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Multiscenario.java
// 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.java 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. import com.gurobi.gurobi.*; public class Multiscenario { public static void main(String[] args) { 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.set(GRB.StringAttr.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.set(GRB.IntAttr.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 = new GRBLinExpr(); for (int w = 0; w < nWarehouses; ++w) { ptot.addTerm(1.0, transport[w][p]); } GRBLinExpr limit = new GRBLinExpr(); limit.addTerm(Capacity[p], open[p]); model.addConstr(ptot, GRB.LESS_EQUAL, limit, "Capacity" + p); } // Demand constraints GRBConstr[] demandConstr = new GRBConstr[nWarehouses]; for (int w = 0; w < nWarehouses; ++w) { GRBLinExpr dtot = new GRBLinExpr(); for (int p = 0; p < nPlants; ++p) { dtot.addTerm(1.0, transport[w][p]); } demandConstr[w] = model.addConstr(dtot, GRB.EQUAL, 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.set(GRB.IntAttr.NumScenarios, 7); // Scenario 0: Base model, hence, nothing to do except giving the // scenario a name model.set(GRB.IntParam.ScenarioNumber, 0); model.set(GRB.StringAttr.ScenNName, "Base model"); // Scenario 1: Increase the warehouse demands by 10% model.set(GRB.IntParam.ScenarioNumber, 1); model.set(GRB.StringAttr.ScenNName, "Increased warehouse demands"); for (int w = 0; w < nWarehouses; w++) { demandConstr[w].set(GRB.DoubleAttr.ScenNRHS, Demand[w] * 1.1); } // Scenario 2: Double the warehouse demands model.set(GRB.IntParam.ScenarioNumber, 2); model.set(GRB.StringAttr.ScenNName, "Double the warehouse demands"); for (int w = 0; w < nWarehouses; w++) { demandConstr[w].set(GRB.DoubleAttr.ScenNRHS, Demand[w] * 2.0); } // Scenario 3: Decrease the plant fixed costs by 5% model.set(GRB.IntParam.ScenarioNumber, 3); model.set(GRB.StringAttr.ScenNName, "Decreased plant fixed costs"); for (int p = 0; p < nPlants; p++) { open[p].set(GRB.DoubleAttr.ScenNObj, FixedCosts[p] * 0.95); } // Scenario 4: Combine scenario 1 and scenario 3 */ model.set(GRB.IntParam.ScenarioNumber, 4); model.set(GRB.StringAttr.ScenNName, "Increased warehouse demands and decreased plant fixed costs"); for (int w = 0; w < nWarehouses; w++) { demandConstr[w].set(GRB.DoubleAttr.ScenNRHS, Demand[w] * 1.1); } for (int p = 0; p < nPlants; p++) { open[p].set(GRB.DoubleAttr.ScenNObj, FixedCosts[p] * 0.95); } // Scenario 5: Force the plant with the largest fixed cost to stay // open model.set(GRB.IntParam.ScenarioNumber, 5); model.set(GRB.StringAttr.ScenNName, "Force plant with largest fixed cost to stay open"); for (int p = 0; p < nPlants; p++) { if (FixedCosts[p] == maxFixed) { open[p].set(GRB.DoubleAttr.ScenNLB, 1.0); break; } } // Scenario 6: Force the plant with the smallest fixed cost to be // closed model.set(GRB.IntParam.ScenarioNumber, 6); model.set(GRB.StringAttr.ScenNName, "Force plant with smallest fixed cost to be closed"); for (int p = 0; p < nPlants; p++) { if (FixedCosts[p] == minFixed) { open[p].set(GRB.DoubleAttr.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].set(GRB.DoubleAttr.Start, 1.0); } // Now close the plant with the highest fixed cost System.out.println("Initial guess:"); for (int p = 0; p < nPlants; ++p) { if (FixedCosts[p] == maxFixed) { open[p].set(GRB.DoubleAttr.Start, 0.0); System.out.println("Closing plant " + p + "\n"); break; } } // Use barrier to solve root relaxation model.set(GRB.IntParam.Method, GRB.METHOD_BARRIER); // Solve multi-scenario model model.optimize(); int nScenarios = model.get(GRB.IntAttr.NumScenarios); // Print solution for each */ for (int s = 0; s < nScenarios; s++) { int modelSense = GRB.MINIMIZE; // Set the scenario number to query the information for this scenario model.set(GRB.IntParam.ScenarioNumber, s); // collect result for the scenario double scenNObjBound = model.get(GRB.DoubleAttr.ScenNObjBound); double scenNObjVal = model.get(GRB.DoubleAttr.ScenNObjVal); System.out.println("\n\n------ Scenario " + s + " (" + model.get(GRB.StringAttr.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 System.out.println("\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 System.out.println("\nNO SOLUTION"); else { System.out.println("\nTOTAL COSTS: " + scenNObjVal); System.out.println("SOLUTION:"); for (int p = 0; p < nPlants; p++) { double scenNX = open[p].get(GRB.DoubleAttr.ScenNX); if (scenNX > 0.5) { System.out.println("Plant " + p + " open"); for (int w = 0; w < nWarehouses; w++) { scenNX = transport[w][p].get(GRB.DoubleAttr.ScenNX); if (scenNX > 0.0001) System.out.println(" Transport " + scenNX + " units to warehouse " + w); } } else System.out.println("Plant " + p + " closed!"); } } } // Print a summary table: for each scenario we add a single summary // line System.out.println("\n\nSummary: Closed plants depending on scenario\n"); System.out.format("%8s | %17s %13s\n", "", "Plant", "|"); System.out.format("%8s |", "Scenario"); for (int p = 0; p < nPlants; p++) System.out.format(" %5d", p); System.out.format(" | %6s %s\n", "Costs", "Name"); for (int s = 0; s < nScenarios; s++) { int modelSense = GRB.MINIMIZE; // Set the scenario number to query the information for this scenario model.set(GRB.IntParam.ScenarioNumber, s); // Collect result for the scenario double scenNObjBound = model.get(GRB.DoubleAttr.ScenNObjBound); double scenNObjVal = model.get(GRB.DoubleAttr.ScenNObjVal); System.out.format("%-8d |", 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 System.out.format(" %-30s| %6s %s\n", "infeasible", "-", model.get(GRB.StringAttr.ScenNName)); 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 System.out.format(" %-30s| %6s %s\n", "no solution found", "-", model.get(GRB.StringAttr.ScenNName)); } else { for (int p = 0; p < nPlants; p++) { double scenNX = open[p].get(GRB.DoubleAttr.ScenNX); if (scenNX > 0.5) System.out.format("%6s", " "); else System.out.format("%6s", "x"); } System.out.format(" | %6g %s\n", scenNObjVal, model.get(GRB.StringAttr.ScenNName)); } } // Dispose of model and environment model.dispose(); env.dispose(); } catch (GRBException e) { System.out.println("Error code: " + e.getErrorCode() + ". " + e.getMessage()); } } }