I am a full-time consultant and provide services related to the design, implementation and deployment of mathematical programming, optimization and data-science applications. I also teach courses and workshops. Usually I cannot blog about projects I am doing, but there are many technical notes I'd like to share. Not in the least so I have an easy way to search and find them again myself. You can reach me at firstname.lastname@example.org.
Thursday, October 30, 2014
Saturday, October 11, 2014
Handling of inventory
In this book and the accompanying web site we see some unusual ways to model inventory. In the first chapters, inventory is not dealt with explicitly and therefore we look at equations such as:
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.