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### sensitivity_c++.cpp

// Copyright 2023, Gurobi Optimization, LLC

// A simple sensitivity analysis example which reads a MIP model from a
// file and solves it. Then uses the scenario feature to analyze the impact
// w.r.t. the objective function of each binary variable if it is set to
// 1-X, where X is its value in the optimal solution.
//
// Usage:
//     sensitivity_c++ <model filename>

#include "gurobi_c++.h"
using namespace std;

// Maximum number of scenarios to be considered
#define MAXSCENARIOS 100

int
main(int   argc,
char *argv[])
{
if (argc < 2) {
cout << "Usage: sensitivity_c++ filename" << endl;
return 1;
}

GRBVar *vars  = NULL;
double *origX = NULL;

try {

// Create environment
GRBEnv env = GRBEnv();

GRBModel model = GRBModel(env, argv[1]);

int scenarios;

if (model.get(GRB_IntAttr_IsMIP) == 0) {
cout << "Model is not a MIP" << endl;
return 1;
}

// Solve model
model.optimize();

if (model.get(GRB_IntAttr_Status) != GRB_OPTIMAL) {
cout << "Optimization ended with status "
<< model.get(GRB_IntAttr_Status) << endl;
return 1;
}

// Store the optimal solution
double origObjVal = model.get(GRB_DoubleAttr_ObjVal);
vars = model.getVars();
int numVars = model.get(GRB_IntAttr_NumVars);
origX = model.get(GRB_DoubleAttr_X, vars, numVars);

scenarios = 0;

// Count number of unfixed, binary variables in model. For each we
// create a scenario.
for (int i = 0; i < numVars; i++) {
GRBVar v     = vars[i];
char   vType = v.get(GRB_CharAttr_VType);

if (v.get(GRB_DoubleAttr_LB) == 0.0               &&
v.get(GRB_DoubleAttr_UB) == 1.0               &&
(vType == GRB_BINARY || vType == GRB_INTEGER)   ) {
scenarios++;

if (scenarios >= MAXSCENARIOS)
break;
}
}

cout << "###  construct multi-scenario model with "
<< scenarios << " scenarios" << endl;

// Set the number of scenarios in the model */
model.set(GRB_IntAttr_NumScenarios, scenarios);

scenarios = 0;

// Create a (single) scenario model by iterating through unfixed binary
// variables in the model and create for each of these variables a
// scenario by fixing the variable to 1-X, where X is its value in the
// computed optimal solution
for (int i = 0; i < numVars; i++) {
GRBVar v     = vars[i];
char   vType = v.get(GRB_CharAttr_VType);

if (v.get(GRB_DoubleAttr_LB) == 0.0               &&
v.get(GRB_DoubleAttr_UB) == 1-0               &&
(vType == GRB_BINARY || vType == GRB_INTEGER) &&
scenarios < MAXSCENARIOS                        ) {

// Set ScenarioNumber parameter to select the corresponding
model.set(GRB_IntParam_ScenarioNumber, scenarios);

// Set variable to 1-X, where X is its value in the optimal solution */
if (origX[i] < 0.5)
v.set(GRB_DoubleAttr_ScenNLB, 1.0);
else
v.set(GRB_DoubleAttr_ScenNUB, 0.0);

scenarios++;
} else {
// Add MIP start for all other variables using the optimal solution
// of the base model
v.set(GRB_DoubleAttr_Start, origX[i]);
}
}

// Solve multi-scenario model
model.optimize();

// In case we solved the scenario model to optimality capture the
// sensitivity information
if (model.get(GRB_IntAttr_Status) == GRB_OPTIMAL) {

// get the model sense (minimization or maximization)
int modelSense = model.get(GRB_IntAttr_ModelSense);

scenarios = 0;

for (int i = 0; i < numVars; i++) {
GRBVar v     = vars[i];
char   vType = v.get(GRB_CharAttr_VType);

if (v.get(GRB_DoubleAttr_LB) == 0.0               &&
v.get(GRB_DoubleAttr_UB) == 1-0               &&
(vType == GRB_BINARY || vType == GRB_INTEGER)   ) {

// Set scenario parameter to collect the objective value of the
// corresponding scenario
model.set(GRB_IntParam_ScenarioNumber, scenarios);

// Collect objective value and bound for the scenario
double scenarioObjVal = model.get(GRB_DoubleAttr_ScenNObjVal);
double scenarioObjBound = model.get(GRB_DoubleAttr_ScenNObjBound);

cout << "Objective sensitivity for variable "
<< v.get(GRB_StringAttr_VarName)
<< " is ";

// Check if we found a feasible solution for this scenario
if (modelSense * scenarioObjVal >= GRB_INFINITY) {
// Check if the scenario is infeasible
if (modelSense * scenarioObjBound >= GRB_INFINITY)
cout << "infeasible"  << endl;
else
cout << "unknown (no solution available)"  << endl;
} else {
// Scenario is feasible and a solution is available
cout << modelSense * (scenarioObjVal - origObjVal) << endl;
}

scenarios++;

if (scenarios >= MAXSCENARIOS)
break;
}
}
}
} catch (GRBException e) {
cout << "Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
} catch (...) {
cout << "Error during optimization" << endl;
}

delete[] vars;
delete[] origX;

return 0;
}


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