Are you using VB9? If so, I'd use a lambda expression to create a Comparer(Of Schedule_PayItem). Otherwise, write a short class to implement IComparer(Of Schedule_PayItem). pass whichever one you've got into List.Sort.
An example for the lambda expression (untested):
m_equipmentList.Sort(Function(p1, p2) p1.ResourceID.CompareTo(p2.ResourceID))
And for the IComparer(Of Schedule_PayItem):
Public Class PayItemResourceComparer Implements IComparer(Of Schedule_PayItem) Public Function Compare(ByVal p1 As Schedule_PayItem, _ ByVal p2 As Schedule_PayItem) As Integer Return p1.ResourceID.CompareTo(p2.ResourceID) End Function End Class ... m_equipmentList.Sort(New PayItemResourceComparer)