facility_cs.cs
/* Copyright 2021, 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. */ using System; using Gurobi; class facility_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; // Model GRBEnv env = new GRBEnv(); GRBModel model = new GRBModel(env); model.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.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 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]); model.AddConstr(dtot == 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].Start = 1.0; } // Now close the plant with the highest fixed cost Console.WriteLine("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].Start = 0.0; Console.WriteLine("Closing plant " + p + "\n"); break; } } // Use barrier to solve root relaxation model.Parameters.Method = GRB.METHOD_BARRIER; // Solve model.Optimize(); // Print solution Console.WriteLine("\nTOTAL COSTS: " + model.ObjVal); Console.WriteLine("SOLUTION:"); for (int p = 0; p < nPlants; ++p) { if (open[p].X > 0.99) { Console.WriteLine("Plant " + p + " open:"); for (int w = 0; w < nWarehouses; ++w) { if (transport[w,p].X > 0.0001) { Console.WriteLine(" Transport " + transport[w,p].X + " units to warehouse " + w); } } } else { Console.WriteLine("Plant " + p + " closed!"); } } // Dispose of model and env model.Dispose(); env.Dispose(); } catch (GRBException e) { Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message); } } }
