Vendor who ships partials

[James Gruetzner]

The gurus here have been helpful in the past; I hope I'm not overstaying my
welcome by asking another question.

Say I place an order with a vendor, Alice, Ltd.:

5 Widgets @ $10.00 EA = $50.00
5 Thingas @ $15.00 EA = $75.00
5 Doodads @ $5.00 EA = $25.00
---
TOTAL:  $150.00

Alice, Ltd., comes back with:
 Insurance for items:  $1.00
 Shipping:                 $15.00
---
Please pay $166.00.

So . . . check #9876 gets written and sent to Alice.  (Alice won't ship
until she has received payment:  unfortunately, that's pretty much the way
it goes in the business.)

I receive a shipment:
4 Widgets @ $10.00 EA = $40.00
1 Widget on backorder
5 Thingas on backorder
5 Doodads no longer carried -- items cancelled
 Insurance:  $0.50
 Shipping $6.00
TOTAL:  $46.50
You have a credit of $119.50

So . . . what is the recommended way of handling this?  I still have some
hair left, and don't want to pull too much more out.

Do I generate an invoice/bill to Liabilities:A/P:Alice for the order, and
they pay it?  How do I handle the partial shipment and backorder?

Again, thanks for the help,
   James