Re: Combinations & Permutations..... sort of

Having faced this problem of applying payments to outstanding invoices, in the end I found that the best first try was to group invoices by billing period. The second try was to start with most recent billing period and working back towards the old items. Since most customers paid their bills once a month, that proved to be pretty effective. There are very few partial payments; the ball-ups generally were with disputed bills which gravitated to the past due columns.

From: roger.harman@xxxxxxxxxxx
To: rpg400-l@xxxxxxxxxxxx
Subject: Combinations & Permutations..... sort of
Date: Mon, 29 Sep 2014 17:17:55 -0700

Put your math hats on......
I'm looking at a means to *attempt* to auto-match payments to invoices. We do not want to apply payments to oldest first and end up with a partial payment or credit leftover.
Pick an arbitrary number of invoices for the attempt - say 10.
Any combination of 1 or more of these 10 invoices that total the payment amount would be considered a match.
Could be invoice 1, or 2, or.... Could be invoices 2 and 5 and 8..... etc.
I assume it's going to have to be a brute force approach but I'm stumped on the total # of possible matches. Combinations & permutations I understand (3 out of 10, etc) but this "1 or 2 or (1 and 2) or (2 and 5 and 8)" is giving me a mind block. I do know it's a big number and I'll likely cut back the sampling size.
Any suggestions or clarifications would be very welcome.
Thanks.


Roger Harman


COMMON Certified Application
Developer – ILE RPG on IBM i on Power