The Economically Impossible Optimum Faring

Let's imagine you've chosen 3 flights for your trip: A, B and C, how can the system (i.e. the GDS) price them ?
1 ticket:
ABC on the same ticket
2 tickets:
A+BC
AC+B
AB+C
3 tickets:
A+B+C

that's already 5 choices. For 4 flights, this number raises to 15, 5, to 52...
here is the table summing the total number of combinations per number of flights... you quickly see that the system can not search for all the combinations in a reasonable amount of time (i.e. what you are OK to wait to get your fare)

Number of flights (legs)	number of combinations
1	1
2	2
3	5
4	15
5	52
6	203
7	877
8	4,140
9	21,147
10	115,975
11	678,570
12	4,213,597
13	27,644,437
14	190,899,322
15	1,382,958,545

The associated VB code:
Function myf(nombre As Long) As Long
Dim i As Integer
i = 0
If nombre <= 1 Then
myf = 1
Else
myf = myf(nombre - 1)
For i = 1 To nombre - 1 Step 1
myf = myf + myf(nombre - 1 - i) * Factorielle(nombre - 1) / (Factorielle(i) * Factorielle(nombre - 1 - i))
Next i
End If
End Function

 Thus manually "breaking" the list of flights in smaller groups (using human knowledge such as Airline alliance, airline partnership, codeshare and so on) can help a lot, in complex trip, to find an optimum fare, better than what the system could offer you.

So far, I haven't found a website or tool using these information to get an optimum fare, if you know one, please share it !

Way more details can be found here.