Determining Combinations to Make a Total

Suppose you have a worksheet with three columns of data. The first column has in sequential order each letter of the alphabet, A through Z. The second column contains a number of occurrences that correlates with the letter in the alphabet. The third column contains a number of hours that correlates with the letter in the alphabet.

What if you want to distribute, as evenly as possible, a combination of the alphabet letters into four groups based on the third column (hours)? For example, if the sum of all the hours for each letter of the alphabet is 4,000 hours, you want to come up with a combination that would segregate the alphabet so that each one of the four groups would have around 1,000 hours per group.

This is actually a well-known problem in the field of discrete mathematics. A variety of algorithms have been developed to provide solutions, and there are certain programming languages (such as LISP) that greatly facilitate creating tree structures that can "search" for optimal solutions.

In this case, however, a simple approach is best, and that involves using a macro. Let's assume that you have your data in columns A through C. The following macro will analyze the range you specify and return a combination of values that fulfill your requirements.

Function DoDist(sRaw As Range, _
  iTCol As Integer, _
  iBuckets As Integer, _
  iWanted As Integer, _
  iRetCol As Integer) As String

    Dim lGTotal As Long
    Dim lPerBucket As Long
    Dim lCells() As Long
    Dim sRet() As String
    Dim lBk() As Long
    Dim sBk() As String
    Dim lTemp As Long
    Dim sTemp As String
    Dim J As Integer
    Dim K As Integer
    Dim L As Integer

    Application.Volatile
    ReDim lCells(sRaw.Rows.Count)
    ReDim sRet(sRaw.Rows.Count)
    ReDim lBk(iBuckets)
    ReDim sBk(iBuckets)

    lGTotal = 0
    For J = 1 To sRaw.Rows.Count
        lCells(J) = sRaw(J, iTCol)
        lGTotal = lGTotal + lCells(J)
        sRet(J) = sRaw(J, iRetCol)
    Next J

    For J = 1 To sRaw.Rows.Count - 1
        For K = J + 1 To sRaw.Rows.Count
            If lCells(J) < lCells(K) Then
                lTemp = lCells(J)
                lCells(J) = lCells(K)
                lCells(K) = lTemp
                sTemp = sRet(J)
                sRet(J) = sRet(K)
                sRet(K) = sTemp
            End If
        Next K
    Next J

    lPerBucket = lGTotal / iBuckets
    For J = 1 To sRaw.Rows.Count
        L = iBuckets
        For K = iBuckets To 1 Step -1
            If lBk(K) <= lBk(L) Then L = K
        Next K
        lBk(L) = lBk(L) + lCells(J)
        sBk(L) = sBk(L) & sRet(J) & ", "
    Next J

    For J = 1 To iBuckets
        If Right(sBk(J), 2) = ", " Then
            sBk(J) = Left(sBk(J), Len(sBk(J)) - 2)
        End If
        sBk(J) = sBk(J) & " (" & lBk(J) & ")"
    Next J

    DoDist = sBk(iWanted)
End Function

Notice that this function is passed five parameters. The first is the range that you want evaluated, the second is the offset of the column within that range that should be totaled, the third is the number of "buckets" you want to use in the evaluation, the fourth is the number of the bucket that you want to return, and the fifth is the offset of the column (in the specified range) that contains the values you want returned.

What the macro does is to grab all the values in the column you want totaled, and then sort them in descending order. These values, from largest to smallest, are then distributed among however many "buckets" you specified that there should be. The number is always added to the bucket that contains the smallest total. The string that is returned by the function represents the return values (whatever is in each cell of the column specified by the fifth parameter) and the total of the bucket.

For instance, if you wanted to evaluate the range A1:C:26, you wanted the distribution to be based on the values in the third column of the range (column C), you wanted there to be four buckets in the analysis, you wanted the third bucket returned, and you wanted to have the function return whatever is in column A of the range, then you would use the following to call the function:

=DoDist(A1:C26,3,4,3,1)