The Economic Lot Scheduling Problem (ELSP) was first described (and named) in 1958 by professor Jack D. Rogers at the University of California, Berkeley, US.(ref.)

It's an important everyday practical issue for almost any manufacturing company involved in planning what to manufacture, when to manufacture it, and how much to manufacture.

The SELSP deals with the make-to-stock production of multiple standardized products on a single machine with limited capacity under random demands, possibly random setup times and possibly random production times. The main task of a production manager in this setting is the construction of a production plan for the machine."

Source : European Journal of Operational Research, Volume 210, Issue 1, Pages 1-9

To date, no exact mathematical formula has been discovered to 'solve' the problem with 100% accuracy in all situations. There are various computational algorithms which can give very usable results - but currently, the only way to obtain an exact result is to iterate through every possible combination of possibilities.