A problem with Linear Programming Problems

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Mostafa Eftekhary Mamaghani
Commented: Ali Naeemah on 15 Oct 2021
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.
  3 Comments
Torsten
Torsten on 24 Aug 2018
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.

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Answers (3)

Matt J
Matt J on 24 Aug 2018
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

Mostafa Eftekhary Mamaghani
Edited: Mostafa Eftekhary Mamaghani on 28 Aug 2018
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
  7 Comments
Soheil sadeghi
Soheil sadeghi on 6 May 2021
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.

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Ali Naeemah
Ali Naeemah on 14 Oct 2021
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.
  1 Comment
Ali Naeemah
Ali Naeemah on 15 Oct 2021
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

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