Predicitng the unpredictable?

[litrelord]

OK, so I'm unashamedly asking for help with my work here.

We deal with people'e cars breaking down and have done for years. Problem is where you put the people who go and fix them. At the moment we have a load of people out on the road ready to go and solve their problems and the places where we put these guys is based on where the breakdowns have happened previously.

I worry that the way we're looking at this isn't very scientific at all and I know it could be greatly improved upon. Unfortunately there's only me and a couple of other people in the company who deal with stats of any kind and the people who ultimately choose where they should be positioned are the guys who used to work out on the road.

Not to belittle their experiences but things change quickly and I'd like a way to better predict where people may break down.

Does anyone here have any experience with similar types of problems (not just breakdowns but things which would follow the same kind of mathematic rules) that could suggest any tools that may be useful in prediction?

Not asking for you to solve our problems, but if you could point me in the direction of something that may help I'd be grateful.

Thanks

Nick

P.S. whilst I like my job I'm afraid I don't like it enough to embark on a 4 year course of higher mathematics at the moment. Although obviously that would be the best way for me to learn how to predict things better I wouldn't then stay doing this job!

 

[Oaktree]

Hi, Nick.

What type of data is available to you? (cars/hour for some intersections, etc.)

In theory, at least, the cars passing through a certain intersection (and subsequently, the number of collisions) should follow a Poisson distribution...

 

[Greg Truby]

In thinking about it, there are so many variables that could impact the "density of breakdowns", that historical frequency data may well be one of the best tools you've got for predicting future frequency. You can't go just by the # of cars alone. The economics of the car owners is going to be a major factor; older cars are going to break down a lot more than newer cars. Traffic flow is also key; stop and go traffic or places where you're stuck idling for long periods of time can be hard on cars with older cooling systems. You should see a correlation between the weather too. I've had older cars that did fine up to about 100°-105°; but once the mercury topped 105° or so I knew better than to take some routes because if I were to get stuck in heavy traffic I knew I was gonna overheat. Does a traffic accident mean you send more cars to a particular area (more cars are jammed and idling and overheating?) or less (most drivers are re-routing around the wreck so you have fewer breakdown?) Again, I'd think you'd need to look at actual data to see if you can pick up on a correlation.

Just my 2¢-worth...

 

[Richard Schollar]

You should see a correlation between the weather too. I've had older cars that did fine up to about 100°-105°; but once the mercury topped 105° or so I knew better than to take some routes because if I were to get stuck in heavy traffic I knew I was gonna overheat.
~G Truby

Greg, note that LitreLord is a Brit - the cars (and people!) are designed for cooler weather, so if it ever got to 105° here, they'd have all melted and be pools of molten metal/rubber...

 

[Andrew Fergus]

Hi Nick

That's an interesting question. You won't be able to build a model to accurately predict the time, place and type of breakdowns but, as Greg mentioned, I suspect your best bet will be to look at whatever data you already have and analyse that. Previous performance / statistics do not provide any guarantees of future performance but they can be a good indicator of trends, e.g. time of day, weather, location (suburb / city and work / home / on road) and demographics etc. - for example you know that between 7am and 9am on cold mornings you will have an above average call-out rate for flat batteries in the suburbs. I'd probably put a wager on that one.....

If the goal is to minimise waiting time for the motorist (or travelling time and fuel for the mechanic) then my guess is that if idle mechanics / technicians were routed to a central or a specific place (instead of simply waiting where they are after the last call-out) then 50% of the time it would result in an increased travelling time to their next job and 50% of the time it would be less (unless the last breakdown was in a rural area). Sometimes doing nothing is the best option - given travelling times and costs you definitely don't want all of your technicians coming back to base to wait for their next job (assuming the labour cost is already spent).

I suppose your requirements aren't too different to those of a taxi scheduler and what do the taxis do when they are idle? They generally sit and wait (well they do here) in the most popular spots.

Another angle - if you have stats on which technicians are not busy or x% utilised, then you know where NOT to send them!

Just my thoughts...

Andrew

 

[litrelord]

Thanks people. Some very interesting points. Almost all of the cars are new (up to 3 years old) so it's really mechanical or electrical failures that we're dealing with. It's true that over-heating isn't too much of a problem!

At the moment we base our assumptions on trends from the previous years, sometimes it works and sometimes it doesn't. Unfortunately our data warehouse doesn't hold vehicle location data for our technicians which is irritating as it makes analysis on driving lengths very difficult.

I think I'll have to find a way to break down the country into smaller chunks than we currently use which is only about sections. Postcodes are out as most people, unless at home, don't have a postcode for the breakdown location. We have an OS grid reference for the assistance so I think I'll try looking at how they're made and hopefully I'll be able to extract each part of the grid reference and write a formula to allocate that assistance to one of the areas I've decided on.

Thanks again for the input. As always, this site and the people on it prove to be invaluable.

Nick

 

[gingerafro]

As mentioned before, the ideal position to place a technician is a mixture of experience and maths.

Andrews point on taxi drivers is very interesting. If I were a one man taxi driver, I would wait in the most popular places (stations, nightclubs etc) so I could be hailed. I might get (say) 30 fares that way. However there is a chance that in a suburb, there might be 50 people needing a taxi, but they would come 100yards outside their haouse to look for one even though that would be the best place for me. Anyway, a slight digression.

If you have the OS reference of the breakdown, then you should be able to use a simple bit of pythagoras to calculate the distance (as the crow flies) from any point in the country. With all things being equal, this probably isn't as bad as it sounds.

You would then make some assumptions like:
I want to place a technician at a point that is within 10 miles of a likely breakdown
How confident am I that there will be a breakdown

You could then use the standard deviation / confidence functions to work out the best places to be...

I think my theory is right. Any second opinions?