Systematic handling of significant future uncertainties in supply chain case studies is an important challenge. Complexity in finding an optimal solution for such cases arises both from the details of the application itself and the multi-stage nature of the decisions and information flow, i.e., information about uncertain parameters is continually received throughout the planning horizon and has to be figured into deisions. Formulating and solving this type of multistage optimization problem generally entails exploring a large number of scenarios or performing multi-dimensional integrals over probability distributions. Number of scenarios to explore typically increases exponentially with the number of decision stages. A quantitative discussion on the complexity of multistage stochastic problem can be found in Shapiro and Nemirovski [1].

In this presentation, we test solution strategies based on dynamic programming and mathematical programming on a supply chain network of the light aromatics in a typical refinery. The supply chain system experiences stochastic variations in demand and price of the main products, which are modeled with Markov chains. Specifically, the solution strategies tested are: a) Real Time Approximate Dynamic Programming (RTADP) [2,3] , and b) 2-Stage Stochastic Programming with shrinking horizon [4].

The structure of the presentation is as follows: First, we bring forward the respective computational obstacles with respect to the dynamic programming and mathematical programming approaches. Then, we establish the connection between Markov Decision Processes (MDP) and stochastic programming. The rest of the presentation will delineate the RTADP methodology[3], the stochastic mathematical programming methodology[4] and the results of the case study.

References: 1. A. Shapiro and A. Nemirovski. “On complexity of multistage stochastic programs.” http://www.optimization-online.org.

2. A. Barto, S.J. Bradtke and S.P. Singh, “Learning to act using Real Time Dynamic Programming ”. Artificial Intelligence 72(1), pp. 81-138 , 1995.

3. N.E. Pratikakis, M. J. Real®, and J. H. Lee. Strategic capacity decisions in manufacturing using stochastic dynamic programming. Naval Research Logistics, Under Review.

4. Balasubramanian, J. and Grossmann, I. E. "Approximation to Multistage Stochastic Optimization in Multiperiod Batch Plant Scheduling under Demand Uncertainty" Submitted for publication (2003).