Due to various advantages in storage and implementation, simple strategies are usually preferred than complex strategies when the performances are close. Strategy optimization for controlled Markov process with descriptive complexity constraint provides a general framework for many such problems. In this paper, we first show by examples that the descriptive complexity and the performance of a strategy could be independent, and use the F-matrix in the No-Free-Lunch Theorem to show the risk that approximating complex strategies may lead to simple strategies that are unboundedly worse in cardinal performance than the original complex strategies. We then develop a method that handles the descriptive complexity constraint directly, which describes simple strategies exactly and only approximates complex strategies during the optimization. The ordinal performance difference between the resulting strategies of this selective approximation method and the global optimum is quantified. Numerical examples on an engine maintenance problem show how this method improves the solution quality. We hope this work sheds some insights to solving general strategy optimization for controlled Markov process with descriptive complexity constraint.
Bottlenecks, the key ingredients for improving the performances of the production networks, have been profoundly studied during the last decade. Yet, because of the complexity of the research results, there is still a significant gap between theory and practice. In this paper, we review various bottleneck definitions, detection methods and the asymptotic results and provide a practical guidance for recognizing and utilizing the bottlenecks in production networks. Queueing theory works as the mathematical foundation in our study. Various definitions of the bottlenecks are classified as either Performance in Processing （PIP） based or sensitivity based definitions, which reflect the preferences of the managers. Detection methods are surveyed closely based on the definitions. These methods are used to recognize the bottlenecks and to provide diagnosis results to managers. Comparisons show that different detection methods may lead to vastly different conclusions. The recognition of the bottlenecks has another advantage： the ultimate phenomena of the bottlenecks can greatly reduce the computation complexity in calculating the system performances. Bottlenecks based approximation and asymptotic results are studied to exhibit the contribution of bottlenecks in performance estimation and theoretical analysis.
