# Multiscenario.java

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### Multiscenario.java

// Copyright 2020, 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 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) {
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) {
}
GRBLinExpr limit = new GRBLinExpr();
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) {
}
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 (scenNObjVal >= modelSense * GRB.INFINITY)
if (scenNObjBound >= modelSense * 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 (scenNObjVal >= modelSense * GRB.INFINITY) {
if (scenNObjBound >= modelSense * 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());
}
}
}