I'm modeling a continuous-time, two-stage manufacturing process with an MIP. There are about 100 finished-goods SKUs, and each of those belongs to about 25 different semi-finished categories in a many-to-one fashion. For approximation, let's say SKU1,SKU2,SKU3,SKU4 belong to semi-finished category A, SKU5,SKU6,SKU7,SKU8 belong to semi-finished cateogry B, etc.
In the first stage, semi-finished WIP materials are produced in one section of the plant (four lines in this section). If a manufacturing line produces 1000 pounds of semi-finished category A, those 1000 WIP pounds can then be "converted" into SKU1,SKU2,SKU3, or SKU4 in a different section of the plant, at different rates across about 20 lines.
Right now, I am treating semi-finished production "as if" it's finished-goods production. E.g., SKU1 is produced in the first section of the plant, then transferred to the other section for completion as a finished good. This is causing significant model complexity that I think could be avoided if I can just model the first stage of manufacturing as 25 semi-finished goods, instead of 100 individual finished SKUs.
The tricky part is that there's a time component - you can't manufacture a unit of SKU1 in the finished-goods process, without having completed sufficient production in the semi-finished section. I'd like to be able to implement some sort of net inventory constraint in my model. E.g., you can't begin to process X units of SKU1 in the second section, unless there are X units of semi-finished category A sitting around. Even more troublesome is that there is a many-to-one relationship between finished-goods SKUs and semi-finished products.
Any advice on how this net inventory relationship may be modeled?