/* 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 to find a set of
   conflicting constraints. Note that there may be additional conflicts
   besides what is reported via IIS. */
using System;
using Gurobi;
class workforce1_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;
            }
            // Do IIS
            Console.WriteLine("The model is infeasible; computing IIS");
            model.ComputeIIS();
            Console.WriteLine("\nThe following constraint(s) "
                + "cannot be satisfied:");
            foreach (GRBConstr c in model.GetConstrs())
            {
                if (c.IISConstr == 1)
                {
                    Console.WriteLine(c.ConstrName);
                }
            }
            // Dispose of model and env
            model.Dispose();
            env.Dispose();
        }
        catch (GRBException e)
        {
            Console.WriteLine("Error code: " + e.ErrorCode + ". " +
                e.Message);
        }
    }
}