Database join in the '60s with tape / punch cards only?

We are a large company, selling frobnication services to tens of thousands of customers via phone calls. Orders get recorded on punch cards, featuring

a customer ID
a date
the dollar amount of frobnication bought.

In order to process these into monthly bills to our users, we're ready to buy computing equipment modern enough for the '60s. I presume we're going to store our user database on a tape (... since... that's where you can store a lot of data with 60s tech, right?).

Sales record punch cards are coming in unsorted. Even if the records on tape are sorted by e.g. customer ID, doing one "seek" / lookup for each punch card / customer ID coming in (to update e.g. a "sum" amount) would be very slow. Meanwhile, if you have e.g. 256k of RAM (even less?), significant parts of the data set just won't fit.

My question is: how can this database operation be done in practice? Do you sort the punch cards first & then go through the tape linearly? How do you even sort punch cards? Or do you copy all of them to a tape first? Do you need multiple batch jobs to do all of this? How much of this is code we'll have to write vs. something that's coming with the OS?

(... yes I've heard about those fridge-size devices with spinning metal disks that can randomly seek many times a second; I don't think we'll be able to afford those.)

Solution

In the 60's you would most likely

You store your data in a Master-File sorted in Key sequence
Sort the Punch-Cards to a temporary Disk file.
Do a Master-File Update using the Temporary Disk file (transaction File) and the master file.

They might of used a Indexed-file or some Database (e.g. IMS) if online access is required.

Master File Update

For a Master File update both files need to be sorted in to the same sequence and you match on keys, it writes an updated master file using the details from the two. It Basically like a SQL Outer join.

Logic

Read Master-File
Read Transaction-file

While not eof-master-file and not eof-Transaction-file
   if Transaction-file-key < Master-File-key
      Write transaction-file details into updated-master-file
      Read Transaction-file
   else_if Transaction-file-key == Master-File-key
      update Master-File-Record with Transaction-file-details
      Write updated-master-file-record to updated-master-file
      Read Transaction-file
   else
      Write master-file-record to updated-master-file
      Read Master-File
   end_if
end_while

Process Remaining Transaction-file records
Process Remaining Master-file records