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workforce5_vb.vb
' Copyright 2020, 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
