Hello Everyone,

Below is the outline of a river basin optimization model which i used to allocates water among different nodes of network for maximum total benefit. this model is working fine…

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Set t time in months /t1*t12/
n nodes /n1*n20/ (supply, demand and junction nodes)

Alias(n,n1);

Set n_f_n(n,n1) node n receives water from node n1

Set n_t_n(n,n1) node n diverts water to node n1(consumption)

Parameter Losscoff(n,n1)

Demand(n,t) water requirement(only for demand nodes)

beg_S(n)

Ret(n,t) Return flow coefficient

depthreq(n,t) depth required

Inriv(n,t)

yrf(n,t);

Positive Variable

Divert(n,t) water diverted to various demand nodes

Q(n,t) Inflows

R(n,t) Releases

S(n,t) Storages

Variable o objective function;

Equations

mass balance at nodes (inflow =outflow + diverted water)

net benefit function by water consumption at different nodes.

objective maximum total benefit

model maximumbenefit /all/;

solve maximumbenefit maximizing o using nlp.

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But I need to extend it further. I want to calculate net benefit could be gained by all the possible coalitions (2^(n)-1) of nodes. Something like…

Set n nodes /A,B,C,D/

t time /1*12/

Parameter W(n,t) water available according to rights for different nodes.

Equation.

eq1…net benefit function for A

eq2…net benefit function for B

eq4…net benefit function for D

eq3…net benefit function for C

I need to calculate the optimized net benefit of all possible combinations of sharing of water among nodes . First when they act alone(A,B,C,D), then combination of two(AB,BC,AC,…) then three and then combination of four (total (2^(n)-1) ). so there would be (2^(n)-1) maximum benefits.

Please if anyone can suggest something. Thanks in advance.

Aditya Chaudhary

Student

M.Tech (Water Resources Engineering)

NIT Karnataka, India

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