The Effect of Forecast Evolution on Production Planning with Resources Subject to Congestion

The value of demand forecast information in production-inventory planning systems has been the subject of numerous studies in the literature. While queuing models of production systems show that lead times increase nonlinearly with resource utilization, there are few models that analyze the effect of forecast evolution on production planning with resources subject to congestion. This dissertation consists of three papers, each addressing one or more aspects of these production systems. In the first paper, we show that the progressive realization of uncertain demands across successive discrete time periods through additive or multiplicative forecast updates results in the evolution of the conditional covariance of demand in addition to its conditional mean. A dynamic inventory model with forecast updates is used to illustrate the application of our method. We show how the optimal inventory policy depends on conditional covariances, and use a model without information updates to quantify the benefit of using the available forecast information in the presence of additive forecast updates. Our approach yields significant reductions in system costs, and is applicable to a wide range of production and inventory models. We also extend our approach to the case of multiplicative forecast updates, and discuss directions for future work.;In the second paper, we consider a single stage production-inventory system with work-load dependent lead times and uncertain demands. The dependency between workload and lead times is captured through clearing functions that take into account the nonlinear relationship between utilization and lead times. We propose a load dependent release policy leading to a tractable chance constrained optimization model. We compare the performance of this approach with that of a multistage stochastic programming model by subjecting them to a simulation of uncertain demand realizations. Computational experiments show promising performance of our chance constrained model.;In the third paper we consider a dynamic production-inventory system with forecast updates based on the martingale model of forecast evolution (MMFE) used in our first paper. The nonlinear dependency between workload and lead times is again captured through clearing functions. In this setting, we first formulate a chance constrained model and show how information affects the performance of the system subject to congestion. We then evaluate the performance of this model compared to that of a multistage stochastic programming model, for which we propose a method to represent the forecast evolution in a set of discrete scenarios. Our computational study helps to quantify the value of forecast update information, and suggests that the chance-constrained models provide a good tradeoff between solution quality and model complexity.