Try our new documentation site (beta).
Filter Content By
Version
Text Search
${sidebar_list_label} - Back
Filter by Language
workforce5_vb.vb
' Copyright 2021, Gurobi Optimization, LLC ' ' Assign workers to shifts; each worker may or may not be available on a ' particular day. We use multi-objective optimization to solve the model. ' The highest-priority objective minimizes the sum of the slacks ' (i.e., the total number of uncovered shifts). The secondary objective ' minimizes the difference between the maximum and minimum number of ' shifts worked among all workers. The second optimization is allowed ' to degrade the first objective by up to the smaller value of 10% and 2 */ Imports System Imports Gurobi Class workforce5_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", "Tobi"} 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} ' 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}, _ {0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1}, _ {1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}} ' Create environment Dim env As New GRBEnv() ' Create initial model Dim model As New GRBModel(env) model.ModelName = "workforce5_vb" ' Initialize assignment decision variables: ' x[w][s] == 1 if worker w is assigned to shift s. ' This is no longer a pure assignment model, so we must ' use binary variables. 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), 0, GRB.BINARY, _ String.Format("{0}.{1}", Workers(w), Shifts(s))) Next Next ' Slack variables for each shift constraint so that the shifts can ' be satisfied Dim slacks As GRBVar() = New GRBVar(nShifts - 1) {} For s As Integer = 0 To nShifts - 1 slacks(s) = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, _ String.Format("{0}Slack", Shifts(s))) Next ' Variable to represent the total slack Dim totSlack As GRBVar = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, "totSlack") ' Variables to count the total shifts worked by each worker Dim totShifts As GRBVar() = New GRBVar(nWorkers - 1) {} For w As Integer = 0 To nWorkers - 1 totShifts(w) = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, _ String.Format("{0}TotShifts", Workers(w))) Next Dim lhs As GRBLinExpr ' Constraint: assign exactly shiftRequirements[s] workers ' to each shift s, plus the slack For s As Integer = 0 To nShifts - 1 lhs = New GRBLinExpr() lhs.AddTerm(1.0, slacks(s)) For w As Integer = 0 To nWorkers - 1 lhs.AddTerm(1.0, x(w, s)) Next model.AddConstr(lhs, GRB.EQUAL, shiftRequirements(s), Shifts(s)) Next ' Constraint: set totSlack equal to the total slack lhs = New GRBLinExpr() lhs.AddTerm(-1.0, totSlack) For s As Integer = 0 To nShifts - 1 lhs.AddTerm(1.0, slacks(s)) Next model.AddConstr(lhs, GRB.EQUAL, 0, "totSlack") ' Constraint: compute the total number of shifts for each worker For w As Integer = 0 To nWorkers - 1 lhs = New GRBLinExpr() lhs.AddTerm(-1.0, totShifts(w)) For s As Integer = 0 To nShifts - 1 lhs.AddTerm(1.0, x(w, s)) Next model.AddConstr(lhs, GRB.EQUAL, 0, String.Format("totShifts{0}", Workers(w))) Next ' Constraint: set minShift/maxShift variable to less <=/>= to the ' number of shifts among all workers Dim minShift As GRBVar = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, "minShift") Dim maxShift As GRBVar = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, "maxShift") model.AddGenConstrMin(minShift, totShifts, GRB.INFINITY, "minShift") model.AddGenConstrMax(maxShift, totShifts, -GRB.INFINITY, "maxShift") ' Set global sense for ALL objectives model.ModelSense = GRB.MINIMIZE ' Set primary objective model.SetObjectiveN(totSlack, 0, 2, 1.0, 2.0, 0.1, "TotalSlack") ' Set secondary objective model.SetObjectiveN(maxShift - minShift, 1, 1, 1.0, 0, 0, "Fairness") ' Save problem model.Write("workforce5_vb.lp") ' Optimize Dim status As Integer = _ solveAndPrint(model, totSlack, nWorkers, Workers, totShifts) If status <> GRB.Status.OPTIMAL Then Return End If ' Dispose of model and environment model.Dispose() env.Dispose() Catch e As GRBException Console.WriteLine("Error code: {0}. {1}", e.ErrorCode, e.Message) End Try End Sub Private Shared Function solveAndPrint(ByVal model As GRBModel, _ ByVal totSlack As GRBVar, _ ByVal nWorkers As Integer, _ ByVal Workers As String(), _ ByVal totShifts As GRBVar()) As Integer model.Optimize() Dim status As Integer = model.Status If status = GRB.Status.INF_OR_UNBD OrElse _ status = GRB.Status.INFEASIBLE OrElse _ status = GRB.Status.UNBOUNDED Then Console.WriteLine("The model cannot be solved " & _ "because it is infeasible or unbounded") Return status End If If status <> GRB.Status.OPTIMAL Then Console.WriteLine("Optimization was stopped with status {0}", status) Return status End If ' Print total slack and the number of shifts worked for each worker Console.WriteLine(vbLf & "Total slack required: {0}", totSlack.X) For w As Integer = 0 To nWorkers - 1 Console.WriteLine("{0} worked {1} shifts", Workers(w), totShifts(w).X) Next Console.WriteLine(vbLf) Return status End Function End Class