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### workforce3_vb.vb

' Copyright 2022, 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.

Imports System
Imports Gurobi

Class workforce3_vb
Shared Sub Main()
Try

' Sample data
' Sets of days and workers
Dim Shifts As String() = New String() {"Mon1", "Tue2", "Wed3", "Thu4", _
"Fri5", "Sat6", "Sun7", "Mon8", _
"Tue9", "Wed10", "Thu11", _
"Fri12", "Sat13", "Sun14"}
Dim Workers As String() = New String() {"Amy", "Bob", "Cathy", "Dan", _
"Ed", "Fred", "Gu"}

Dim nShifts As Integer = Shifts.Length
Dim nWorkers As Integer = Workers.Length

' Number of workers required for each shift
Dim shiftRequirements As Double() = 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
Dim pay As Double() = New Double() {10, 12, 10, 8, 8, 9, 11}

' Worker availability: 0 if the worker is unavailable for a shift
Dim availability As Double(,) = 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
Dim env As New GRBEnv()
Dim model As New GRBModel(env)

model.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.
Dim x As GRBVar(,) = New GRBVar(nWorkers - 1, nShifts - 1) {}
For w As Integer = 0 To nWorkers - 1
For s As Integer = 0 To nShifts - 1
x(w, s) = model.AddVar(0, availability(w, s), pay(w), _
GRB.CONTINUOUS, _
Workers(w) & "." & Shifts(s))
Next
Next

' The objective is to minimize the total pay costs
model.ModelSense = GRB.MINIMIZE

' Constraint: assign exactly shiftRequirements[s] workers
' to each shift s
For s As Integer = 0 To nShifts - 1
Dim lhs As GRBLinExpr = 0.0
For w As Integer = 0 To nWorkers - 1
Next
Next

' Optimize
model.Optimize()
Dim status As Integer = model.Status
If status = GRB.Status.UNBOUNDED Then
Console.WriteLine("The model cannot be solved " & _
"because it is unbounded")
Return
End If
If status = GRB.Status.OPTIMAL Then
Console.WriteLine("The optimal objective is " & model.ObjVal)
Return
End If
If (status <> GRB.Status.INF_OR_UNBD) AndAlso _
(status <> GRB.Status.INFEASIBLE) Then
Console.WriteLine("Optimization was stopped with status " & _
status)
Return
End If

' Relax the constraints to make the model feasible
Console.WriteLine("The model is infeasible; relaxing the constraints")
Dim orignumvars As Integer = model.NumVars
model.FeasRelax(0, False, False, True)
model.Optimize()
status = model.Status
If (status = GRB.Status.INF_OR_UNBD) OrElse _
(status = GRB.Status.INFEASIBLE) OrElse _
(status = GRB.Status.UNBOUNDED) Then
Console.WriteLine("The relaxed model cannot be solved " & _
"because it is infeasible or unbounded")
Return
End If
If status <> GRB.Status.OPTIMAL Then
Console.WriteLine("Optimization was stopped with status " & status)
Return
End If

Console.WriteLine(vbLf & "Slack values:")
Dim vars As GRBVar() = model.GetVars()
For i As Integer = orignumvars To model.NumVars - 1
Dim sv As GRBVar = vars(i)
If sv.X > 1E-06 Then
Console.WriteLine(sv.VarName & " = " & sv.X)
End If
Next

' Dispose of model and environment
model.Dispose()

env.Dispose()
Catch e As GRBException
Console.WriteLine("Error code: " + e.ErrorCode & ". " + e.Message)
End Try
End Sub
End Class

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