Try our new documentation site (beta).
Filter Content By
Version
Text Search
${sidebar_list_label} - Back
Filter by Language
multiscenario_c++.cpp
// Copyright 2022, 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. open = model.addVars(nPlants, GRB_BINARY); 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++) { transport[w] = model.addVars(nPlants); 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; }