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Facility.java
/* Copyright 2022, 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? Based on an example from Frontline Systems: http://www.solver.com/disfacility.htm Used with permission. */ import gurobi.*; public class Facility { 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; // Model GRBEnv env = new GRBEnv(); GRBModel model = new GRBModel(env); model.set(GRB.StringAttr.ModelName, "facility"); // 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 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]); } model.addConstr(dtot, GRB.EQUAL, Demand[w], "Demand" + w); } // 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:"); double maxFixed = -GRB.INFINITY; for (int p = 0; p < nPlants; ++p) { if (FixedCosts[p] > maxFixed) { maxFixed = FixedCosts[p]; } } 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 model.optimize(); // Print solution System.out.println("\nTOTAL COSTS: " + model.get(GRB.DoubleAttr.ObjVal)); System.out.println("SOLUTION:"); for (int p = 0; p < nPlants; ++p) { if (open[p].get(GRB.DoubleAttr.X) > 0.99) { System.out.println("Plant " + p + " open:"); for (int w = 0; w < nWarehouses; ++w) { if (transport[w][p].get(GRB.DoubleAttr.X) > 0.0001) { System.out.println(" Transport " + transport[w][p].get(GRB.DoubleAttr.X) + " units to warehouse " + w); } } } else { System.out.println("Plant " + p + " closed!"); } } // Dispose of model and environment model.dispose(); env.dispose(); } catch (GRBException e) { System.out.println("Error code: " + e.getErrorCode() + ". " + e.getMessage()); } } }