OK, so I've forgotten too much math...

[Aglifter]

Say, mostly for grins and giggles, as we're not that complicated, I want an equation to determine the most efficient location for a distribution system.

Some locations need regular deliveries, and a more steady basis, others have periods of much more frequent deliveries, but only during a certain time period.

The overall volume may be assumed to be the same, for all locations.

Currently, lets say distribution is along a line, for all intents and purposes.

If this is too simple, then we could start assigning costs, aside from mere distance, to certain directions, and go 3D, but I think the easiest way to deal w. that would just treat the increased cost as a factor which increases distance.

[BobbyK]

You're trying to ID the best location for your distribution center, while optimizing for delivery time constraints, and minimizing the number of trucks on the road at the same time?

[MarkD]

It's a network. You've got a series of fixed nodes (the locations you need to deliver to) and you're trying to find the ideal location for a new node that can connect to all nodes within a certain number of steps (determined by the capacity of the truck and the amount of each delivery, i.e. how many places can one truck deliver to?). Each connection has a weight (not necessarily just distance, five miles across a city will "cost" you more than fifteen down the highway). You then optimize getting to all nodes with the smallest costs.

You do realize, don't you, that as soon as you find the ideal distribution center you'll add new delivery sites that will blow the whole thing, right?

[Aglifter]

Sounds right I think - we have a periodic delivery rate over most of the year to certain customers, and a high frequency, unpredictable but compressed rate to 3 others

I "know" the right answer, currently, as I also have to calculate where I want to live, but I was trying to think of a way to derive the location via an equation.

Thinking the factors have to be some combination of distance time and cost - may be as simple as hours of operation; frequency of delivery - so again, how many hours of delivery per something or other; criticality of delivery; operating costs -labor, fuel, taxation, etc; and probably some more

[MarkD]

Your primary factor is probably time. You're paying your driver the same amount if he spends two hours at 30 mph or two hours at 60 mph, and probably not burning a whole lot more fuel in the latter.

Finding a "most efficient" network is hard though, and probably not worth the bother over finding a "reasonably efficient" network for a couple reasons:

1) That most efficient network goes out the window when you add new nodes, so you either turn down business, move, or deal with a reasonably efficient network.

2) Even with the same nodes, things change. What happens when there's road work, and the road you're counting on is closed/reduced speed?

So IMHO you're better off finding a site that's fairly centrally located to your highest-volume, and take other things into consideration like where you want to live, security, availability of labor, building/utility costs, etc.

Just my nickel's worth of free advice, guaranteed to be worth what you paid for it.

[oilcrash]

yay traveling salesman problem!

[PawPaw]

When I was in B-school (early 1980s), we didn't use a lot of math in transportation models, except route measuring and predictive modeling. However, your question prompted me to Google around a bit, and evidently we've progressed some in transportation analysis.

There's a .pdf here from the Univ of Mass that should be able to help you with the mathematics. Good luck with that, because I see calculus, and I was never any good at calc. (My brain revolts when we're talking about imaginary numbers.)

[MarkD]

yay traveling salesman problem!

Yeah, but a bit more complex, multiple travelling salesmen who shouldn't visit the same cities (although they may for large deliveries), plus the requirement that each truck can only hold so much product so it has to return to base to get more before completing the rounds.

It's not a trivial problem even for a static network, which this isn't.

[blackeagle603]

achhhh, shades of Ops Research word problems...


It's going to be a dynamic problem since demand and market expand and contract. Maybe focus on the pull signals from the market, and on improving your visibility to pull signals + improving ability to respond to them.

Simple as possible model may be the way to go. Emphasize flexibility to allow changing your response/routes/frequency of delivery based on pull signals from the market.

Think Kanban paradigm across a larger playing field.

[Weetabix]

Really quick and dirty approach: Go to Google Earth or something and get the lat and long for each delivery location. Put the lat and long of each delivery for a given time period in a spreadsheet. Average the lats & longs and plot it.

This ignores all of the time issues the other guys are talking about, but it's quick. You have to remember, though, that you're entering in your spreadsheet each delivery rather than each location. So if one location has 10 deliveries in that time period, it gets entered 10 times. A location with one delivery gets one entry. It's like a center of gravity calculation.

Like I said, easy but dirty.

You could weight the slower ones a bit by adding a few more entries for it. Say two locations are the about the same except you know that one takes longer. Give it a 1.2 weighting or something.