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## Cloud Guide

Workforce3.java

### Workforce3.java

/* Copyright 2018, Gurobi Optimization, LLC */

/* Assign workers to shifts; each worker may or may not be available on a
particular day. If the problem cannot be solved, relax the model
to determine which constraints cannot be satisfied, and how much
they need to be relaxed. */

import gurobi.*;

public class Workforce3 {

public static void main(String[] args) {
try {

// Sample data
// Sets of days and workers
String Shifts[] =
new String[] { "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6",
"Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13",
"Sun14" };
String Workers[] =
new String[] { "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu" };

int nShifts = Shifts.length;
int nWorkers = Workers.length;

// Number of workers required for each shift
double shiftRequirements[] =
new double[] { 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 };

// Amount each worker is paid to work one shift
double pay[] = new double[] { 10, 12, 10, 8, 8, 9, 11 };

// Worker availability: 0 if the worker is unavailable for a shift
double availability[][] =
new double[][] { { 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 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } };

// Model
GRBEnv env = new GRBEnv();
GRBModel model = new GRBModel(env);
model.set(GRB.StringAttr.ModelName, "assignment");

// Assignment variables: x[w][s] == 1 if worker w is assigned
// to shift s. Since an assignment model always produces integer
// solutions, we use continuous variables and solve as an LP.
GRBVar[][] x = new GRBVar[nWorkers][nShifts];
for (int w = 0; w < nWorkers; ++w) {
for (int s = 0; s < nShifts; ++s) {
x[w][s] =
Workers[w] + "." + Shifts[s]);
}
}

// The objective is to minimize the total pay costs
model.set(GRB.IntAttr.ModelSense, GRB.MINIMIZE);

// Constraint: assign exactly shiftRequirements[s] workers
// to each shift s
for (int s = 0; s < nShifts; ++s) {
GRBLinExpr lhs = new GRBLinExpr();
for (int w = 0; w < nWorkers; ++w) {
}
}

// Optimize
model.optimize();
int status = model.get(GRB.IntAttr.Status);
if (status == GRB.UNBOUNDED) {
System.out.println("The model cannot be solved "
+ "because it is unbounded");
return;
}
if (status == GRB.OPTIMAL) {
System.out.println("The optimal objective is " +
model.get(GRB.DoubleAttr.ObjVal));
return;
}
if (status != GRB.INF_OR_UNBD &&
status != GRB.INFEASIBLE    ) {
System.out.println("Optimization was stopped with status " + status);
return;
}

// Relax the constraints to make the model feasible
System.out.println("The model is infeasible; relaxing the constraints");
int orignumvars = model.get(GRB.IntAttr.NumVars);
model.feasRelax(0, false, false, true);
model.optimize();
status = model.get(GRB.IntAttr.Status);
if (status == GRB.INF_OR_UNBD ||
status == GRB.INFEASIBLE  ||
status == GRB.UNBOUNDED     ) {
System.out.println("The relaxed model cannot be solved "
+ "because it is infeasible or unbounded");
return;
}
if (status != GRB.OPTIMAL) {
System.out.println("Optimization was stopped with status " + status);
return;
}

System.out.println("\nSlack values:");
GRBVar[] vars = model.getVars();
for (int i = orignumvars; i < model.get(GRB.IntAttr.NumVars); ++i) {
GRBVar sv = vars[i];
if (sv.get(GRB.DoubleAttr.X) > 1e-6) {
System.out.println(sv.get(GRB.StringAttr.VarName) + " = " +
sv.get(GRB.DoubleAttr.X));
}
}

// Dispose of model and environment
model.dispose();
env.dispose();

} catch (GRBException e) {
System.out.println("Error code: " + e.getErrorCode() + ". " +
e.getMessage());
}
}
}