workforce3_cs.cs
/* Copyright 2011, Gurobi Optimization, Inc. */
/* Assign workers to shifts; each worker may or may not be available on a
particular day. If the problem cannot be solved, add slack variables
to determine which constraints cannot be satisfied, and how much
they need to be relaxed. */
using System;
using System.Collections.Generic;
using Gurobi;
class workforce3_cs
{
static void Main()
{
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] =
model.AddVar(0, availability[w,s], pay[w], GRB.CONTINUOUS,
Workers[w] + "." + Shifts[s]);
}
}
// The objective is to minimize the total pay costs
model.Set(GRB.IntAttr.ModelSense, 1);
// Update model to integrate new variables
model.Update();
// Constraint: assign exactly shiftRequirements[s] workers
// to each shift s
LinkedList<GRBConstr> reqCts = new LinkedList<GRBConstr>();
for (int s = 0; s < nShifts; ++s) {
GRBLinExpr lhs = 0.0;
for (int w = 0; w < nWorkers; ++w)
lhs += x[w,s];
GRBConstr newCt =
model.AddConstr(lhs == shiftRequirements[s], Shifts[s]);
reqCts.AddFirst(newCt);
}
// Optimize
model.Optimize();
int status = model.Get(GRB.IntAttr.Status);
if (status == GRB.Status.UNBOUNDED) {
Console.WriteLine("The model cannot be solved "
+ "because it is unbounded");
return;
}
if (status == GRB.Status.OPTIMAL) {
Console.WriteLine("The optimal objective is " +
model.Get(GRB.DoubleAttr.ObjVal));
return;
}
if ((status != GRB.Status.INF_OR_UNBD) &&
(status != GRB.Status.INFEASIBLE)) {
Console.WriteLine("Optimization was stopped with status " + status);
return;
}
// Add slack variables to make the model feasible
Console.WriteLine("The model is infeasible; adding slack variables");
// Set original objective coefficients to zero
model.SetObjective(new GRBLinExpr());
// Add a new slack variable to each shift constraint so that the shifts
// can be satisfied
LinkedList<GRBVar> slacks = new LinkedList<GRBVar>();
foreach (GRBConstr c in reqCts) {
GRBColumn col = new GRBColumn();
col.AddTerm(1.0, c);
GRBVar newvar =
model.AddVar(0, GRB.INFINITY, 1.0, GRB.CONTINUOUS, col,
c.Get(GRB.StringAttr.ConstrName) + "Slack");
slacks.AddFirst(newvar);
}
// Solve the model with slacks
model.Optimize();
status = model.Get(GRB.IntAttr.Status);
if ((status == GRB.Status.INF_OR_UNBD) ||
(status == GRB.Status.INFEASIBLE) ||
(status == GRB.Status.UNBOUNDED)) {
Console.WriteLine("The model with slacks cannot be solved "
+ "because it is infeasible or unbounded");
return;
}
if (status != GRB.Status.OPTIMAL) {
Console.WriteLine("Optimization was stopped with status " + status);
return;
}
Console.WriteLine("\nSlack values:");
foreach (GRBVar sv in slacks) {
if (sv.Get(GRB.DoubleAttr.X) > 1e-6) {
Console.WriteLine(sv.Get(GRB.StringAttr.VarName) + " = " +
sv.Get(GRB.DoubleAttr.X));
}
}
// Dispose of model and env
model.Dispose();
env.Dispose();
} catch (GRBException e) {
Console.WriteLine("Error code: " + e.ErrorCode + ". " +
e.Message);
}
}
}