facility_vb.vb
' Copyright 2021, Gurobi Optimization, LLC ' ' 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
