Convert Array Formula to Non-Array

Don't use whole column references in MATCH for a start...

try:

=IF([@Shipper]=[@Consignee],
INDEX([DataFile.xlsx]Partner!$B:$B,MATCH([@Consignee],[DataFile.xlsx]Partner!$A$2:$A$150000,0)),
INDEX([DataFile.xlsx]Partner!$B:$B,MATCH(1,([@Shipper]=[DataFile.xlsx]Partner!$A$2:$A$150000)+([@Consignee]=[DataFile.xlsx]Partner!$A$2:$A$150000),0)))

or maybe:

=IF([@Shipper]=[@Consignee],
INDEX([DataFile.xlsx]Partner!$B:$B,MATCH([@Consignee],[DataFile.xlsx]Partner!$A$2:$A$150000,0)),
INDEX([DataFile.xlsx]Partner!$B:$B,INDEX(MATCH(1,([@Shipper]=[DataFile.xlsx]Partner!$A$2:$A$150000)+([@Consignee]=[DataFile.xlsx]Partner!$A$2:$A$150000),0),0)))


non-array. Hard to check as no sample file was provided

I am not sure if merely changing to a non-array formula will make much difference in calculation time. I notice that you are using very slow linear "exact match" lookups. I would expect that the biggest gains in computation speed are going to be realized by changing those lookups to much more efficient binary "approximate match" lookups (where the 3rd argument of the MATCH() function is 1 or -1).

The first step to making such a change is to look at the source database and sort the database by the lookup column. In your sample file (which is clearly mock data), the database in "Partner" is already sorted, but I cannot be sure that this is the case in your real database.

Once the database is sorted, then you can edit the lookup functions to use the approximate match option. Exactly what that looks like depends on what adjustments were needed to account for the sorting of the database. For the first "value_if_true" argument in the existing formula, that might be as simple as replacing the 0 with a 1 in the MATCH() function. If there are other considerations then the changes will be more complex. For the second "value_if_false" argument in the existing formula, you will need to some major re-writing. Details depend largely on how sorting the database changes the necessary steps to the lookup.

Because the details of the formula are going to depend on what needs to happen after the sorting step, I cannot offer any detailed suggestions. Because your example is clearly a mockup, I cannot see or understand how sorting the database changes the search step. If I had 100000+ rows to search through and computation time was important, I would go to some lengths to avoid linear "exact match" lookups in favor of much more efficient binary "approximate match" lookups. My suggestion is to look at your database and see what needs to happen in order to sort that list by original name.