I.e. we add up all production up to now, add initial inventory and subtract all demand up to now (either final demand by customers or intermediate demand because of production of other products).
This is in general not how we would like to write such equations. It is much better to explicitly introduce inventory variables Ii,t≥0 and write:
I.e. inventory = previous inventory + production – demand. We add variables but the model becomes much sparser (fewer nonzero elements).
Even when they add inventory explicitly in models later on, they still do it wrong. They write:
This is not how we want it, as we repeat many expressions over different equations. A better formulation is:
There are different ways to write down the initial inventory. Here are some possibilities:
I have a preference for the last formulation.