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# multiscenario_cs.cs

    // Copyright 2025, Gurobi Optimization, LLC

    // Facility location: a company currently ships its product from 5 plants
    // to 4 warehouses. It is considering closing some plants to reduce
    // costs. What plant(s) should the company close, in order to minimize
    // transportation and fixed costs?
    //
    // Since the plant fixed costs and the warehouse demands are uncertain, a
    // scenario approach is chosen.
    //
    // Note that this example is similar to the facility_cs.cs example. Here we
    // added scenarios in order to illustrate the multi-scenario feature.
    //
    // Based on an example from Frontline Systems:
    // http://www.solver.com/disfacility.htm
    // Used with permission.

    using System;
    using Gurobi;

    class multiscenario_cs
    {
      static void Main()
      {
        try {

          // Warehouse demand in thousands of units
          double[] Demand = new double[] { 15, 18, 14, 20 };

          // Plant capacity in thousands of units
          double[] Capacity = new double[] { 20, 22, 17, 19, 18 };

          // Fixed costs for each plant
          double[] FixedCosts =
            new double[] { 12000, 15000, 17000, 13000, 16000 };

          // Transportation costs per thousand units
          double[,] TransCosts =
            new double[,] { { 4000, 2000, 3000, 2500, 4500 },
                            { 2500, 2600, 3400, 3000, 4000 },
                            { 1200, 1800, 2600, 4100, 3000 },
                            { 2200, 2600, 3100, 3700, 3200 } };

          // Number of plants and warehouses
          int nPlants = Capacity.Length;
          int nWarehouses = Demand.Length;

          double maxFixed = -GRB.INFINITY;
          double minFixed = GRB.INFINITY;
          for (int p = 0; p < nPlants; ++p) {
            if (FixedCosts[p] > maxFixed)
              maxFixed = FixedCosts[p];

            if (FixedCosts[p] < minFixed)
              minFixed = FixedCosts[p];
          }

          // Model
          GRBEnv env = new GRBEnv();
          GRBModel model = new GRBModel(env);

          model.ModelName = "multiscenario";

          // Plant open decision variables: open[p] == 1 if plant p is open.
          GRBVar[] open = new GRBVar[nPlants];
          for (int p = 0; p < nPlants; ++p) {
            open[p] = model.AddVar(0, 1, FixedCosts[p], GRB.BINARY, "Open" + p);
          }

          // Transportation decision variables: how much to transport from
          // a plant p to a warehouse w
          GRBVar[,] transport = new GRBVar[nWarehouses,nPlants];
          for (int w = 0; w < nWarehouses; ++w) {
            for (int p = 0; p < nPlants; ++p) {
              transport[w,p] = model.AddVar(0, GRB.INFINITY, TransCosts[w,p],
                                            GRB.CONTINUOUS, "Trans" + p + "." + w);
            }
          }

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

          // Production constraints
          // Note that the right-hand limit sets the production to zero if
          // the plant is closed
          for (int p = 0; p < nPlants; ++p) {
            GRBLinExpr ptot = 0.0;
            for (int w = 0; w < nWarehouses; ++w)
              ptot.AddTerm(1.0, transport[w,p]);
            model.AddConstr(ptot <= Capacity[p] * open[p], "Capacity" + p);
          }

          // Demand constraints
          GRBConstr[] demandConstr = new GRBConstr[nWarehouses];
          for (int w = 0; w < nWarehouses; ++w) {
            GRBLinExpr dtot = 0.0;
            for (int p = 0; p < nPlants; ++p)
              dtot.AddTerm(1.0, transport[w,p]);
            demandConstr[w] = model.AddConstr(dtot == Demand[w], "Demand" + w);
          }

          // We constructed the base model, now we add 7 scenarios
          //
          // Scenario 0: Represents the base model, hence, no manipulations.
          // Scenario 1: Manipulate the warehouses demands slightly (constraint right
          //             hand sides).
          // Scenario 2: Double the warehouses demands (constraint right hand sides).
          // Scenario 3: Manipulate the plant fixed costs (objective coefficients).
          // Scenario 4: Manipulate the warehouses demands and fixed costs.
          // Scenario 5: Force the plant with the largest fixed cost to stay open
          //             (variable bounds).
          // Scenario 6: Force the plant with the smallest fixed cost to be closed
          //             (variable bounds).

          model.NumScenarios = 7;

          // Scenario 0: Base model, hence, nothing to do except giving the
          //             scenario a name
          model.Parameters.ScenarioNumber = 0;
          model.ScenNName = "Base model";

          // Scenario 1: Increase the warehouse demands by 10%
          model.Parameters.ScenarioNumber = 1;
          model.ScenNName = "Increased warehouse demands";

          for (int w = 0; w < nWarehouses; w++) {
            demandConstr[w].ScenNRHS = Demand[w] * 1.1;
          }

          // Scenario 2: Double the warehouse demands
          model.Parameters.ScenarioNumber = 2;
          model.ScenNName = "Double the warehouse demands";

          for (int w = 0; w < nWarehouses; w++) {
            demandConstr[w].ScenNRHS = Demand[w] * 2.0;
          }

          // Scenario 3: Decrease the plant fixed costs by 5%
          model.Parameters.ScenarioNumber = 3;
          model.ScenNName = "Decreased plant fixed costs";

          for (int p = 0; p < nPlants; p++) {
            open[p].ScenNObj = FixedCosts[p] * 0.95;
          }

