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workforce2_vb.vb
' Copyright 2024, 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, use IIS iteratively to ' find all conflicting constraints. Imports System Imports System.Collections.Generic Imports Gurobi Class workforce2_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 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") Exit Sub End If If status = GRB.Status.OPTIMAL Then Console.WriteLine("The optimal objective is " & model.ObjVal) Exit Sub End If If (status <> GRB.Status.INF_OR_UNBD) AndAlso _ (status <> GRB.Status.INFEASIBLE) Then Console.WriteLine("Optimization was stopped with status " & status) Exit Sub End If ' Do IIS Console.WriteLine("The model is infeasible; computing IIS") Dim removed As LinkedList(Of String) = New LinkedList(Of String)() ' Loop until we reduce to a model that can be solved While True model.ComputeIIS() Console.WriteLine(vbLf & "The following constraint cannot be satisfied:") For Each c As GRBConstr In model.GetConstrs() If c.IISConstr = 1 Then Console.WriteLine(c.ConstrName) ' Remove a single constraint from the model removed.AddFirst(c.ConstrName) model.Remove(c) Exit For End If Next Console.WriteLine() model.Optimize() status = model.Status If status = GRB.Status.UNBOUNDED Then Console.WriteLine("The model cannot be solved " & _ "because it is unbounded") Exit Sub End If If status = GRB.Status.OPTIMAL Then Exit While End If If (status <> GRB.Status.INF_OR_UNBD) AndAlso _ (status <> GRB.Status.INFEASIBLE) Then Console.WriteLine("Optimization was stopped with status " & _ status) Exit Sub End If End While Console.WriteLine(vbLf & "The following constraints were removed " & _ "to get a feasible LP:") For Each s As String In removed Console.Write(s & " ") Next Console.WriteLine() ' 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