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Facility.java

Facility.java

```/* Copyright 2018, 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());
}
}
}
```