Try our new documentation site.


workforce3_vb.vb


' Copyright 2019, 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
                    lhs.AddTerm(1.0, x(w, s))
                Next
                model.AddConstr(lhs = shiftRequirements(s), Shifts(s))
            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

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search