facility_vb.vb


' Copyright 2017, Gurobi Optimization, Inc.
'
' Facility location: a company currently ships its product from 5 plants
' to 4 warehouses. It is considering closing some plants to reduce
' costs. What plant(s) should the company close, in order to minimize
' transportation and fixed costs?
'
' Based on an example from Frontline Systems:
' http://www.solver.com/disfacility.htm
' Used with permission.

Imports System
Imports Gurobi

Class facility_vb
    Shared Sub Main()
        Try

            ' Warehouse demand in thousands of units
            Dim Demand As Double() = New Double() {15, 18, 14, 20}

            ' Plant capacity in thousands of units
            Dim Capacity As Double() = New Double() {20, 22, 17, 19, 18}

            ' Fixed costs for each plant
            Dim FixedCosts As Double() = New Double() {12000, 15000, 17000, 13000, _
                                                       16000}

            ' Transportation costs per thousand units
            Dim TransCosts As Double(,) = New Double(,) {{4000, 2000, 3000, 2500, 4500}, _
                                                         {2500, 2600, 3400, 3000, 4000}, _
                                                         {1200, 1800, 2600, 4100, 3000}, _
                                                         {2200, 2600, 3100, 3700, 3200}}

            ' Number of plants and warehouses
            Dim nPlants As Integer = Capacity.Length
            Dim nWarehouses As Integer = Demand.Length

            ' Model
            Dim env As New GRBEnv()
            Dim model As New GRBModel(env)

            model.ModelName = "facility"

            ' Plant open decision variables: open(p) == 1 if plant p is open.
            Dim open As GRBVar() = New GRBVar(nPlants - 1) {}
            For p As Integer = 0 To nPlants - 1
                open(p) = model.AddVar(0, 1, FixedCosts(p), GRB.BINARY, "Open" & p)
            Next

            ' Transportation decision variables: how much to transport from
            ' a plant p to a warehouse w
            Dim transport As GRBVar(,) = New GRBVar(nWarehouses - 1, nPlants - 1) {}
            For w As Integer = 0 To nWarehouses - 1
                For p As Integer = 0 To nPlants - 1
                    transport(w, p) = model.AddVar(0, GRB.INFINITY, _
                                                   TransCosts(w, p), GRB.CONTINUOUS, _
                                                   "Trans" & p & "." & w)
                Next
            Next

            ' The objective is to minimize the total fixed and variable costs
            model.ModelSense = GRB.MINIMIZE

            ' Production constraints
            ' Note that the right-hand limit sets the production to zero if
            ' the plant is closed
            For p As Integer = 0 To nPlants - 1
                Dim ptot As GRBLinExpr = 0
                For w As Integer = 0 To nWarehouses - 1
                    ptot.AddTerm(1.0, transport(w, p))
                Next
                model.AddConstr(ptot <= Capacity(p) * open(p), "Capacity" & p)
            Next

            ' Demand constraints
            For w As Integer = 0 To nWarehouses - 1
                Dim dtot As GRBLinExpr = 0
                For p As Integer = 0 To nPlants - 1
                    dtot.AddTerm(1.0, transport(w, p))
                Next
                model.AddConstr(dtot = Demand(w), "Demand" & w)
            Next

            ' Guess at the starting point: close the plant with the highest
            ' fixed costs; open all others

            ' First, open all plants
            For p As Integer = 0 To nPlants - 1
                open(p).Start = 1.0
            Next

            ' Now close the plant with the highest fixed cost
            Console.WriteLine("Initial guess:")
            Dim maxFixed As Double = -GRB.INFINITY
            For p As Integer = 0 To nPlants - 1
                If FixedCosts(p) > maxFixed Then
                    maxFixed = FixedCosts(p)
                End If
            Next
            For p As Integer = 0 To nPlants - 1
                If FixedCosts(p) = maxFixed Then
                    open(p).Start = 0.0
                    Console.WriteLine("Closing plant " & p & vbLf)
                    Exit For
                End If
            Next

            ' Use barrier to solve root relaxation
            model.Parameters.Method = GRB.METHOD_BARRIER

            ' Solve
            model.Optimize()

            ' Print solution
            Console.WriteLine(vbLf & "TOTAL COSTS: " & model.ObjVal)
            Console.WriteLine("SOLUTION:")
            For p As Integer = 0 To nPlants - 1
                If open(p).X > 0.99 Then
                    Console.WriteLine("Plant " & p & " open:")
                    For w As Integer = 0 To nWarehouses - 1
                        If transport(w, p).X > 0.0001 Then
                            Console.WriteLine("  Transport " & _
                                              transport(w, p).X & _
                                              " units to warehouse " & w)
                        End If
                    Next
                Else
                    Console.WriteLine("Plant " & p & " closed!")
                End If

            Next

            ' Dispose of model and env
            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