Alternatives for 250+ cross-dimensional operators

Question

Our geographical product segmentation has altered. I have to change the outline. We have departments and products. Normally we could report on the sum of departments and on the sum of products. Now because of the switch in segmentation we can only report on products. Some of the same products are made by mutiple regions. I have to make an hierarchy which can report on products for regions. In this instance in the outline, there is one product member and two department members. I have made formulas to pull the product apart to regions.
I have done this with cross dimensional operators:
For example product A is made by department 1 and 2. I made two formulas in the product dimension ProdAdep1 and ProdAdep2:
Member formulas:
ProdAdep1 = Product A -> Department 1;
ProdAdep2 = Product A -> Department 2;
Product A is now made ~ and ProdAdep1,ProdBdep1, ProdCdep1 count up to Total products department 1.
I made all these formulas dynamic calc. Both the product and department dimension are sparse. There are now 250+ formulas and the caculation of the database became very slow. In my Essbase bible 'Look smarter than you are with Essbase 11' I found that the usage of a lot of cross dimensional operators is unseemly and slow.
So I figured out an alternative, a calcscript with a fix.
FIX("Product A")
ProdAdep1 = "Department 1";
ProdAdep2 = "Department 2";
ENDFIX
But this doens't work either. Can anyone help me to think out the best solution?

Answer 1

Thank you Steve, its a bit more complicated.
Departments roll up to regions, products also roll up to regions, but we also have shared (central) products.
For example department 1 in region X (department dimension) can have product A (product dimension) and department 2 in region Y (department dimension) can have product A (product dimension) also. The wish is to report on products and have a full view of the regions within the product dimension.
How it is now:
Department dimension:
Total Region X
|- Department 1
|- Department 3
Total region Y
|- Department 2
|- Department 4
Product dimension:
Total Region X
|-Product C
|-Product D
Total Region Y
|- Product E
|- Product F
Central Products
|- Product A
The Wish:
Department dimension:
Total Region X
|- Department 1
|- Department 3
Total region Y
|- Department 2
|- Department 4
Product dimension:
Total Region X
|-Product C
|-Product D
|-Product A (for region X based on department)
Total Region Y
|- Product E
|- Product F
|- Product A (for region Y based on department)
Central Products
|- Product A ~
It isnt possible to add a dimension, because the problem occurs on level 0.