Try our new documentation site.


workforce2_c++.cpp


/* Copyright 2019, Gurobi Optimization, LLC */

/* Assign workers to shifts; each worker may or may not be available on a
   particular day. If the problem cannot be solved, use IIS iteratively to
   find all conflicting constraints. */

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

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

    // 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;
    }

    // do IIS
    cout << "The model is infeasible; computing IIS" << endl;
    deque<string> removed;

    // Loop until we reduce to a model that can be solved
    while (1)
    {
      model.computeIIS();
      cout << "\nThe following constraint cannot be satisfied:" << endl;
      c = model.getConstrs();
      for (int i = 0; i < model.get(GRB_IntAttr_NumConstrs); ++i)
      {
        if (c[i].get(GRB_IntAttr_IISConstr) == 1)
        {
          cout << c[i].get(GRB_StringAttr_ConstrName) << endl;
          // Remove a single constraint from the model
          removed.push_back(c[i].get(GRB_StringAttr_ConstrName));
          model.remove(c[i]);
          break;
        }
      }
      delete[] c;
      c = 0;

      cout << endl;
      model.optimize();
      status = model.get(GRB_IntAttr_Status);

      if (status == GRB_UNBOUNDED)
      {
        cout << "The model cannot be solved because it is unbounded" << endl;
        return 0;
      }
      if (status == GRB_OPTIMAL)
      {
        break;
      }
      if ((status != GRB_INF_OR_UNBD) && (status != GRB_INFEASIBLE))
      {
        cout << "Optimization was stopped with status " << status << endl;
        return 1;
      }
    }
    cout << "\nThe following constraints were removed "
    << "to get a feasible LP:" << endl;

    for (deque<string>::iterator r = removed.begin();
         r != removed.end();
         ++r)
    {
      cout << *r << " ";
    }
    cout << 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 env;
  return 0;
}

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search