Robust Decomposable Markov Decision Processes Motivated by Allocating School Budgets Nedialko B. Dimitrov a , Stanko Dimitrov b , Stefanka Chukova c a Operations Research Department Naval Postgraduate School, USA b Management Sciences University of Waterloo, Canada c School of Mathematics, Statistics and Operations Research Victoria University of Wellington, New Zealand Abstract Motivated by an application to school funding, we introduce the notion of a robust decomposable Markov decision process (MDP). A robust decomposable MDP model applies to situations where several MDPs, with the transition probabilities in each only known through an uncertainty set, are coupled together by joint resource constraints. Robust decomposable MDPs are different than both decomposable MDPs, and robust MDPs and can not be solved by a direct application of the solution methods from either of those areas. In fact, to the best of our knowledge, there is no known method to tractably compute optimal policies in robust, decomposable MDPs. We show how to tractably compute good policies for this model, and apply the derived method to a stylized school funding example. Keywords: Markov processes, Dynamic Programming-optimal control, School Funding 1. Introduction Allocation of school funding is critical to improving school performance. Unfortu- nately, there is no consensus on how this limited resource should be allocated. As such, the allocation of school funding is a recurring topic of political discussion (Shutt, 1979; Fensterwald, 2013; Blume, 2013; Garber, 1997). For example, the state of California passed an initiative in 2012 to raise taxes specifically to fund schools. In 2013, a major debate was how to allocate this schools funding: should it be allocated by population or should poorer schools receive more funding? Motivated by allocating funding to school, in this paper we propose a new method of allocating finite resources, based on control theory. Our method extends previous work on using Markov decision processes (MDPs) for budget allocation. The main contributions of this paper are 1) to introduce the concept of robust, decomposable MDPs 2) to propose a computationally tractable method of computing good policies in such MDPs and 3) to illustrate, through a stylized example, that funding allocation based on these MDPs Email addresses: ned@nps.edu (Nedialko B. Dimitrov), sdimitro@uwaterloo.ca (Stanko Dimitrov), stefanka@gmail.com (Stefanka Chukova) Preprint submitted to Elsevier May 9, 2014