Try our new documentation site (beta).
Filter Content By
Version
Text Search
${sidebar_list_label} - Back
Filter by Language
multiscenario_cs.cs
// Copyright 2024, 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); } } }