          // Scenario 4: Combine scenario 1 and scenario 3 */
          model.Parameters.ScenarioNumber = 4;
          model.ScenNName = "Increased warehouse demands and decreased plant fixed costs";

          for (int w = 0; w < nWarehouses; w++) {
            demandConstr[w].ScenNRHS = Demand[w] * 1.1;
          }
          for (int p = 0; p < nPlants; p++) {
            open[p].ScenNObj = FixedCosts[p] * 0.95;
          }

          // Scenario 5: Force the plant with the largest fixed cost to stay
          //             open
          model.Parameters.ScenarioNumber = 5;
          model.ScenNName = "Force plant with largest fixed cost to stay open";

          for (int p = 0; p < nPlants; p++) {
            if (FixedCosts[p] == maxFixed) {
              open[p].ScenNLB = 1.0;
              break;
            }
          }

          // Scenario 6: Force the plant with the smallest fixed cost to be
          //             closed
          model.Parameters.ScenarioNumber = 6;
          model.ScenNName = "Force plant with smallest fixed cost to be closed";

          for (int p = 0; p < nPlants; p++) {
            if (FixedCosts[p] == minFixed) {
              open[p].ScenNUB = 0.0;
              break;
            }
          }

          // Guess at the starting point: close the plant with the highest
          // fixed costs; open all others

          // First, open all plants
          for (int p = 0; p < nPlants; ++p) {
            open[p].Start = 1.0;
          }

          // Now close the plant with the highest fixed cost
          Console.WriteLine("Initial guess:");
          for (int p = 0; p < nPlants; ++p) {
            if (FixedCosts[p] == maxFixed) {
              open[p].Start = 0.0;
              Console.WriteLine("Closing plant " + p + "\n");
              break;
            }
          }

          // Use barrier to solve root relaxation
          model.Parameters.Method = GRB.METHOD_BARRIER;

          // Solve multi-scenario model
          model.Optimize();

          int nScenarios = model.NumScenarios;

          for (int s = 0; s < nScenarios; s++) {
            int modelSense = GRB.MINIMIZE;

            // Set the scenario number to query the information for this scenario
            model.Parameters.ScenarioNumber = s;

            // collect result for the scenario
            double scenNObjBound = model.ScenNObjBound;
            double scenNObjVal = model.ScenNObjVal;

            Console.WriteLine("\n\n------ Scenario " + s
                              + " (" +  model.ScenNName + ")");

            // Check if we found a feasible solution for this scenario
            if (modelSense * scenNObjVal >= GRB.INFINITY)
              if (modelSense * scenNObjBound >= GRB.INFINITY)
                // Scenario was proven to be infeasible
                Console.WriteLine("\nINFEASIBLE");
              else
                // We did not find any feasible solution - should not happen in
                // this case, because we did not set any limit (like a time
                // limit) on the optimization process
                Console.WriteLine("\nNO SOLUTION");
            else {
              Console.WriteLine("\nTOTAL COSTS: " + scenNObjVal);
              Console.WriteLine("SOLUTION:");
              for (int p = 0; p < nPlants; p++) {
                double scenNX = open[p].ScenNX;

                if (scenNX > 0.5) {
                  Console.WriteLine("Plant " + p + " open");
                  for (int w = 0; w < nWarehouses; w++) {
                    scenNX = transport[w,p].ScenNX;

                    if (scenNX > 0.0001)
                      Console.WriteLine("  Transport " + scenNX
                                        + " units to warehouse " + w);
                  }
                } else
                  Console.WriteLine("Plant " + p + " closed!");
              }
            }
          }

          // Print a summary table: for each scenario we add a single summary
          // line
          Console.WriteLine("\n\nSummary: Closed plants depending on scenario\n");
          Console.WriteLine("{0,8} | {1,17} {2,13}", "", "Plant", "|");

          Console.Write("{0,8} |", "Scenario");
          for (int p = 0; p < nPlants; p++)
            Console.Write("{0,6}", p);
          Console.WriteLine(" | {0,6}  Name", "Costs");

          for (int s = 0; s < nScenarios; s++) {
            int modelSense = GRB.MINIMIZE;

            // Set the scenario number to query the information for this scenario
            model.Parameters.ScenarioNumber = s;

            // Collect result for the scenario
            double scenNObjBound = model.ScenNObjBound;
            double scenNObjVal = model.ScenNObjVal;

            Console.Write("{0,-8} |", s);

            // Check if we found a feasible solution for this scenario
            if (modelSense * scenNObjVal >= GRB.INFINITY) {
              if (modelSense * scenNObjBound >= GRB.INFINITY)
                // Scenario was proven to be infeasible
                Console.WriteLine(" {0,-30}| {1,6}  " + model.ScenNName,
                                  "infeasible", "-");
              else
                // We did not find any feasible solution - should not happen in
                // this case, because we did not set any limit (like a time
                // limit) on the optimization process
                Console.WriteLine(" {0,-30}| {1,6}  " + model.ScenNName,
                                  "no solution found", "-");
            } else {
              for (int p = 0; p < nPlants; p++) {
                double scenNX = open[p].ScenNX;
                if (scenNX  > 0.5)
                  Console.Write("{0,6}", " ");
                else
                  Console.Write("{0,6}", "x");
              }

              Console.WriteLine(" | {0,6}  "+ model.ScenNName, scenNObjVal);
            }
          }

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

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

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