It won't help having multiple bins all called 1A1. It will most likely be very confusing. As far as a computer system goes, you ought to add an autonumber key to uniquely identify that bin. (or use a composite key of bin +area). However, the problem is that if you have multiple bins called 1A1, then a BIN combobox will have multiple entries for 1A1, and you won't necessarily know which one to use. Anyway, ignore that for a moment
The atomic level of storage is the BIN, I assume. Products are allocated to BINs.
What you therefore need is table design that helps identify where the bin is located.
It may be sufficient to have a BIN located in an Area. Alternatively as JDraw said, if you have an Amazon size warehouse, you may need to pinpoint the bin within the warehouse, with a more complex structure.
Once you get a table design you can either "Zoom in " to a bin, by selecting more focussed sub-units of a warehouse.
warehouse, aisle, compartment, level, etc -----> BIN
if you want to start directly from a bin and work out then you need a bin reference that uniquely identifies the bin, and it would be better to have a system that did not have duplicate BIN references, in my opinion, for that reason.
But it's your company's system, and changing your BIN ID's would probably be a significant decision for someone to make.
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ignoring the BIN Descriptions, let's assume you add an autonumber to your bin table, (and indeed all tables) and that Area A, Bin 1A1 has a system ID of 24876. (just a unique number). If you have read about autonumbers, you may realize that they are a very efficient way of relating records in different tables. Importantly the autonumber is distinct to the BIN description (or other entity description). So if Bin# 24876 refers to Bin 1A1 - you can actually change the description of 1A1 to a different value, without affecting any other data in your system, and avoiding the need for what are called cascading updates.
When you get a stock movement, you might decide to store 50 green widgets in BIN 24876. So you have a part record for Green Widget (Part# 12888). And you end up with an entry in your stock movement record table showing
BIN# 24876, Part# 12888, Qty 50, Date Sep 15 2015, Movement Record# 2345
So you end up with a table that looks like this
BIN PART Qty DATE DOCUMENT
24876 12888 50 15/09/2015 2345
24876 12888 12 18/09/2015 2346
24876 12888 -17 18/09/2015 3012
24876 12888 31 04/10/2015 3126
23679 12888 87 15/09/2015 2387 'same part in another bin
the total stock of part 12888 is 163 (sum of all the movements)
by bin, you have
Bin 24876 76
Bin 23679 87
If you want to issue 100 items for some reason, you can identify which bin(s) the picker needs to go to fulfil the issue requirement. Generally there is no need to store a running total of items in a bin. It is easier to sum the movement records. At some point (say during a stock take) you can collapse records historically to a single count record, and start again.
Hope this helps.