This is a little hard to explain, and would be a lot easier if I could just attach the spreadsheet. But I'll give it a go with a screen shot (pardon if it looks out of place, my job's network filters it out >:0 ).
The top table can be setup however you want. The important items are the part numbers and the Days. The lower table uses the formula above to get the Row and Column of the Part Number and Day and finds the Index (or intersection) of that Row and Column pair within the upper table.
Stepping through the formula:
$D$2:$H$4 is the table of daily sales for the three parts
The first MATCH() finds the index (or row) of B$7 (or part 123) in the array $B$2:$B$4
The second MATCH() finds the index (or column) of $A8 (of DayOne) in the array $D$1:$H$1
Thus, INDEX() finds the cell at the intersection of the first MATCH() (row) and the second MATCH() (column) in the table $D$2:$H$4
Finally, a little additional subtraction in the lower table will give you daily remaining inventory (not shown in the formula above to keep it simpler).
Hopefully this is understandable.