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workforce5_c++.cpp
/* Copyright 2023, Gurobi Optimization, LLC */
/* Assign workers to shifts; each worker may or may not be available on a
particular day. We use multi-objective optimization to solve the model.
The highest-priority objective minimizes the sum of the slacks
(i.e., the total number of uncovered shifts). The secondary objective
minimizes the difference between the maximum and minimum number of
shifts worked among all workers. The second optimization is allowed
to degrade the first objective by up to the smaller value of 10% and 2 */
#include "gurobi_c++.h"
#include <sstream>
using namespace std;
int solveAndPrint(GRBModel& model, GRBVar& totSlack,
int nWorkers, string* Workers,
GRBVar* totShifts);
int
main(int argc,
char *argv[])
{
GRBEnv *env = 0;
GRBVar **x = 0;
GRBVar *slacks = 0;
GRBVar *totShifts = 0;
int xCt = 0;
int s, w;
try {
// Sample data
const int nShifts = 14;
const int nWorkers = 8;
// Sets of days and workers
string Shifts[] =
{ "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6",
"Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13",
"Sun14" };
string Workers[] =
{ "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu", "Tobi" };
// Number of workers required for each shift
double shiftRequirements[] =
{ 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 };
// Worker availability: 0 if the worker is unavailable for a shift
double availability[][14] =
{ { 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 },
{ 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1 },
{ 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1 },
{ 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } };
// Create environment
env = new GRBEnv("workforce5_c++.log");
// Create initial model
GRBModel model = GRBModel(*env);
model.set(GRB_StringAttr_ModelName, "workforce5_c++");
// Initialize assignment decision variables:
// x[w][s] == 1 if worker w is assigned to shift s.
// This is no longer a pure assignment model, so we must
// use binary variables.
x = new GRBVar*[nWorkers];
for (w = 0; w < nWorkers; w++) {
x[w] = model.addVars(nShifts, GRB_BINARY);
xCt++;
for (s = 0; s < nShifts; s++) {
ostringstream vname;
vname << Workers[w] << "." << Shifts[s];
x[w][s].set(GRB_DoubleAttr_UB, availability[w][s]);
x[w][s].set(GRB_StringAttr_VarName, vname.str());
}
}
// Initialize slack decision variables
slacks = model.addVars(nShifts);
for (s = 0; s < nShifts; s++) {
ostringstream vname;
vname << Shifts[s] << "Slack";
slacks[s].set(GRB_StringAttr_VarName, vname.str());
}
// Variable to represent the total slack
GRBVar totSlack = model.addVar(0, GRB_INFINITY, 0, GRB_CONTINUOUS,
"totSlack");
// Initialize variables to count the total shifts worked by each worker
totShifts = model.addVars(nWorkers);
for (w = 0; w < nWorkers; w++) {
ostringstream vname;
vname << Workers[w] << "TotShifts";
totShifts[w].set(GRB_StringAttr_VarName, vname.str());
}
GRBLinExpr lhs;
// Constraint: assign exactly shiftRequirements[s] workers
// to each shift s, plus the slack
for (s = 0; s < nShifts; s++) {
lhs = 0;
lhs += slacks[s];
for (w = 0; w < nWorkers; w++) {
lhs += x[w][s];
}
model.addConstr(lhs == shiftRequirements[s], Shifts[s]);
}
// Constraint: set totSlack column equal to the total slack
lhs = 0;
for (s = 0; s < nShifts; s++) {
lhs += slacks[s];
}
model.addConstr(lhs == totSlack, "totSlack");
// Constraint: compute the total number of shifts for each worker
for (w = 0; w < nWorkers; w++) {
lhs = 0;
for (s = 0; s < nShifts; s++) {
lhs += x[w][s];
}
ostringstream vname;
vname << "totShifts" << Workers[w];
model.addConstr(lhs == totShifts[w], vname.str());
}
// Constraint: set minShift/maxShift variable to less <=/>= to the
// number of shifts among all workers
GRBVar minShift = model.addVar(0, GRB_INFINITY, 0, GRB_CONTINUOUS,
"minShift");
GRBVar maxShift = model.addVar(0, GRB_INFINITY, 0, GRB_CONTINUOUS,
"maxShift");
model.addGenConstrMin(minShift, totShifts, nWorkers, GRB_INFINITY, "minShift");
model.addGenConstrMax(maxShift, totShifts, nWorkers, -GRB_INFINITY, "maxShift");
// Set global sense for ALL objectives
model.set(GRB_IntAttr_ModelSense, GRB_MINIMIZE);
// Set primary objective
model.setObjectiveN(totSlack, 0, 2, 1.0, 2.0, 0.1, "TotalSlack");
// Set secondary objective
model.setObjectiveN(maxShift - minShift, 1, 1, 1.0, 0, 0, "Fairness");
// Save problem
model.write("workforce5_c++.lp");
// Optimize
int status = solveAndPrint(model, totSlack, nWorkers, Workers, totShifts);
// Delete local variables
if (status != GRB_OPTIMAL)
return 1;
}
catch (GRBException e){
cout << "Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
}
catch (...) {
cout << "Exception during optimization" << endl;
}
for (s = 0; s < xCt; s++)
delete[] x[s];
delete[] x;
delete[] slacks;
delete[] totShifts;
delete env;
return 0;
}
int solveAndPrint(GRBModel& model,
GRBVar& totSlack,
int nWorkers,
string* Workers,
GRBVar* totShifts)
{
model.optimize();
int status = model.get(GRB_IntAttr_Status);
if ((status == GRB_INF_OR_UNBD) ||
(status == GRB_INFEASIBLE) ||
(status == GRB_UNBOUNDED) ) {
cout << "The model cannot be solved " <<
"because it is infeasible or unbounded" << endl;
return status;
}
if (status != GRB_OPTIMAL) {
cout << "Optimization was stopped with status " << status << endl;
return status;
}
// Print total slack and the number of shifts worked for each worker
cout << endl << "Total slack required: " <<
totSlack.get(GRB_DoubleAttr_X) << endl;
for (int w = 0; w < nWorkers; ++w) {
cout << Workers[w] << " worked " <<
totShifts[w].get(GRB_DoubleAttr_X) << " shifts" << endl;
}
cout << endl;
return status;
}
