Real life-and-death issue that requires a mathematical solution | Hacker News Reader

Real life-and-death issue that requires a mathematical solution

math.stackexchange.com

9 pointslaurencei5 comments

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. :-)

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

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...

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).

"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).

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