how to solve this linear program with objective function variable in time
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hi everybody I'm an italian student and I have a question about this problem. I have this objective function: min ∑t pv (x1 + x2) - ∑t ps (x3+x4) where t is a discrete variable from 0 to 24 with 1hour step; x are my variables and pv & ps are 2 parameters changing during 24 hours (I have 24 value for each one)
my constraints are formulated in this way: x1 + x5 <= cp;
x6 + x7 + x2 = dm ;
and others 3 similar. cp and dm are also variable in 24 hours. totally I have 8 variables. Furthermore 1 of this 8 variables is continue during 24 hourse instead other 7 are discrete. for this continue variable I have the law:
x8(t) - x8 (t-1) = 0.85 (x5 + x1) - 1/0.85 (x7+x4).
My answer is...how I can solve this problem?? I want optimal value of my 8 variables in each hour..so I need a result matrix [24*8] . Do I have to use simulink? help me!! thank you and I'm sorry for my non-perfect english! bye
回答（2 个）
Alan Weiss
2013-5-30
I believe you can formulate this problem without time, but with more variables, something along the following lines:
z(1) = x1(1); % x1 at time 1
z(2) = x2(1); % x2 at time 1
...
z(8) = x8(1);
z(9) = x1(2); % x1 at time 2
z(10) = x2(2);
...
z(8*24) = x8(24);
Now you have all your variables defined in terms of one long vector z. Express your constraints in terms of the vector z and you are done.
Alan Weiss
MATLAB mathematical toolbox documentation
You can use LINPROG to solve for x1...x7 if you have the optimization toolbox. When you do so, you would ignore x(8) and the equation
x8(t) - x8 (t-1) = 0.85 (x5 + x1) - 1/0.85 (x7+x4).
The right hand side of the above will become known, once you've solved the other variables and constraints using LINPROG. The equation for x(8) then reduces to a first order difference equation, which you can solve with appropriate initial conditions.
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