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multiscenario_cs.cs
// Copyright 2023, 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_cs.cs 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.
using System;
using Gurobi;
class multiscenario_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;
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.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) {
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
GRBConstr[] demandConstr = new GRBConstr[nWarehouses];
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]);
demandConstr[w] = model.AddConstr(dtot == 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.NumScenarios = 7;
// Scenario 0: Base model, hence, nothing to do except giving the
// scenario a name
model.Parameters.ScenarioNumber = 0;
model.ScenNName = "Base model";
// Scenario 1: Increase the warehouse demands by 10%
model.Parameters.ScenarioNumber = 1;
model.ScenNName = "Increased warehouse demands";
for (int w = 0; w < nWarehouses; w++) {
demandConstr[w].ScenNRHS = Demand[w] * 1.1;
}
// Scenario 2: Double the warehouse demands
model.Parameters.ScenarioNumber = 2;
model.ScenNName = "Double the warehouse demands";
for (int w = 0; w < nWarehouses; w++) {
demandConstr[w].ScenNRHS = Demand[w] * 2.0;
}
// Scenario 3: Decrease the plant fixed costs by 5%
model.Parameters.ScenarioNumber = 3;
model.ScenNName = "Decreased plant fixed costs";
for (int p = 0; p < nPlants; p++) {
open[p].ScenNObj = FixedCosts[p] * 0.95;
}
// Scenario 4: Combine scenario 1 and scenario 3 */
model.Parameters.ScenarioNumber = 4;
model.ScenNName = "Increased warehouse demands and decreased plant fixed costs";
for (int w = 0; w < nWarehouses; w++) {
demandConstr[w].ScenNRHS = Demand[w] * 1.1;
}
for (int p = 0; p < nPlants; p++) {
open[p].ScenNObj = FixedCosts[p] * 0.95;
}
// Scenario 5: Force the plant with the largest fixed cost to stay
// open
model.Parameters.ScenarioNumber = 5;
model.ScenNName = "Force plant with largest fixed cost to stay open";
for (int p = 0; p < nPlants; p++) {
if (FixedCosts[p] == maxFixed) {
open[p].ScenNLB = 1.0;
break;
}
}
// Scenario 6: Force the plant with the smallest fixed cost to be
// closed
model.Parameters.ScenarioNumber = 6;
model.ScenNName = "Force plant with smallest fixed cost to be closed";
for (int p = 0; p < nPlants; p++) {
if (FixedCosts[p] == minFixed) {
open[p].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].Start = 1.0;
}
// Now close the plant with the highest fixed cost
Console.WriteLine("Initial guess:");
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 multi-scenario model
model.Optimize();
int nScenarios = model.NumScenarios;
for (int s = 0; s < nScenarios; s++) {
int modelSense = GRB.MINIMIZE;
// Set the scenario number to query the information for this scenario
model.Parameters.ScenarioNumber = s;
// collect result for the scenario
double scenNObjBound = model.ScenNObjBound;
double scenNObjVal = model.ScenNObjVal;
Console.WriteLine("\n\n------ Scenario " + s
+ " (" + model.ScenNName + ")");
// Check if we found a feasible solution for this scenario
if (modelSense * scenNObjVal >= GRB.INFINITY)
if (modelSense * scenNObjBound >= GRB.INFINITY)
// Scenario was proven to be infeasible
Console.WriteLine("\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
Console.WriteLine("\nNO SOLUTION");
else {
Console.WriteLine("\nTOTAL COSTS: " + scenNObjVal);
Console.WriteLine("SOLUTION:");
for (int p = 0; p < nPlants; p++) {
double scenNX = open[p].ScenNX;
if (scenNX > 0.5) {
Console.WriteLine("Plant " + p + " open");
for (int w = 0; w < nWarehouses; w++) {
scenNX = transport[w,p].ScenNX;
if (scenNX > 0.0001)
Console.WriteLine(" Transport " + scenNX
+ " units to warehouse " + w);
}
} else
Console.WriteLine("Plant " + p + " closed!");
}
}
}
// Print a summary table: for each scenario we add a single summary
// line
Console.WriteLine("\n\nSummary: Closed plants depending on scenario\n");
Console.WriteLine("{0,8} | {1,17} {2,13}", "", "Plant", "|");
Console.Write("{0,8} |", "Scenario");
for (int p = 0; p < nPlants; p++)
Console.Write("{0,6}", p);
Console.WriteLine(" | {0,6} Name", "Costs");
for (int s = 0; s < nScenarios; s++) {
int modelSense = GRB.MINIMIZE;
// Set the scenario number to query the information for this scenario
model.Parameters.ScenarioNumber = s;
// Collect result for the scenario
double scenNObjBound = model.ScenNObjBound;
double scenNObjVal = model.ScenNObjVal;
Console.Write("{0,-8} |", s);
// Check if we found a feasible solution for this scenario
if (modelSense * scenNObjVal >= GRB.INFINITY) {
if (modelSense * scenNObjBound >= GRB.INFINITY)
// Scenario was proven to be infeasible
Console.WriteLine(" {0,-30}| {1,6} " + model.ScenNName,
"infeasible", "-");
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
Console.WriteLine(" {0,-30}| {1,6} " + model.ScenNName,
"no solution found", "-");
} else {
for (int p = 0; p < nPlants; p++) {
double scenNX = open[p].ScenNX;
if (scenNX > 0.5)
Console.Write("{0,6}", " ");
else
Console.Write("{0,6}", "x");
}
Console.WriteLine(" | {0,6} "+ model.ScenNName, scenNObjVal);
}
}
// Dispose of model and env
model.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message);
}
}
}
