Warren Powell’s Post

I love Anand Subramanian's post that brings out the origins of the field of linear programming. I recently came to the realization that all the motivating applications of linear programming used by Dantzig were in fact fully sequential (and stochastic). Which means, you do not just solve a single linear program - you have to solve them sequentially over time, where a decision at one point in time affects what you can do the next time you solve it. We would call these "dynamic programs", but if you call them a "dynamic program" everyone in operations research would then go running to Bellman's equation, which is virtually useless for the large resource allocation problems that arise in military applications. While we *may* use approximate dynamic programming to capture the impact of decisions on the future, another way is to solve suitably parameterized linear programs that are tuned so that the solution works well over time (think of buffer stocks and schedule slack). This is what people already do in practice, but in an ad hoc way. I call this approach a parametric cost function approximation (CFA). See https://lnkd.in/eEcpM4Ex ("tinyurl.com/" with "cfapolicy")