Try our new documentation site (beta).


workforce3_cs.cs


/* Copyright 2024, 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, relax the model
   to determine which constraints cannot be satisfied, and how much
   they need to be relaxed. */

using System;
using Gurobi;

class workforce3_cs
{
  static void Main()
  {
    try {

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

      int nShifts = Shifts.Length;
      int nWorkers = Workers.Length;

      // Number of workers required for each shift
      double[] shiftRequirements =
          new double[] { 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 = new double[] { 10, 12, 10, 8, 8, 9, 11 };

      // Worker availability: 0 if the worker is unavailable for a shift
      double[,] availability =
          new double[,] { { 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
      GRBEnv env = new GRBEnv();
      GRBModel model = new GRBModel(env);

      model.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.
      GRBVar[,] x = new GRBVar[nWorkers,nShifts];
      for (int w = 0; w < nWorkers; ++w) {
        for (int s = 0; s < nShifts; ++s) {
          x[w,s] =
              model.AddVar(0, availability[w,s], pay[w], GRB.CONTINUOUS,
                           Workers[w] + "." + Shifts[s]);
        }
      }

      // The objective is to minimize the total pay costs
      model.ModelSense = GRB.MINIMIZE;

      // Constraint: assign exactly shiftRequirements[s] workers
      // to each shift s
      for (int s = 0; s < nShifts; ++s) {
        GRBLinExpr lhs = 0.0;
        for (int w = 0; w < nWorkers; ++w) {
          lhs.AddTerm(1.0, x[w,s]);
        }
        model.AddConstr(lhs == shiftRequirements[s], Shifts[s]);
      }

      // Optimize
      model.Optimize();
      int status = model.Status;
      if (status == GRB.Status.UNBOUNDED) {
        Console.WriteLine("The model cannot be solved "
            + "because it is unbounded");
        return;
      }
      if (status == GRB.Status.OPTIMAL) {
        Console.WriteLine("The optimal objective is " + model.ObjVal);
        return;
      }
      if ((status != GRB.Status.INF_OR_UNBD) &&
          (status != GRB.Status.INFEASIBLE)) {
        Console.WriteLine("Optimization was stopped with status " + status);
        return;
      }

      // Relax the constraints to make the model feasible
      Console.WriteLine("The model is infeasible; relaxing the constraints");
      int orignumvars = model.NumVars;
      model.FeasRelax(0, false, false, true);
      model.Optimize();
      status = model.Status;
      if ((status == GRB.Status.INF_OR_UNBD) ||
          (status == GRB.Status.INFEASIBLE) ||
          (status == GRB.Status.UNBOUNDED)) {
        Console.WriteLine("The relaxed model cannot be solved "
            + "because it is infeasible or unbounded");
        return;
      }
      if (status != GRB.Status.OPTIMAL) {
        Console.WriteLine("Optimization was stopped with status " + status);
        return;
      }

      Console.WriteLine("\nSlack values:");
      GRBVar[] vars = model.GetVars();
      for (int i = orignumvars; i < model.NumVars; ++i) {
        GRBVar sv = vars[i];
        if (sv.X > 1e-6) {
          Console.WriteLine(sv.VarName + " = " + sv.X);
        }
      }

      // Dispose of model and environment
      model.Dispose();
      env.Dispose();

    } catch (GRBException e) {
      Console.WriteLine("Error code: " + e.ErrorCode + ". " +
          e.Message);
    }
  }
}

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

Gurobi Optimization