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### workforce3_c++.cpp

/* Copyright 2016, Gurobi Optimization, Inc. */

/* Assign workers to shifts; each worker may or may not be available on a
particular day. If the problem cannot be solved, relax the model
to determine which constraints cannot be satisfied, and how much
they need to be relaxed. */

#include "gurobi_c++.h"
#include <sstream>
using namespace std;

int
main(int argc,
char *argv[])
{
GRBEnv* env = 0;
GRBConstr* c = 0;
GRBVar** x = 0;
GRBVar* vars = 0;
int xCt = 0;
try
{

// Sample data
const int nShifts = 14;
const int nWorkers = 7;

// Sets of days and workers
string Shifts[] =
{ "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6",
"Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13",
"Sun14" };
string Workers[] =
{ "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu" };

// Number of workers required for each shift
double shiftRequirements[] =
{ 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 };

// Amount each worker is paid to work one shift
double pay[] = { 10, 12, 10, 8, 8, 9, 11 };

// Worker availability: 0 if the worker is unavailable for a shift
double availability[][nShifts] =
{ { 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 },
{ 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1 },
{ 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } };

// Model
env = new GRBEnv();
GRBModel model = GRBModel(*env);
model.set(GRB_StringAttr_ModelName, "assignment");

// Assignment variables: x[w][s] == 1 if worker w is assigned
// to shift s. Since an assignment model always produces integer
// solutions, we use continuous variables and solve as an LP.
x = new GRBVar*[nWorkers];
for (int w = 0; w < nWorkers; ++w)
{
x[w] = model.addVars(nShifts);
xCt++;
model.update();
for (int s = 0; s < nShifts; ++s)
{
ostringstream vname;
vname << Workers[w] << "." << Shifts[s];
x[w][s].set(GRB_DoubleAttr_UB, availability[w][s]);
x[w][s].set(GRB_DoubleAttr_Obj, pay[w]);
x[w][s].set(GRB_StringAttr_VarName, vname.str());
}
}

// The objective is to minimize the total pay costs
model.set(GRB_IntAttr_ModelSense, 1);

// Update model to integrate new variables
model.update();

// Constraint: assign exactly shiftRequirements[s] workers
// to each shift s
for (int s = 0; s < nShifts; ++s)
{
GRBLinExpr lhs = 0;
for (int w = 0; w < nWorkers; ++w)
{
lhs += x[w][s];
}
model.addConstr(lhs == shiftRequirements[s], Shifts[s]);
}

// Optimize
model.optimize();
int status = model.get(GRB_IntAttr_Status);
if (status == GRB_UNBOUNDED)
{
cout << "The model cannot be solved "
<< "because it is unbounded" << endl;
return 1;
}
if (status == GRB_OPTIMAL)
{
cout << "The optimal objective is " <<
model.get(GRB_DoubleAttr_ObjVal) << endl;
return 0;
}
if ((status != GRB_INF_OR_UNBD) && (status != GRB_INFEASIBLE))
{
cout << "Optimization was stopped with status " << status << endl;
return 1;
}

// Relax the constraints to make the model feasible
cout << "The model is infeasible; relaxing the constraints" << endl;
int orignumvars = model.get(GRB_IntAttr_NumVars);
model.feasRelax(0, false, false, true);
model.optimize();
status = model.get(GRB_IntAttr_Status);
if ((status == GRB_INF_OR_UNBD) || (status == GRB_INFEASIBLE) ||
(status == GRB_UNBOUNDED))
{
cout << "The relaxed model cannot be solved " <<
"because it is infeasible or unbounded" << endl;
return 1;
}
if (status != GRB_OPTIMAL)
{
cout << "Optimization was stopped with status " << status << endl;
return 1;
}

cout << "\nSlack values:" << endl;
vars = model.getVars();
for (int i = orignumvars; i < model.get(GRB_IntAttr_NumVars); ++i)
{
GRBVar sv = vars[i];
if (sv.get(GRB_DoubleAttr_X) > 1e-6)
{
cout << sv.get(GRB_StringAttr_VarName) << " = " <<
sv.get(GRB_DoubleAttr_X) << endl;
}
}

}
catch (GRBException e)
{
cout << "Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
}
catch (...)
{
cout << "Exception during optimization" << endl;
}

delete[] c;
for (int i = 0; i < xCt; ++i) {
delete[] x[i];
}
delete[] x;
delete[] vars;
delete env;
return 0;
}


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