| This dissertation explores the use of stochastic programming for a variety of production planning problems. We develop methods for approximately solving these by generating representative sets of outcomes. We extend the approach first suggested by Birge (1985a), which we refer to as sequential bounding, where scenarios are generated in an iterative fashion based on a deterministic measure of the error in the approximation. This approach is extended to general two-stage and multi-stage stochastic programs, and methods are developed to improve convergence through a sequence of iterations. First, we present new sequential bounding approaches for two-stage stochastic programs and apply these approaches to a single-period production planning problem with downward product substitutions. Next, we present a multi-stage sequential bounding approach, and compare this with several other scenario generation approaches for a production planning problem with uncertain demand and constant work in process inventory. Finally, we develop a multi-stage stochastic program to model the evolution of demand forecasting for production planning with load dependent lead times. We compare a sequential bounding approach to solving this model with other models and solution methodologies. |
