Why do I get non integer results from MILP problem ?

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omar khater
omar khater 2019-10-19
I have a script for diet linear programming problem. I am trying to compare results of linearprog or(intlinprog) with results of cplexlp(or cplexmilp) functions provided by toolbox CPLEX for matlab by IBM
here is the script
%% Defining Variables
clear;clc
Pnames = ["BEEF";
"CHK";
"FISH";
"HAM";
"MCH";
"MTL";
"SPG";
"TUR" ];
Packs = optimvar('Packs',Pnames,'Type','integer');
Packs.LowerBound = 2*ones(length(Pnames),1);
Packs.UpperBound = 10*ones(length(Pnames),1);
%% Setting the problem data
CostPerPack = [3.19;2.59;2.29;2.89;1.89;1.99;1.99;2.49];
VitA = [60;8;8;40;15;70;25;60];
VitC = [20;0;10;40;35;30;50;20];
VitB1 = [10;20;15;35;15;15;25;15];
VitB2 = [15;20;10;10;15;15;15;10];
NA = [938;2180;945;278;1182;896;1329;1397];
CAL = [295;770;440;430;315;400;370;450];
% Amount Per package table
TAMT = table(VitA,VitC,VitB1,VitB2,NA,CAL,...
'VariableNames',{'A','C','B1','B2','NA','CAL'},...
'RowNames',Pnames);
%% Objective
TotCost = sum(CostPerPack .* Packs); % Objective
obj = TotCost;
%% Constraints
prob = optimproblem('Objective',obj,'ObjectiveSense','min');
prob.Constraints.c1 = sum(VitA.*Packs) >= 700;
prob.Constraints.c1a = sum(VitA.*Packs) <= 20000;
prob.Constraints.c2 = sum(VitC.*Packs) >= 700;
prob.Constraints.c2a = sum(VitC.*Packs) <= 20000;
prob.Constraints.c3 = sum(VitB1.*Packs) >= 700;
prob.Constraints.c3a = sum(VitB1.*Packs) <= 20000;
prob.Constraints.c4 = sum(VitB2.*Packs) >= 700;
prob.Constraints.c4a = sum(VitB2.*Packs) <= 20000;
prob.Constraints.c5 = sum(NA.*Packs) >= 0;
prob.Constraints.c5a = sum(NA.*Packs) <= 40000;
prob.Constraints.c5 = sum(CAL.*Packs) >= 16000;
prob.Constraints.c5a = sum(CAL.*Packs) <= 24000;
%% Putting the problem together and solving
problem = prob2struct(prob);
% LP
% [sol,fval,exitflag,output1] = linprog(problem);
% [sol2,fval2,exitflag2,output2] = cplexlp(problem);
% MILP problem
[sol,fval,exitflag,output1] = intlinprog(problem);
[sol2,fval2,exitflag2,output2] =cplexmilp(problem);
%% Display
disp('Linear Prog function results')
if (~isempty(sol) )
T1 = table(sol,sol.*VitA,sol.*VitC,sol.*VitB1,sol.*VitB2,sol.*NA,sol.*CAL,sol.*CostPerPack,...
'VariableNames',{'NuofPacks','PerVitA','PerVitC','PerVitB1','PerVitB2','NA','CAL','Cost'},...
'RowNames',Pnames);
sumrow = array2table(sum(T1.Variables),...
'VariableNames',...
{'NuofPacks','PerVitA','PerVitC','PerVitB1','PerVitB2','NA','CAL','Cost'},...
'RowNames',"Sum");
T1 = [T1;sumrow];
disp(T1)
else
disp(['No feasible Solution with exit flag = ' ,num2str(exitflag)])
end
%% Display Cplex
disp('Cplex function results')
if (~isempty(sol2) )
T2 = table(sol2,sol2.*VitA,sol2.*VitC,sol2.*VitB1,sol2.*VitB2,sol2.*NA,sol2.*CAL,sol2.*CostPerPack,...
'VariableNames',{'NuofPacks','PerVitA','PerVitC','PerVitB1','PerVitB2','NA','CAL','Cost'},...
'RowNames',Pnames);
sumrow2 = array2table(sum(T2.Variables),...
'VariableNames',...
{'NuofPacks','PerVitA','PerVitC','PerVitB1','PerVitB2','NA','CAL','Cost'},...
'RowNames',"Sum");
T2 = [T2;sumrow2];
disp(T2)
else
disp(['No feasible Solution with exit flag = ' ,num2str(exitflag2)])
end
and here is the results
intlinprog.JPG
cplexmilp.jpg
The reults for this MILP from intlinprog seems good but from cplexmilp I get non-ineger value for SPG package.
Can anyone help me to know the problem here ?
Thanks in advance

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