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Simple example modelling

Posted: Tue Apr 07, 2020 11:01 pm
by dobrica3
Dear GAMS experts,

I appeal to your kindness and goodwill to help a novice in GAMS modelling.
I'm stuggling with simple optimization problem.

I will describe the context:
Let assume that a garden needs 4277 litres of irrigation water in a day. There are three pipes that feed the garden: pipe1, pipe2 and pipe3.
Pipe1 feeds - 44% or 1882 litres
Pipe2 feeds - 31% or 1325 litres
Pipe3 feeds - 24% or 1026 litres
Each pipe is connected to several mini water collecting rezervoirs, such as:
Pipe1 has 920 rezervoirs
Pipe2 has 703 rezervoirs
Pipe3 has 317 rezervoirs
Simple calculations show the following parameters:
Pipe1 collects about 2.045 litres from each rezervoir
Pipe2 collects about 1.88 litres from each rezervoir
Pipe3 collects about 3.23 litres from each rezervoir. These can be interpreted as parameters:
Pipe1 2.045
Pipe2 1.88
Pipe3 3.23

My problem is how to model this simple example in order to optimize the number of rezervoirs by giving a total volume of water as constraint.
Let say that in a day we need 2352 litres of water in that pool or about 55%.

I've tried to set the exogenous variables, by setting values, positive variables, constraints but to no avail. My problem is how to construct the equations so that GAMS minimizes x number of rezervoirs per pipe using the above mentioned parameters in order to provide a volume of 2352 litres of water in total.

Many thanks in advance.