This one will take me a while. The client has chosen to not have a procedure that helps in suggesting, but will to it all by hand, since they expect it will be not that often that real difficult problems arise…

I will try to built this in my spare time though… It sounds like an interesting problem that should be solvable, My basic idea: If I can solve it manually, all I need to do is analyse what I do, and explain that to the stupid computer

The ‘basic’ code by Kccrosser is a great start, and recursion is the only viable option here I suppose…

Thank you, and I’ll return here when I’ve had time to complete this (or need help )

I thought about also rolling up all the credit invoices first and “adding” that amount to the payment, then only evaluating the invoices with amounts due (so you can stop evaluating when the sum of the invoices exceeds the payment+credit amount), but that will fail if one or more of the credit amounts was NOT taken into account in the payment.

A more complex algorithm may be best, like (all comparisons are done in oldest-first order):
1. Try to apply the payment to a single invoice – this requires only N comparisons.
2. If there are any outstanding credit invoices, add the sum of the outstanding credit invoices to the payment and try to apply the payment to a single invoice – another N comparisons.
3. If there are multiple credit invoices outstanding, try
For i = 1 to num_credit_invoices
credit_sum = sum(credit_invoice1..credit_invoicei)
payment_sum = payment + credit_sum
run recursive algorithm on amount due invoices – stopping the recursion whenever the sum of the invoices exceeds the payment_sum (order N^2 evaluations)
4. Run the full recursive algorithm on the first X (10-12?) invoices.
5. Give up (or do a partial payment).

Here’s my first notion. What if I do a pre-check on all the available invoices. should there not be any negative ones (no credit invoices, which will be the case most of the time), I could perhaps choose to order the invoices from high to low and stop recursion as soon as I would exceed the total of the payment…

The might be some other tricks to speed things up be using some kind of prediction…. let me sleep on it

Wow… that is some answer, and some code for me to try and comprehend! It’s close to midnight here, will spend tomorrow trying to get this to work for me.

Thank you so much!

Thanks for your input!

I agree with you that this is not a desired *first* way to do things. But, when all automatic fail-save options fail, I need to let someone book the invoices manually, and I would like to make this manual booking easier by being able to suggest possible combinations that will match up to the desired amount.
Obviously, I will only be searching through invoices that have passed the ‘do they belong to this client’ check.

Usually, our invoices will not be neatly rounded to $50 amounts (that would make matching them by hand very doable), but they will be amounts like $79.32 and $182.14 etc…

I’m curious to hear if there are any mathematical or programming algorithms that would be able to help me solve this…

Say you have 5 invoices: 1) $100, 2) $100, 3) $50, 4)$50, 5) $150

If you want to apply a $200 payment, are you going to apply it to invoices 1 and 2, or 1 and 3 and 4, or 3 and 5, or 4 and 5, etc ?

I think some policy should be defined, so you don’t have to guess what invoices you have to apply the payment to.