Mean-Variance Analysis of Stochastic Dynamic Programming Models: An Application to Capacity Expansion

DOI: 10.5176/2251-1938_ORS64

Authors: Preetam Basu

Abstract:

This paper studies risk-reward trade-offs in finite-horizon stochastic dynamic programming models. Stochastic dynamic programming models are extensively used for sequential decision making when outcomes are uncertain. The objective in these models is to deduce optimal policies based on expected reward criteria. Nevertheless, in many cases, managers are concerned about the risks or the variability associated with a set of policies and not just the expected reward. However, considering risk and reward simultaneously in a stochastic dynamic setting is a cumbersome task and often difficult to implement for practical purposes. Here we develop a heuristic that systematically track the variance and the average reward for a set of policies in a stochastic dynamic setting, and instead of identifying one policy to achieve the stated objective, finds the set of policies that form the efficient frontier. In this paper, we apply our heuristic to a capacity expansion model. Our heuristic performs creditably in providing efficient risk-reward curves.

Keywords: Stochastic Dynamic Programming, Risk-Reward Heuristic, Efficient Frontier Analysis, Capacity Expansion