Section: Research Program
Stochastic Operations Research
Stochastic Operations Research is a collection of modeling, optimization and numerical computation techniques, aimed at assessing the behavior of man-made systems driven by random phenomena, and at helping to make decisions in such a context.
The discipline is based on applied probability and focuses on effective computations and algorithms. Its core theory is that of Markov chains over discrete state spaces. This family of stochastic processes has, at the same time, a very large modeling capability and the potential of efficient solutions. By “solution” is meant the calculation of some performance metric, usually the distribution of some random variable of interest, or its average, variance, etc. This solution is obtained either through exact “analytic” formulas, or numerically through linear algebra methods. Even when not analytically or numerically tractable, Markovian models are always amenable to “Monte-Carlo” simulations with which the metrics can be statistically measured.
An example of this is the success of classical Queueing Theory, with its numerous analytical formulas. Another important derived theory is that of the Markov Decision Processes, which allows to formalize optimal decision problems in a random environment. This theory allows to characterize the optimal decisions, and provides algorithms for calculating them.
Strong trends of Operations Research are: a) an increasing importance of multi-criteria multi-agent optimization, and the correlated introduction of Game Theory in the standard methodology; b) an increasing concern of (deterministic) Operations Research with randomness and risk, and the consequent introduction of topics like Chance Constrained Programming and Stochastic Optimization. Data analysis is also more and more present in Operations Research: techniques from statistics, like filtering and estimation, or Artificial Intelligence like clustering, are coupled with modeling in Machine Learning techniques like Q-Learning.