Optimization simulation: the case of multi-stage stochastic decision models

Abstract

In this paper we present a new approach to solving multi-stage stochastic decision models in the presence of constraints. The models themselves are stochastic linear programs (SLP), but we presume that their deterministic equivalent problems are too large to be solved exactly. We seek an asymptotically optimum solution by simulating the stochastic decomposition (SD) algorithmic process, originally designed for two-stage SLPs. When SD is implemented in a time-staged manner the algorithm begins to take the flavor of a simulation leading to what we refer to as optimization simulation. Among its major advantages, it can work directly with sample paths, and this feature makes the new algorithm much easier to integrate within a simulation. We also overcome certain limitations such as a stage-wise independence assumption required by other sampling-based algorithms for multi-stage stochastic programming. Finally, we also discuss how these methods can be interpreted as close relatives of approximate dynamic programming.