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towr
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supply and demand
« on: Feb 11th, 2010, 5:05am » |
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Suppose you have a graph with at each node some amount of production, a limited storage, and some demand (using up goods). Goods can be moved along the edge from one node to the next each step in time.
How can you best optimize the transmission of goods along the network each step, to satisfy demand as quickly as possible?
Also bare in mind that supply and demand can change, so ideally you would want to anticipate, and be able to get goods quickly in new places if there's a sudden increase in demand.
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Grimbal
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Re: supply and demand
« Reply #1 on: Feb 11th, 2010, 5:49am » |
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Are production and demand a daily quantity?
Do you want to optimize the average time between production and delivery, or the worst delivery time?
If you want to anticipate, are production and demand now a function of time?
To find a way to satisfy the demand, I would say Ford-Fulkerson. But to optimize for minimum time, I don't know.
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towr
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Re: supply and demand
« Reply #2 on: Feb 11th, 2010, 6:42am » |
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on Feb 11th, 2010, 5:49am, Grimbal wrote:| Are production and demand a daily quantity? |
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Yes, but they don't change frequently. So they are constant in most places for long stretches of time.
Quote:| Do you want to optimize the average time between production and delivery, or the worst delivery time? |
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I guess I want to minimize the worst time till the demands are met everywhere (or until we come as close to possible, in case a bottleneck in the network prevents supplying some subgraph adequately). The idea is to get to a steady-state as quickly as possible (provided demands don't change)
The goods are a fungible non-perishable commodity, so delivery time doesn't matter, as long as demand is met.
Quote:| If you want to anticipate, are production and demand now a function of time? |
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Well, basically the problem is that some nodes may at some time in the future have a demand, and you want to be able to meet it asap.
So one simple way, if the network is fairly uniform, would be to ensure (excess) supplies are distributed uniformly around the network (storage allowing). That way you'd have some resilience to meet demand wherever it crops up. But if the network is oddly shaped it's harder to say what would work.
Hmm, I just realized that if you have a subnet where all the storage is used, you really need to funnel all excess production away asap, either to places where it will be used or to available storage, otherwise it is just wasted.
Quote:| To find a way to satisfy the demand, I would say Ford-Fulkerson. But to optimize for minimum time, I don't know. |
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I'll have a look, thanks.
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