how to solve a weighted completion time minimization problem to cplex/c++? - c++

Question

a scheduling problem that wants to minimize a weighted completion time
I would like to pass the image problem to the c++ language and solve it with cplex solver.
Problem:
Min ∑WiCi
xi ∈ 0,1
t= ∆ + ∑_{i} xi*pi1
Ci1 = ∑_{j=1}^{i} xj*pj1
Ci2 = t + ∑_{j=1}^{i} (1−xj)*pj2
Ci ≥ Ci1
Ci ≥ Ci2−Ωxi
Ω = ∆ + ∑_i max(pi1, pi2)
The goal is to minimize the weighted completion time of a problem with one machine with at most one machine reconfiguration. I have a boolean variable Xi that tells me if the job is done before or after the reconfiguration. The variable t is the instant after the reconfiguration(delta is the time to reconfigure the machine). pi1 is the processing time in configuration 1 and pi2 is the processing time in configuration 2. Besides, I have restrictions due to Ci (completion time of a job i).
The example of code I made is not working. I know I have a problem writing the C variable (but I don't know how to solve it).
#include <iostream>
#include <ilcplex/ilocplex.h>
#include <ilcp/cp.h>
#include <vector>
#include <algorithm>
using namespace std;
int main()
{
int nbJob = 4;
int delta = 2;
int nbConf = 2;
vector<int> w_job;
w_job.push_back(1); w_job.push_back(1); w_job.push_back(1); w_job.push_back(1);
vector<vector<int>>p_job;
p_job.resize(nbJob);
p_job[0].push_back(6); p_job[0].push_back(3);
p_job[1].push_back(1); p_job[1].push_back(2);
p_job[2].push_back(10); p_job[2].push_back(2);
p_job[3].push_back(1); p_job[3].push_back(9);
int max_p = 0;
int aux;
for (size_t i = 0; i < nbJob - 1; i++) {
aux = max(p_job[i][0], p_job[i][1]);
max_p = max(max_p, aux);
}
cout << max_p << endl;
int max_w = 0;
aux = 0;
for (size_t i = 0; i < nbJob - 1; i++) {
aux = max(w_job[i], w_job[i + 1]);
max_w = max(aux, max_w);
}
cout << max_w << endl;
int omega = 0;
for (size_t i = 0; i < nbJob; i++) {
omega += max(p_job[i][0], p_job[i][1]);
}
omega += delta;
cout << omega << endl;
try {
IloEnv env;
IloModel model(env);
IloBoolVarArray x(env, nbJob);
for (size_t i = 0; i < nbJob; i++) {
IloBoolVar xi(env, 0, 1, "xi");
x[i] = xi;
}
IloArray<IloExprArray> C(env, nbJob);
for (size_t i = 0; i < nbJob; i++) {
IloExprArray Ci(env);
for (size_t j = 0; j < nbConf; j++) {
IloExpr Cij(env);
Ci.add(Cij);
}
C[i] = Ci;
}
IloNumVarArray C_final(env, nbJob);
for (size_t i = 0; i < nbJob; i++) {
IloNumVar C_finali(env, 0, IloInfinity, ILOINT); //
C_final[i] = C_finali;
}
IloExpr t(env);
for (int i = 0; i < nbJob; i++) {
t += x[i] * p_job[i][0];
}
t += delta;
for (size_t i = 0; i < nbJob; i++) {
for (size_t j = 0; j < nbJob; j++) {
if (j <= i) {
C[i][0] += x[j] * p_job[j][0];
}
}
}
for (size_t i = 0; i < nbJob; i++) {
for (size_t j = 0; j < nbJob; j++) {
if (j <= i) {
C[i][1] += ((1 - x[j]) * p_job[j][1]);
}
}
C[i][1] += t;
}
for (size_t i = 0; i < nbJob; i++) {
model.add(C_final[i] >= C[i][0]);
}
for (size_t i = 0; i < nbJob; i++) {
model.add(C_final[i] >= C[i][1] - (omega * x[i]));
}
IloExpr wiCi(env);
for (size_t i = 0; i < nbJob; i++) {
wiCi += w_job[i] * C_final[i];
}
model.add(IloMinimize(env, wiCi));
IloCplex solver(model);
solver.solve();
for (int i = 0; i < nbJob; i++) {
cout << "C " << i + 1 << " = " << solver.getValue(C_final[i]) << " x" << i+1 << " = " << solver.getValue(x[i]) << endl;
}
cout << endl;
cout << "t = " << solver.getValue(t) << endl;
cout << "wiCi = " << solver.getObjValue() << endl << endl;
}
catch (IloException e) {
cout << e.getMessage();
}
}