# multiscenario_c++.cpp

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### multiscenario_c++.cpp

// 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_c++.cpp 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.

#include "gurobi_c++.h"
#include <sstream>
#include <iomanip>
using namespace std;

int
main(int   argc,
char *argv[])
{
GRBEnv     *env          = 0;
GRBVar     *open         = 0;
GRBVar    **transport    = 0;
GRBConstr  *demandConstr = 0;

int transportCt = 0;

try {
// Number of plants and warehouses
const int nPlants = 5;
const int nWarehouses = 4;

// Warehouse demand in thousands of units
double Demand[] = { 15, 18, 14, 20 };

// Plant capacity in thousands of units
double Capacity[] = { 20, 22, 17, 19, 18 };

// Fixed costs for each plant
double FixedCosts[] =
{ 12000, 15000, 17000, 13000, 16000 };

// Transportation costs per thousand units
double TransCosts[][nPlants] = {
{ 4000, 2000, 3000, 2500, 4500 },
{ 2500, 2600, 3400, 3000, 4000 },
{ 1200, 1800, 2600, 4100, 3000 },
{ 2200, 2600, 3100, 3700, 3200 }
};

double maxFixed = -GRB_INFINITY;
double minFixed = GRB_INFINITY;

int p;
for (p = 0; p < nPlants; p++) {
if (FixedCosts[p] > maxFixed)
maxFixed = FixedCosts[p];

if (FixedCosts[p] < minFixed)
minFixed = FixedCosts[p];
}

// Model
env = new GRBEnv();
GRBModel model = GRBModel(*env);
model.set(GRB_StringAttr_ModelName, "multiscenario");

// Plant open decision variables: open[p] == 1 if plant p is open.

for (p = 0; p < nPlants; p++) {
ostringstream vname;
vname << "Open" << p;
open[p].set(GRB_DoubleAttr_Obj, FixedCosts[p]);
open[p].set(GRB_StringAttr_VarName, vname.str());
}

// Transportation decision variables: how much to transport from
// a plant p to a warehouse w
transport = new GRBVar* [nWarehouses];
int w;
for (w = 0; w < nWarehouses; w++) {
transportCt++;

for (p = 0; p < nPlants; p++) {
ostringstream vname;
vname << "Trans" << p << "." << w;
transport[w][p].set(GRB_DoubleAttr_Obj, TransCosts[w][p]);
transport[w][p].set(GRB_StringAttr_VarName, vname.str());
}
}

// 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 (p = 0; p < nPlants; p++) {
GRBLinExpr ptot = 0;
for (w = 0; w < nWarehouses; w++) {
ptot += transport[w][p];
}
ostringstream cname;
cname << "Capacity" << p;
model.addConstr(ptot <= Capacity[p] * open[p], cname.str());
}

// Demand constraints
demandConstr = new GRBConstr[nWarehouses];
for (w = 0; w < nWarehouses; w++) {
GRBLinExpr dtot = 0;
for (p = 0; p < nPlants; p++)
dtot += transport[w][p];

ostringstream cname;
cname << "Demand" << w;
demandConstr[w] = model.addConstr(dtot == Demand[w], cname.str());
}

// 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 (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 (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 (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 (w = 0; w < nWarehouses; w++) {
demandConstr[w].set(GRB_DoubleAttr_ScenNRHS, Demand[w] * 1.1);
}
for (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 (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 (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 (p = 0; p < nPlants; p++)
open[p].set(GRB_DoubleAttr_Start, 1.0);

// Now close the plant with the highest fixed cost
cout << "Initial guess:" << endl;
for (p = 0; p < nPlants; p++) {
if (FixedCosts[p] == maxFixed) {
open[p].set(GRB_DoubleAttr_Start, 0.0);
cout << "Closing plant " << p << endl << endl;
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);

cout << endl << endl << "------ Scenario " << s
<< " (" << model.get(GRB_StringAttr_ScenNName) << ")" << endl;

// 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
cout << endl << "INFEASIBLE" << endl;
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
cout << endl << "NO SOLUTION" << endl;
else {
cout << endl << "TOTAL COSTS: " << scenNObjVal << endl;
cout << "SOLUTION:" << endl;
for (p = 0; p < nPlants; p++) {
double scenNX = open[p].get(GRB_DoubleAttr_ScenNX);

if (scenNX > 0.5) {
cout << "Plant " << p << " open" << endl;
for (w = 0; w < nWarehouses; w++) {
scenNX = transport[w][p].get(GRB_DoubleAttr_ScenNX);

if (scenNX > 0.0001)
cout << "  Transport " << scenNX
<< " units to warehouse " << w << endl;
}
} else
cout << "Plant " << p << " closed!" << endl;
}
}
}

// Print a summary table: for each scenario we add a single summary
// line
cout << endl << endl << "Summary: Closed plants depending on scenario" << endl << endl;
cout << setw(8) << " " << " | " << setw(17) << "Plant" << setw(14) << "|" << endl;

cout << setw(8) << "Scenario" << " |";
for (p = 0; p < nPlants; p++)
cout << " " << setw(5) << p;
cout << " | " << setw(6) << "Costs" << "  Name" << endl;

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);

cout << left << setw(8) << s << right << " |";

// 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
cout << " " << left << setw(30) << "infeasible" << right;
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
cout << " " << left << setw(30) << "no solution found" << right;

cout << "| " << setw(6) << "-"
<< "  " << model.get(GRB_StringAttr_ScenNName)
<< endl;
} else {
for (p = 0; p < nPlants; p++) {
double scenNX = open[p].get(GRB_DoubleAttr_ScenNX);
if (scenNX  > 0.5)
cout << setw(6) << " ";
else
cout << " " << setw(5) << "x";
}

cout << " | " << setw(6) << scenNObjVal
<< "  " << model.get(GRB_StringAttr_ScenNName)
<< endl;
}
}
}
catch (GRBException e) {
cout << "Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
}
catch (...) {
cout << "Exception during optimization" << endl;
}

delete[] open;
for (int i = 0; i < transportCt; ++i) {
delete[] transport[i];
}
delete[] transport;
delete[] demandConstr;
delete env;
return 0;
}