Multistage Stochastic Programming with Parametric Cost Function Approximations

Abstract

A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized for its use of a deterministic approximation of a stochastic problem, which is the major motivation for stochastic programming. This dissertation recasts this debate by identifying both deterministic and stochastic approaches as policies for solving a stochastic base model, which may be a simulator or the real world. Stochastic lookahead models (stochastic programming) require a range of approximations to keep the problem tractable. By contrast, so-called deterministic models are actually parametrically modified cost function approximations which use parametric adjustments to the objective function and/or the constraints. These parameters are then optimized in a stochastic base model which does not require making any of the types of simplifications required by stochastic programming. This dissertation formalizes this strategy, describes a gradient-based stochastic search strategy to optimize policies, and presents a series of energy related numerical experiments to illustrate the efficacy of this approach.