im using proc netflow to minimize the cost of transferring water from the source to the consumers.
example: i have 1 source passing through 3 connections to 3 consumers. with a supply of 1000 cubic meters and demand of 300 cubic meters for each consumer. Each connection is subject to a water loss with coefficient of 3%.
supply to connection1
supply to connection2
supply to connection3
connection1 to consumer1
connection1 to consumer2
connection3 to consumer2
connection3 to consumer3
how can i code the water loss constraint? like if you will deliver 100 cubic meter of water going through connection1 then you can just supply 97 cubic meter of water..how can you incorporate this in the optimization?
Since I am not that familliar with PROC NETFLOW I will just keep my comments to methods to deal with this in the traditional NA method.
If your network is simple enough, which it sounds like it maybe [i.e. every path experiences the same loss rate] then you can "Gross Up" your demand [i.e. if you know each and every path is going to have a 3% loss and your demand is 100 then adjust your demands to [100/0.97]=103.0928
However, a more robust way to do it is to have each path have a dummy sink which is constrained to demand loss from the main connection, this way it doesn't matter if the rates are diffferent. The idea being each real line flows to two sinks, 97% to the real one [consumer] and 3% to the virtual one [loss]