Question regarding linprog formulation

Dear MATLAB users,

I am trying to solve a simple linear problem without success. I have tried reading the `linprog' manual several times, and I have searched the forum finding no similar question, prior to posting here. So, there I am, stuck and asking for your help.

I have written a script to solve a linear problem -both script and problem shared with you in the following- that gives me different results to the one I tested in Excel (using Open Solver) and R accordingly. I am fairly confident that the Excel solver gives me correct results, which I also validated in R later on. Therefore, I am sure that there's something wrong with this script.

Anyway, I am trying to solve the following problem:

where, I have 8 variables ( out1, out2, out3, inp1, inp2, inp3, inp4, inp5) with 70 observations (j=1,2,....,70), and starting from observation 1 (jo=1), I want to maximize μ1*out1(jo)+μ2*οut2(jo)+μ3*out3(jo) // where μ1,μ2,μ3 varying cells, subject to ν1*inp1(jo) + ν2*inp2(jo) + ν3*inp3(jo) + ν4*inp4(jo) + ν5*inp5(jo) = 1 // where ν1,ν2,ν3,ν4,ν5 again, varying cells and subject to μ1*out1(all j=1,...,70)+μ2*οut2(all j=1,...,70)+μ3*out3(all j=1,...,70) <= ν1*inp1(all j=1,...,70) + ν2*inp2(all j=1,...,70) + ν3*inp3(all j=1,...,70) + ν4*inp4(all j=1,...,70) + ν5*inp5(all j=1,...,70) and finally, ν1,ν2,ν3,ν4,ν5,μ1,μ2,μ3 >=0.

Admittedly, this should be a straightforward easy formulation for linprog, and I have tried myself coding it, yet I get different results, so I am sure that I am stuck at some point that I cannot seem to find myself.

For your convenience, I attach the matlab file and the script, which I also quote in the following:

n=70;  
j0=1;
i = setdiff(1:n,j0);
f=[out1(j0), out2(j0), out3(j0), 0,0,0,0,0];
lb=[0 0 0 0 0 0 0 0];
ub=[inf inf inf inf inf inf inf inf];
A=[out1(:), out2(:), out3(:), -inp1(:), -inp2(:), -inp3(:), -inp4(:), -inp5(:)];
b=zeros(n,1);
Aeq=[0, 0, 0, inp1(j0),inp2(j0),inp3(j0),inp4(j0),inp5(j0)];
beq = 1;  
m = linprog(f,A,b,Aeq,beq,lb,ub);

obviously, I start with io=1, and I enclose this into a loop later on, so that I solve this problem for every observation io=1....70.

I greatly appreciate your help and time considering my question in advance!

Sincerely, M.

Answer 1

[Torsten]

f=[-out1(j0), -out2(j0), -out3(j0), 0,0,0,0,0];

Best wishes

Torsten.

[Menelaos]

Wow, I can't believe I'm THAT blind!

Dear Torsten, thank you so much for your quick response! I was busting my head to see what was wrong, but I couldn't see it. Just made sure that it checks out, thanks again!