arXiv:0802.0733), by Jason Steffen. Via Cosmic Variance. Apparently Steffen is a physicist who was sufficiently annoyed while boarding airplanes to start thinking there has to be a better way.
The conventional method (boarding from back to front), although it looks efficient from the point of view of someone in the airport, is quite bad; Steffen describes it as the second worst method, after the obviously bad front-to-back boarding If you stop to think about it you realize that the real sticking point is not getting onto the plane, but loading luggage into the overhead compartment. So the trick is something to parallelize by, say, boarding all window seats first, then all middle seats, then all aisle seats. Heuristically, you'd expect a speedup factor on the order of the number of people sharing each overhead compartment. This isn't exactly Steffen's method -- his simulations show that it's best to divide the people on the plane into four groups, which correspond to people in even- or odd-numbered rows on the left and right sides, and board each group in turn -- but his simulations as far as I can tell treat the entire plane as one long row. Still, either of these makes you realize that there's work to be done.)
Plus, if you board people so that the people loading their luggage at the same time aren't on top of each other, then you get less people hitting each other with their bags. Everybody wins! Except perhaps the people in the aisle seat, in my scheme -- since they get to load their bags last, and people try to get some pretty big carry-ons on planes these days, there might not be room in the overhead compartment for them. But that's got to happen to somebody.
The conventional method (boarding from back to front), although it looks efficient from the point of view of someone in the airport, is quite bad; Steffen describes it as the second worst method, after the obviously bad front-to-back boarding If you stop to think about it you realize that the real sticking point is not getting onto the plane, but loading luggage into the overhead compartment. So the trick is something to parallelize by, say, boarding all window seats first, then all middle seats, then all aisle seats. Heuristically, you'd expect a speedup factor on the order of the number of people sharing each overhead compartment. This isn't exactly Steffen's method -- his simulations show that it's best to divide the people on the plane into four groups, which correspond to people in even- or odd-numbered rows on the left and right sides, and board each group in turn -- but his simulations as far as I can tell treat the entire plane as one long row. Still, either of these makes you realize that there's work to be done.)
Plus, if you board people so that the people loading their luggage at the same time aren't on top of each other, then you get less people hitting each other with their bags. Everybody wins! Except perhaps the people in the aisle seat, in my scheme -- since they get to load their bags last, and people try to get some pretty big carry-ons on planes these days, there might not be room in the overhead compartment for them. But that's got to happen to somebody.
20 June 2007
Good health is worth $631,000 a year?
Nattavudh Powdthavee claims that improving your health from "very poor" to "excellent" makes you as much happier as $631,000 extra per year would.
Does this seem reasonable to you? It doesn't to me. From what I understand, studies such as this are done by asking people to assume they are in excellent health, and then asking how much money they would accept to have (say) a 1% chance of being in very poor health. On average they say $6,310 a year. (In the case of health, it might work by looking at how much people are willing to pay for health insurance; this seems like the sort of thing the folks at Freakonomics might do, although I don't know if they've done it.) Divide by .01 and you get this $631,000 figure.
It gets even weirder when you look at it in reverse. The article claims that "Widowhood packs a psychic punch of $421,000 a year in losses". Taken literally, this means that the average widow would pay $421,000 to have her husband back for a year -- despite the fact that this is almost certainly a large multiple of her entire annual income. Maybe more than her house costs. She'd become homeless in order to have her husband back? For a year?
Or: Increasing face time with friends and relatives from "once or twice a month" to "on most days" feels like getting a $179,000 raise. That's about $500 a day. Are you saying you'd go out today to see your friends if I offered you five hundred bucks to stay in?
I suspect the problem here is that it's hard to express happiness in terms of money. Dollars are not the natural unit of happiness. If you gave me an extra $20,000 a year, I'd be happy -- that would be about a doubling of my income. If you gave the punks who hang out on the street in my neighborhood that money who have no income, they'd be even happier -- now they'd have a roof over their head! But if you gave Bill Gates that money, he wouldn't care at all. For him it's a rounding error. Some people have claimed that, say, getting a 10% raise feels the same to everybody, which seems a lot more reasonable. So what people are trying to maximize is actually the logarithm of the amount of money they have.
Note that if you choose to redistribute all the money in the world so that the sum of the logarithms of everybody's net worth (or income) is maximized, then everybody should have the same amount of money. Intuitively, if I have $30,000 and you have $10,000, then the total amount of happiness is less than if we both have $20,000; if you apply this to all pairs of people then you get this flat distribution. I leave critiquing this argument as an exercise for the reader.
Does this seem reasonable to you? It doesn't to me. From what I understand, studies such as this are done by asking people to assume they are in excellent health, and then asking how much money they would accept to have (say) a 1% chance of being in very poor health. On average they say $6,310 a year. (In the case of health, it might work by looking at how much people are willing to pay for health insurance; this seems like the sort of thing the folks at Freakonomics might do, although I don't know if they've done it.) Divide by .01 and you get this $631,000 figure.
It gets even weirder when you look at it in reverse. The article claims that "Widowhood packs a psychic punch of $421,000 a year in losses". Taken literally, this means that the average widow would pay $421,000 to have her husband back for a year -- despite the fact that this is almost certainly a large multiple of her entire annual income. Maybe more than her house costs. She'd become homeless in order to have her husband back? For a year?
Or: Increasing face time with friends and relatives from "once or twice a month" to "on most days" feels like getting a $179,000 raise. That's about $500 a day. Are you saying you'd go out today to see your friends if I offered you five hundred bucks to stay in?
I suspect the problem here is that it's hard to express happiness in terms of money. Dollars are not the natural unit of happiness. If you gave me an extra $20,000 a year, I'd be happy -- that would be about a doubling of my income. If you gave the punks who hang out on the street in my neighborhood that money who have no income, they'd be even happier -- now they'd have a roof over their head! But if you gave Bill Gates that money, he wouldn't care at all. For him it's a rounding error. Some people have claimed that, say, getting a 10% raise feels the same to everybody, which seems a lot more reasonable. So what people are trying to maximize is actually the logarithm of the amount of money they have.
Note that if you choose to redistribute all the money in the world so that the sum of the logarithms of everybody's net worth (or income) is maximized, then everybody should have the same amount of money. Intuitively, if I have $30,000 and you have $10,000, then the total amount of happiness is less than if we both have $20,000; if you apply this to all pairs of people then you get this flat distribution. I leave critiquing this argument as an exercise for the reader.
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