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### workforce1_cs.cs

/* Copyright 2016, 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, use IIS to find a set of
conflicting constraints. Note that there may be additional conflicts
besides what is reported via IIS. */

using System;
using Gurobi;

class workforce1_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] =
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
for (int s = 0; s < nShifts; ++s) {
GRBLinExpr lhs = 0.0;
for (int w = 0; w < nWorkers; ++w)
}

// 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;
}

// Do IIS
Console.WriteLine("The model is infeasible; computing IIS");
model.ComputeIIS();
Console.WriteLine("\nThe following constraint(s) "
+ "cannot be satisfied:");
foreach (GRBConstr c in model.GetConstrs()) {
if (c.Get(GRB.IntAttr.IISConstr) == 1) {
Console.WriteLine(c.Get(GRB.StringAttr.ConstrName));
}
}

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

} catch (GRBException e) {
Console.WriteLine("Error code: " + e.ErrorCode + ". " +
e.Message);
}
}
}


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