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# Workforce5.java

    /* Copyright 2025, Gurobi Optimization, LLC */

    /* Assign workers to shifts; each worker may or may not be available on a
       particular day. We use multi-objective optimization to solve the model.
       The highest-priority objective minimizes the sum of the slacks
       (i.e., the total number of uncovered shifts). The secondary objective
       minimizes the difference between the maximum and minimum number of
       shifts worked among all workers.  The second optimization is allowed
       to degrade the first objective by up to the smaller value of 10% and 2 */

    import com.gurobi.gurobi.*;

    public class Workforce5 {

      public static void main(String[] args) {

        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", "Tobi" };

          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 };

          // 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 },
                  { 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1 },
                  { 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } };

          // Create environment
          GRBEnv env = new GRBEnv();

          // Create initial model
          GRBModel model = new GRBModel(env);
          model.set(GRB.StringAttr.ModelName, "Workforce5");

          // Initialize assignment decision variables:
          // x[w][s] == 1 if worker w is assigned to shift s.
          // This is no longer a pure assignment model, so we must
          // use binary variables.
          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], 0, GRB.BINARY,
                               Workers[w] + "." + Shifts[s]);
            }
          }

          // Slack variables for each shift constraint so that the shifts can
          // be satisfied
          GRBVar[] slacks = new GRBVar[nShifts];
          for (int s = 0; s < nShifts; ++s) {
            slacks[s] =
                model.addVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
                             Shifts[s] + "Slack");
          }

          // Variable to represent the total slack
          GRBVar totSlack = model.addVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
                                         "totSlack");

          // Variables to count the total shifts worked by each worker
          GRBVar[] totShifts = new GRBVar[nWorkers];
          for (int w = 0; w < nWorkers; ++w) {
            totShifts[w] = model.addVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
                                        Workers[w] + "TotShifts");
          }

          GRBLinExpr lhs;

          // Constraint: assign exactly shiftRequirements[s] workers
          // to each shift s, plus the slack
          for (int s = 0; s < nShifts; ++s) {
            lhs = new GRBLinExpr();
            lhs.addTerm(1.0, slacks[s]);
            for (int w = 0; w < nWorkers; ++w) {
              lhs.addTerm(1.0, x[w][s]);
            }
            model.addConstr(lhs, GRB.EQUAL, shiftRequirements[s], Shifts[s]);
          }

          // Constraint: set totSlack equal to the total slack
          lhs = new GRBLinExpr();
          lhs.addTerm(-1.0, totSlack);
          for (int s = 0; s < nShifts; ++s) {
            lhs.addTerm(1.0, slacks[s]);
          }
          model.addConstr(lhs, GRB.EQUAL, 0, "totSlack");

          // Constraint: compute the total number of shifts for each worker
          for (int w = 0; w < nWorkers; ++w) {
            lhs = new GRBLinExpr();
            lhs.addTerm(-1.0, totShifts[w]);
            for (int s = 0; s < nShifts; ++s) {
              lhs.addTerm(1.0, x[w][s]);
            }
            model.addConstr(lhs, GRB.EQUAL, 0, "totShifts" + Workers[w]);
          }

          // Constraint: set minShift/maxShift variable to less <=/>= to the
          // number of shifts among all workers
          GRBVar minShift = model.addVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
                                         "minShift");
          GRBVar maxShift = model.addVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
                                         "maxShift");
          model.addGenConstrMin(minShift, totShifts, GRB.INFINITY, "minShift");
          model.addGenConstrMax(maxShift, totShifts, -GRB.INFINITY, "maxShift");

          // Set global sense for ALL objectives
          model.set(GRB.IntAttr.ModelSense, GRB.MINIMIZE);

          // Set primary objective
          GRBLinExpr obj0 = new GRBLinExpr();
          obj0.addTerm(1.0, totSlack);
          model.setObjectiveN(obj0, 0, 2, 1.0, 2.0, 0.1, "TotalSlack");

          // Set secondary objective
          GRBLinExpr obj1 = new GRBLinExpr();
          obj1.addTerm(1.0, maxShift);
          obj1.addTerm(-1.0, minShift);
          model.setObjectiveN(obj1, 1, 1, 1.0, 0.0, 0.0, "Fairness");

          // Save problem
          model.write("Workforce5.lp");

          // Optimize
          int status = solveAndPrint(model, totSlack, nWorkers, Workers, totShifts);

          if (status != GRB.OPTIMAL)
            return;

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

        } catch (GRBException e) {
          System.out.println("Error code: " + e.getErrorCode() + ". " +
              e.getMessage());
        }
      }

      private static int solveAndPrint(GRBModel model, GRBVar totSlack,
                                       int nWorkers, String[] Workers,
                                       GRBVar[] totShifts) throws GRBException {

        model.optimize();
        int status = model.get(GRB.IntAttr.Status);
        if (status == GRB.Status.INF_OR_UNBD ||
            status == GRB.Status.INFEASIBLE  ||
            status == GRB.Status.UNBOUNDED     ) {
          System.out.println("The model cannot be solved "
              + "because it is infeasible or unbounded");
          return status;
        }
        if (status != GRB.Status.OPTIMAL ) {
          System.out.println("Optimization was stopped with status " + status);
          return status;
        }

        // Print total slack and the number of shifts worked for each worker
        System.out.println("\nTotal slack required: " +
                           totSlack.get(GRB.DoubleAttr.X));
        for (int w = 0; w < nWorkers; ++w) {
          System.out.println(Workers[w] + " worked " +
                             totShifts[w].get(GRB.DoubleAttr.X) + " shifts");
        }
        System.out.println("\n");
        return status;
      }

    }

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