Decision, Operations & Information Technologies Research Works
Permanent URI for this collectionhttp://hdl.handle.net/1903/1588
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Item Online Appendix for “Ranking and Selection as Stochastic Control”(2017-04) Peng, Yijie; Chong, Edwin K. P.; Chen, Chun-Hung; Fu, Michael C.Item A Large Deviations Analysis of Quantile Estimation with Application to Value at Risk(2005-07-01T12:31:49Z) Jin, Xing; Fu, Michael C.Quantile estimation has become increasingly important, particularly in the financial industry, where Value-at-Risk has emerged as a standard measurement tool for controlling portfolio risk. In this paper we apply the theory of large deviations to analyze various simulation-based quantile estimators. First, we show that the coverage probability of the standard quantile estimator converges to one exponentially fast with sample size. Then we introduce a new quantile estimator that has a provably faster convergence rate. Furthermore, we show that the coverage probability for this new estimator can be guaranteed to be 100% with sufficiently large, but finite, sample size. Numerical experiments on a VaR example illustrate the potential for dramatic variance reduction.Item Multi-Echelon Models for Repairable Items: A Review(2005-07-01T12:31:37Z) Diaz, Angel; Fu, Michael C.We review multi-echelon inventory models for repairable items. Such models have been widely applied to the management of critical spare parts for military equipment for around three decades, but the application to manufacturing and service industries seems to be much less documented. We feel that the appropriate use of models in the management of spare parts for heavily utilized equipment in industry can result in significant cost savings, in particular in those settings where repair facilities are resource constrained. In our review, we provide a strategic framework for making these decisions, place the modeling problem in the broader context of inventory control, and review the prominent models in the literature under a unified setting, highlighting some key relationships. We concentrate on describing those models which we feel are most applicable for practical application, revisiting in detail the Multi-Echelon Technique for Recoverable Item Control (METRIC) model and its variations, and then discussing a variety of more general queueing models. We then discuss the components which we feel must be addressed in the models in order to apply them practically to industrial settings.Item Stochastic Gradient Estimation(2005-07-01T12:31:02Z) Fu, Michael C.We consider the problem of efficiently estimating gradients from stochastic simulation. Although the primary motivation is their use in simulation optimization, the resulting estimators can also be useful in other ways, e.g., sensitivity analysis. The main approaches described are finite differences (including simultaneous perturbations), perturbation analysis, the likelihood ratio/score function method, and the use of weak derivatives.