Equally divide tasks

[Mindstorms]

Hi,

I have a problem with dividing tasks between people. I have 4 tasks, and somewhere between 4 and 11 people to do these tasks on a weekly basis. If there are 11 people, you can just loop through the tasks and the people, and everyone does every task the same amount of times. However, if you have 10 people and loop through the chores, every person gets the same two tasks over and over again, which is unfair. What would be the correct way of dividing the tasks for the even amount of people?

Regards,
Mindstorms

[techgnome]

Record who you started with, and each time you start, start with the next person.... so the first time:
1,2,3,4,5,6,7,8,9,10... then the next time, start with person 2... 2,3,4,5,6,7,8,9,10,1... and then 3... and so on,...

-tg

[Mindstorms]

Interesting point. I should have mentioned that I would also like to divide the workload equally in time. That is, not doing chores for weeks in a row and then weeks of nothing. With 11 people, the scheme now looks like:

Time	Person 1	Person 2	Person 3	Person 4	Person 5	Person 6	Person 7	Person 8	Person 9	Person 10	Person 11
Week 1	Task A	Task B	Task C	Task D
Week 2					Task A	Task B	Task C	Task D
Week 3	Task D								Task A	Task B	Task C
Week 4		Task A	Task B	Task C	Task D
Week 5						Task A	Task B	Task C	Task D
Week 6	Task C	Task D								Task A	Task B
Week 7			Task A	Task B	Task C	Task D
Week 8							Task A	Task B	Task C	Task D
Week 9											Task A
Week 10	Task B	Task C	Task D
Week 11				Task A	Task B	Task C	Task D
Week 12								Task A	Task B	Task C	Task D

But if you have an even amount of people, you have to somehow swap some tasks to recreate this sort of scheme.

[passel]

Well, there may be some easier way to do it, but off the top of my head I would create a list for each person containing the tasks they can do.
Then I would loop through the people, and inside that loop, loop through the tasks to be done. If the person can do one of the tasks (i.e. it is still in his list of tasks) then assign the task to that person.
That would spread the tasks, and a given person wouldn't do the same task again until he has done all of them.

Example code that prints out the person (0 to x) and task (1 to 4) for each person on one line.
It arbitrarily prints 10 lines of schedule for the number of persons selected (in the immediate or output window, depending on your IDE setup) so you can see the pattern of tasks being assigned.

  Private Sub Button1_Click(sender As System.Object, e As System.EventArgs) Handles Button1.Click
    Dim taskLists(10) As List(Of Integer)
    Dim selectedTask As Integer

    For i As Integer = 0 To 10  'create 11 lists for up to 11 people to be tasked
      taskLists(i) = New List(Of Integer)
    Next

    Dim currenttasks As New List(Of Integer)  'tasks to be scheduled
    currenttasks.AddRange({1, 2, 3, 4})

    Dim NumOfPeople As Integer = 10   'Change this from 4 to 11 to create a schedule

    For k As Integer = 1 To 10   'arbitrary, generates 10 lines of schedule for NumOfPeople
      For i As Integer = 0 To NumOfPeople - 1
        If taskLists(i).Count = 0 Then taskLists(i).AddRange({1, 2, 3, 4}) 'If a person has no tasks available, refresh his list
        For Each task As Integer In currenttasks                          'for the four tasks to be scheduled
          If taskLists(i).Contains(task) Then                             '  If the current person hasn't done this task yet this cycle
            taskLists(i).Remove(task)                                     '    Remove this task from the persons list
            currenttasks.Remove(task)                                     '    Remove this task from the list of tasks to be completed
            selectedTask = task                                           '    Note the task to be done by this person for the printout
            Exit For
          End If
        Next
        If currenttasks.Count = 0 Then currenttasks.AddRange({1, 2, 3, 4}) 'If all tasks have been scheduled, refresh the task list
        Debug.Write(String.Format("{0},{1} : ", i, selectedTask))          'Write which person is doing what task
      Next
      Debug.WriteLine("")                                                  'All persons have been assign a task, start a new line
    Next
  End Sub

Change the Dim NumOfPeople line to try different numbers of people.
Example output with 10 people

0,1 : 1,2 : 2,3 : 3,4 : 4,1 : 5,2 : 6,3 : 7,4 : 8,1 : 9,2 : 
0,3 : 1,4 : 2,1 : 3,2 : 4,3 : 5,4 : 6,1 : 7,2 : 8,3 : 9,4 : 
0,2 : 1,1 : 2,4 : 3,3 : 4,2 : 5,1 : 6,4 : 7,3 : 8,2 : 9,1 : 
0,4 : 1,3 : 2,2 : 3,1 : 4,4 : 5,3 : 6,2 : 7,1 : 8,4 : 9,3 : 
0,1 : 1,2 : 2,3 : 3,4 : 4,1 : 5,2 : 6,3 : 7,4 : 8,1 : 9,2 : 
0,3 : 1,4 : 2,1 : 3,2 : 4,3 : 5,4 : 6,1 : 7,2 : 8,3 : 9,4 : 
0,2 : 1,1 : 2,4 : 3,3 : 4,2 : 5,1 : 6,4 : 7,3 : 8,2 : 9,1 : 
0,4 : 1,3 : 2,2 : 3,1 : 4,4 : 5,3 : 6,2 : 7,1 : 8,4 : 9,3 : 
0,1 : 1,2 : 2,3 : 3,4 : 4,1 : 5,2 : 6,3 : 7,4 : 8,1 : 9,2 : 
0,3 : 1,4 : 2,1 : 3,2 : 4,3 : 5,4 : 6,1 : 7,2 : 8,3 : 9,4 :

Of course, you're not limited to 4 to 11 people, here is the print out for 3 and 2 people

0,1 : 1,2 : 2,3 : 
0,4 : 1,1 : 2,2 : 
0,3 : 1,4 : 2,1 : 
0,2 : 1,3 : 2,4 : 
0,1 : 1,2 : 2,3 : 
0,4 : 1,1 : 2,2 : 
0,3 : 1,4 : 2,1 : 
0,2 : 1,3 : 2,4 : 
0,1 : 1,2 : 2,3 : 
0,4 : 1,1 : 2,2 :
 
0,1 : 1,2 : 
0,3 : 1,4 : 
0,2 : 1,1 : 
0,4 : 1,3 : 
0,1 : 1,2 : 
0,3 : 1,4 : 
0,2 : 1,1 : 
0,4 : 1,3 : 
0,1 : 1,2 : 
0,3 : 1,4 :

p.s. I'll leave it to you to figure out how to print it out by weeks.

[2kaud]

This doesn't take into account task (what?) preferences (if relevant?). Someone might like doing tasks A, B but not D, E but another may prefer C, E. Also nothing seems to be mentioned re the time constraints (person assigned has time to do it) or length of time (are they all the same?) for the various tasks. It also doesn't take into account the workload of the people. You might need one person to do more than one task one week - or to be able to move a scheduled task from say Person 1 to Person 7. What about holidays, absences etc etc? This sounds quite easy in theory, but in practice can get quite complicated!