Filter Content By
Version

### workforce5_vb.vb

' Copyright 2022, 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()
For w As Integer = 0 To nWorkers - 1
Next
Next

' Constraint: set totSlack equal to the total slack
lhs = New GRBLinExpr()
For s As Integer = 0 To nShifts - 1
Next

' Constraint: compute the total number of shifts for each worker
For w As Integer = 0 To nWorkers - 1
lhs = New GRBLinExpr()
For s As Integer = 0 To nShifts - 1
Next
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")

' 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


Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

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.
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.