A problem with Linear Programming Problems

Hi everyone, I need a guidance on a problem with linprog. I have an optimization problem that weights and the minimum value of the objective function are needed, but I can't allocate the parameters properly. The form of problem and subjects are like this. The picture of the problem is attached.

Any help regarding understanding the problem and getting a solution would be much appreciated.

P.S.: The object here is to code BWM(Best Worst Method) By Dr. Jafar Rezaei in matlab.

Ws and Ksi are the optimal weights and objective function we want to obtain and As are the vector that its values are present.

[Torsten]

In the first constraint, w_j appears in the denominator. Thus it seems your problem is not linear. Or is it simply an error in notation ?

[Mostafa Eftekhary Mamaghani]

Yes, you are right, I forgot to include the other form, you can change the form of the formula.

[Torsten]

You forgot to multiply Xi_L with w_j in the first inequality. This makes the problem nonlinear since Xi_L itself is a solution variable.

Answer 1

[Ali Naeemah]

Please kindly gentlemen, can you highlight the parts that can be changed with my values, please because I am confused about what values I have to change exactly.

[Ali Naeemah]

Hello sir

Please kindly,

Can you highlight or identify the place that I have to insert my values, please? I am confused about where I have to insert my values exactly in the code.

Thank you so much

Answer 2

[Matt J]

It should be straightforward to cast this into the form of linear in/equalities, once you recognize that

|P|<=q

is equivalent to the simultaneous constraints

   p-q<=0
  -p-q<=0

Answer 3

[Mostafa Eftekhary Mamaghani]

Here is the code to BMW(Best-Worst Method) in matlab.

clc;clear;close all;

delete Data.mat
DATA = xlsread("Data.xlsx");

NumOfExperts        = size(DATA , 1) / 2;
NumOfCriteria       = size(DATA , 2);
BestData            = DATA( 1:NumOfExperts , : );
WorstData           = DATA( NumOfExperts + 1: end , :);
WorstData           = WorstData';
ConsistencyIndex  = [0 , .44 , 1 , 1.63 , 2.3 ,3 , 3.73 , 4.47 , 5.23];

DATA = struct;

for i = 1:NumOfExperts

      IndexOfBest     = find(BestData(i , :) == 0);
      IndexOfWorst  = find(WorstData(: , i) == 0);

      BestData(i , IndexOfBest)  = 1;
      WorstData(IndexOfWorst , i)  = 1;

      DATA(i).Best        = BestData(i , :);
    DATA(i).Worst       = WorstData(: , i);
      DATA(i).BestIndex  = IndexOfBest;
      DATA(i).WorstIndex  = IndexOfWorst;   

end
clear BestData .. WorstData .. IndexOfBest .. IndexOfWorst;

MeanWeight = zeros(1 , NumOfCriteria);
for i = 1:NumOfExperts
    Data = DATA(i);
    save Data

      EqualCoefftMat  = ones(1 , NumOfCriteria);
      InitialPoints  = rand(1 , NumOfCriteria);
      LowerBound = zeros(1 , NumOfCriteria);
      UpperBound = ones(1 , NumOfCriteria);
      options = optimoptions(@fmincon , 'Algorithm' , 'interior-point' , 'MaxFunctionEvaluations' , 50000 , 'MaxIterations' , 5000 );

      [DATA(i).Weights , DATA(i).Ksi] = fmincon(@Epsilon , InitialPoints , [] , [] , EqualCoefftMat , 1 , LowerBound , UpperBound , [],  options);

      DATA(i).ConsistencyRatio = DATA(i).Ksi/ConsistencyIndex(max(max(DATA(i).Best) , max(DATA(i).Worst)));
      MeanWeight = MeanWeight + DATA(i).Weights; 
  end

MeanWeight = MeanWeight/NumOfExperts;
bar(MeanWeight);
xlabel('Criterias');
ylabel('Weights');
title(['Mean Of Weights is: ', num2str(mean(MeanWeight))]);

[Result.Weights , Result.IndexOfWeight] = sort(MeanWeight , 'descend');

function Out = Epsilon(x)
    load Data

      for i = 1:NumOfCriteria
          f(i) = abs(x(Data.BestIndex)/x(i) - Data.Best(i));
          g(i) = abs(x(i)/x(Data.WorstIndex) - Data.Worst(i));
      end
      Out = (sum(f) + sum(g) - g(Data.BestIndex))*2/NumOfCriteria;
  end

[Torsten]

You implemented an optimization problem, but it's not the one you presented above.

[Mostafa Eftekhary Mamaghani]

Yes, you're right. I had a problem understanding the procedure. At first, I wanted to implement it in linear-programming but I couldn't do it with this problem, so changed it to nonlinear form and it worked.

[Torsten]

But you are aware that you can also implement your original problem in "fmincon", aren't you ?

[Mostafa Eftekhary Mamaghani]

Yes, I know. I wanted to implement it in linprog(as requested by my friend whom this code is for her research) but couldn't do it with the parameters was presented or at least I couldn't form the objective function based on linear programming.

[JAIRAM RAIGAR]

Can you tell me what is in data which is read from excel file ???

[Mostafa Eftekhary Mamaghani]

Sorry for delay

It was an aggregation of questionnaires filled by experts with a fixed amount of criteria. Each criterion gets the normalized amount between 1 to 9 based on the significance of that criterion in the respective phase of the method("best" or "worst").

[Soheil sadeghi]

Is it possible to upload an Excel file as well?

Because it seems that in the Excel file associated with this code, a set of cells are named.