Need help for solving an Optimization problem

I have written a code for my problem My problem is Min L

Subject to:

0 ≤ Qt ≤ Qm

St = St-1 + It - Qt

Sd ≤ St ≤ Sm

Qt ≤ L

%Read the excel file containing time series inflow data
data = xlsread('Reservoir.xlsx');
t = data(:,1); % days
I(:,1) = data(:,2); % m^3
T = data(end,1); % days
S_0 = data(1,5); % m^3
S_d = data(2,5); % m^3
S_m = data(3,5); % m^3
Q_m = data(4,5); % m^3
L = optimvar('L',1,'LowerBound',0,'UpperBound',Q_m);
Q = optimvar('Q',T,'LowerBound',0,'UpperBound',Q_m);
S = optimvar('L',T,'LowerBound',S_d,'UpperBound',S_m);
waterbalance = optimconstr(T,1);
for t = 1:T
    if t == 1
        storage = S_0;
    else
        storage = S(t-1);
    end
    waterbalance(t) = S(t) == storage + I(t) - Q(t);
end
discharge = optimconstr(T,1);
for t= 1:T
  discharge(t) = Q(t)<=L;
end
prob.Constraints.waterbalance = waterbalance;
prob.Constraints.discharge = discharge;
prob = optimproblem;
prob.Objective = L;
sol = solve(prob)

I need the minimized value for L. But i am getting answer as 0. Please help me.

[Guillaume]

I've closed your other duplicate of this question as this one describes the problem better.

[Torsten]

Please include your optimization problem in the usual mathematical notation.

[Torsten]

I always use "linprog" to solve this kind of problems.

[VISHNUPRIYA M S]

Can you please tell me how to use "linprog" here?

Answer 1

[Torsten]

- Take L, Qt, St as variables to be solved for.

- Define upper bounds ub and lower bounds lb to account for

0 ≤ Qt ≤ Qm

Sd ≤ St ≤ Sm

- Define matrix Aeq and vector beq to account for

St - St-1 + Qt = It

- Define matrix A and vector b to account for

Qt -  L ≤ 0

- Define the vector f as (1,0,0,...,0).

- Call linprog.

Best wishes

Torsten.