Well this might be a shot in the dark but perhaps someone can help. I have to draw the network representation of the following network flow problem.
MIN (7X12+6X14+3X23+4X24+5X32+9X43+8X52+5X54...
Subject to:
X12 +X14 = 5
X12 + X52 +X32-X24-X23=4
X23+X43-X32=8
X24+X14+X54-X43=0
X52+X54=7
I understand the objective function and how to draw it. For example 7X12 means it takes 7 units from node 1 to node 2. However I don't understand how you include the constraints. I assume it's with regards to demand/supply but I don't really understand it. So what is the logic behind those constraints? What do they mean and how would you draw them? Any help would be appreciated.
Network flow problem ... drawing network representation given the following data.?
The nodes in this problem can represent cities and the decision variables Xij represent the amount of product you are going to ship from city i to city j.
The objective function coefficients represent costs. For example, the 7X12 term means it costs $7 to ship a unit from city 1 to city 2. The objective is to minimize total shipping costs.
The constraints represent the fact that some cities have excess product and want to get rid of some of it while other cities don't have enough product and are demanding more of it. For example, the X12 + X14 = 5 constraint means that city 1 needs to get rid of 5 units of product, and the only way it can do this is by sending product out to cities 2 and 4 (I suppose there are only two roads heading out of city 1). The second constraint says that the flow into city 2 minus the flow out of city 2 must be 4, so city 2 must be demanding 4 units of product. The third constraint says that the flow into city 3 minus the flow out of city 3 must equal 8, so city 3 must be demanding 8 units. City 4 doesn't need any units, and city 5 is trying to get rid of 7 units.
Reply:Have you tried your local library, a book will be able to give you a far better answer with diagrams etc than we can give you on here.
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