I have a linear programming problem to solve that is very simple, except one aspect that is driving me nuts.
GOAL: maximize the gain of a set of devices.
I have an inventory of parts, which are used to build devices of different types. Note: only one device per type can be build. And, until here, all nice and clean.
What I am struggling to model is that the devices can only be built in a specific order.
For example, if I have DEV1, DEV2 and DEV3 that haven't be built already, I can only build DEV2 after building DEV1 and DEV3 only after building DEV1 and DEV2.
I thought to split the optimization and run it for all the "first" devices that haven't been built, see what the solver says, mark them as built and iterate until the inventory is empty, but I have the feeling this will almost always give me a very much sub-optimal solution.
Many thanks in advance,