Matricial distribution - vba

Question

I have a list of projects with hours to be consumed, distributed linearly through the months:
Hours Aug Sep Oct Nov Dec
100 20 20 20 20 20
200 40 40 40 40 40
300 60 60 60 60 60
600 120 120 120 120 120
Some projects will end in different months, so it shoudn't mark any hour in the next months (must be 0):
Hours Aug Sep Oct Nov Dec End
100 33.3 33.3 33.3 0 0 Oct
200 50 50 50 50 0 Nov
300 60 60 60 60 60 Dec
600 143.3 143.3 143.3 110 60
However, we have to keep the proportion of 20% of the sum (20% * 600 = 120. I've put 20% because we have 5 months, but it could be different percentages) on each month, so:
Hours Aug Sep Oct Nov Dec End
100 20 30 50 0 0 Oct
200 60 50 30 60 0 Nov
300 40 40 40 60 120 Dec
600 120 120 120 120 120
I have a Sudoku-like problem here, where I need to respect the proportion of the column and keep the sum of the line on each project. I've tried in many ways (VBA or functions) to make this distribution, but I've failed so far. I believe someone has crossed with this problem before, so is there a way of doing this distribution programatically? Is there a name for this kind of distribution?

Answer 1

See the image below. Once you have the marginal sums filled in, enter this formula into B2 and fill in the rest of the table (enter it as an array formula with ctrl+shift+enter):
=IF(MATCH($H2,$B$1:$F$1,0)<COLUMNS($B$1:B$1),0,($A2-SUM(C2:$G2))/(SUM(IF(MATCH($H$2:$H$4,$B$1:$F$1,0)<COLUMNS($B$1:B$1),0,$A$2:$A$4))-SUM(IF(MATCH($H$2:$H$4,$B$1:$F$1,0)<COLUMNS($B$1:B$1),0,C$2:$G$4)))*B$5)
The example given will not have a unique solution, so the aim with the above formula is to balance the hours by starting at the end and moving backwards in time while applying hours proportionally to how many hours are left on each project. For example, after resolving Dec, the project on row 2 still has 200 hours to allocate and the project on row 3 still has 180 hours to allocate. The formula will therefore apply 120 * 200 / (200 + 180) hours in Nov from the project on row 2 and 120 * 180 / (200 + 180) hours from the project in row 3.
This methodology assumes that all projects start at the same time. If this assumption doesn't hold, VBA would probably be the way to go. I would sort the months by the number of active projects, smallest to largest, then apply the same sort of calculation as here.

Answer 2

I'm not 100% sure I got your question right, but hopefully yes because it took me quite a lot of time. It actually looks deceptively easy, but is in fact quite tricky.
So let's presume we have this table:
Now if I got it right, we basically want to count, how many hours we
used up already, and now we want to distribute what we have left
depending on the unused (empty) months
So, for example, in Row 3 (100 hours) we don't want to distribute any hours, because we already used up all 100 out of 100 hours
In the next row (4), we want to distribute 115 hours (200-85) to the remaining 2 cells => which would leave us with 57.5 hours per month left on shift
and et cetera...
Under presumption, that's what you want the algorhytm to do:
Private Sub divide_time()
Dim tbl As ListObject: Set tbl = Sheets("Sheet1").ListObjects("Table1")
Dim hour_dist() As Integer
ReDim hour_dist(1 To 3)
' first we need to learn how many hours total we have available per project
For i = 1 To 3
With tbl.ListColumns(1)
hour_dist(i) = .Range(i + 1) ' we store each value into an array per project
End With
Next i
Dim current As Double
Dim sumof As Double
Dim hours_left As Double
Dim empty_counter As Integer
For i = 1 To 3
'we reset all of the counters per row
sumof = 0
empty_counter = 0
'looping through all the column values in the row
For j = 2 To 6
current = tbl.ListRows(1).Range(i, j)
sumof = sumof + current ' we get a sum of the current values in the row
If (current = 0) Then 'if there is an empty cell, we keep track of it _
(so we know into how many cells we can still divide the remaining time)
empty_counter = empty_counter + 1
End If
Next j
' so we get how many hours we have left for the project _
in comparison to how many months are free to distribute
hours_left = (hour_dist(i) - sumof)
'if we also want to store the info, _
'what month we ended on before we distribute the remaining hours
If (hours_left = 0) Then
Select Case empty_counter
Case 0
tbl.ListRows(1).Range(i, 7) = "Dec"
Case 1
tbl.ListRows(1).Range(i, 7) = "Nov"
Case 2
tbl.ListRows(1).Range(i, 7) = "Oct"
Case 3
tbl.ListRows(1).Range(i, 7) = "Sep"
Case 4
tbl.ListRows(1).Range(i, 7) = "Aug"
End Select
Else
tbl.ListRows(1).Range(i, 7) = "Dec"
End if
If (empty_counter <> 0) Then '( we dont want to be dividing by 0 )
For n = 6 To (6 - empty_counter + 1) Step -1
'for each month we divide what we have left _
depending on the % of the months available
tbl.ListRows(1).Range(i, n) = (hours_left / empty_counter)
Next n
End If
' and we loop it for each and every row
Next i
End Sub
The resulting table will look like this:

Answer 3

I guess you need to think "backwards".
First distribute hours among active projects in month n (December).
Deduct these hours from respective project and move to month n-1, etc.