main code.m

%function []=solv_opt()
clear all;

n = 20; m = 10;

w = rand(1, n);
w= w./sum(w);
lambda=randi([1,5],1,n);
V = rand(m,n)/3;
for v=1:1:60
    s=v*.1;
    
    
cvx_begin quiet
variables X(m,n) C
minimize(C)
subject to
sum(X,1)<=C
sum(X,2)<=C
sum(X.*V)  == ones(1,n)*s;
X(:)>=0
cvx_end



l(v)=C;
obj=0
for u=1:n
    obj = obj + w(u)*(1-exp(-s*lambda(u)));
end

z(v)=obj;
end

for v=1:1:120
    T=v*.1;
    
    
cvx_begin quiet
variables X(m,n) p(n)
obj=0
for u=1:n
    obj = obj + w(u)*(1-exp(-p(u)*lambda(u)));
end
maximize(obj)
subject to
sum(X,1)<=1

sum(X,2)<=1
sum(X.*V,1)*T  == p'
p>=0
X(:)>=0
cvx_end



x(v)=T;
obj=0
for u=1:n
    obj = obj + w(u)*(1-exp(-p(u)*lambda(u)));
end

y(v)=obj;
end

figure;
plot(x,y,'r', 'linewidth', 5);
grid on;
hold on;
plot(l,z,'b', 'linewidth', 5);
set(gca, 'fontsize', 18)
legend('Our Algorithm','Baseline Algorithm');
axis([0 12 0 1])
xlabel('Makespan', 'fontsize', 18)
ylabel('Weighted Accuracy', 'fontsize', 18)