

Real life-and-death issue that requires a mathematical solution - laurencei
http://math.stackexchange.com/questions/232220/real-life-death-issue-that-requires-a-mathematical-solution

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EvaPeron
Cool problem. I LOVE optimization problems like this, lol. A good "start up"
kind of idea too. Scheduling ambulances. Requires not just optimizing for
streets, etc., but for time, times of night there are more calls, etc.
Requires forecasting, historical data, and so on. Really a very cool problem.
In a nutshell, you need a probablistic model of what times have more calls,
and where these are likely to come from, and spread out your buses
accordingly. Perfect for machine learning solutions. You could have a neural
net to give you your probablistic model, then some kind of cost-based
heuristic to make decisions based upon the model and real-time data. The
coolest problems are the ones with no one right answer, but with "better" and
"worse" answers, because, well, they are just more fun, lol. Contact me at
FrankErdman2000 AT yahoo dot com if you want to discuss more - I can't get
into too many details on a public forum due to things like NDA etc. :-) Put
bus scheduling or something in subject line. Seriously though, thanks for this
post. Anything to prevent boredom. :-)

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laurencei
Thanks - I'll contact you to discuss more :)

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laurencei
I'm the author of the stack exchange post. I work as a paramedic, but I do
start ups as my weekend work. I was lying awake at 3am this morning at work
trying to solve this issue.

I know there has to be a better way - but I need to be able to 'prove' it...

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saurik
Is this truly a math problem (in which case, that's fine), or is this a
serious interest in industrial engineering problem of optimal ambulance
allocation? I am presuming it is the former, given the specific Stack Exchange
family site it was posted to, but there seems to be a bunch of evidence that
it could be the latter.

If it is, it honestly seems weird to me that you so rapidly discount the more
obvious answers without attempting to first prove them out of the way (as one
would insist from a mathematical analysis of the situation).

As an example: you point out that sometimes you get another call while
ambulance A is moving to the former position of C, but do not weight that
against the probability that no call will come subsequent to the previous call
in the vicinity of C.

As another example: you seem to simply ignore that the real suggestion many
people are making is not to move A to C, but to redistribute _all_ the
ambulances for a new equilibrium state of "optimal coverage".

You then want to use the result to prove something about ambulance usage, but
that is somewhat disingenuous: maybe the A/B--C situation comes up rarely
enough that the probability of a call coming in that makes C a bad choice is
so low that you really should always just choose C.

Alternatively, the entire premise might be flawed: maybe ambulance A and B are
stuck in the same location (as you indicate there are any number of reasons
why just moving them might not be practical) because of external factors that
would make it infeasible to use them for this call on the other side of the
map anyway.

In essence, taking this one problem alone simply seems strange: the model
should include the speed ambulances can travel and the probability
distribution of the rate of incoming calls; from that, you can attempt to
extrapolate what the globally optimal algorithm might be (assuming there is
one, and assuming it is efficiently implementable).

~~~
laurencei
"As an example: you point out that sometimes you get another call while
ambulance A is moving to the former position of C, but do not weight that
against the probability that no call will come subsequent to the previous call
in the vicinity of C."

Yes - that is correct - but for the example given the whole idea was to keep
it simple.

Things such as "fluid deployment" (which is moving A to C's old location) is a
process that we already do. There is an attempt to redistribute ambulance
resources for optimal coverage.

But in reality, we find that, especially due to things like traffic, is the A
will never get to C's location in time, and thus we dont actually have an
optimal coverage of location in peak times.

Also - there are so many reasons why we cannot always relocate A anyway. For
example, perhaps A+B have just finished offloading patients at a hospital, or
they are at their station/depot having lunch.

"maybe the A/B--C situation comes up rarely enough that the probability of a
call coming in that makes C a bad choice is so low that you really should
always just choose C."

This might be true - certainly the frequency of the calls will be a factor. We
have one of the largest frequency of calls in the world, with an average
around 1.5 incidents every minute 24/7 (but weighted with more of those
occurring in peak times such as mid-afternoon and less at 3am in the morning).

