Mathematical Modeling and Information Acquisition: An Integrated Approach for Dynamic Decision-Making

实践中遇到的许多运营问题需要基于不断变化的运营环境的不完全信息进行动态决策。决策者通常有机会在作出决定之前获得有关系统当前状态的更多信息。获得更多信息可以使用更准确和更详细的模型，从而提高最终决策的质量，例如以预期收益衡量。然而，获取信息通常是昂贵的(特别是如果包括时间延迟的估算成本)，更准确和更广泛的信息所产生的成本更高。因此，收集完整的信息可能并不总是具有成本效益。这项拟议的研究探索了在运筹学模型用于决策的背景下的这种成本-收益权衡。不是将问题说明与模型制定和优化分开，而是以一种集成的方式处理这两者。定义了一个“元”模型，用于评估通过提高模型精度来提高决策质量和为实现更高精度而获取信息的成本之间的权衡。在该框架下，研究了网络中的消息路由问题，并提出了求解该问题的最优元算法和良好的启发式方法。在最近由美国国家安全局赞助的题为“运筹学--未来十年”的研讨会上，强调的研究主题之一是发展一种关于数据收集、模型规范和决策之间权衡的理论。这项研究的结果应该会促进这一领域的知识。

Many operational problems encountered in practice require dynamic decision-making based on incomplete information about the constantly changing operating environment. Often decision-makers have the opportunity to acquire additional information about the current state of the system before making a decision. Obtaining more information enables the use of a more accurate and detailed model, thus improving the quality of final decisions as measured, for instance, by the expected payoff. However, acquiring information is usually expensive (especially if imputed costs for time delays are included), with higher costs incurred for more accurate and extensive information. Thus, gathering complete information may not always be cost effective. The proposed research explores this cost-benefit tradeoff in contexts where operations research models are employed for decision-making. Rather than separate the problem specification from the model formulation and optimization, the two are treated in an integrated manner. A 'meta' model is defined for evaluating the tradeoff between improving the quality of decisions through increased model precision and the cost of information acquisition to achieve the increased precision. The problem of routing messages in a network is examined in this framework and both optimal meta algorithms and good heuristic approaches are proposed for solving the problem. In a recent N.S.F. sponsored workshop entitled "OR - The Next Decade," one of the research topics emphasized was the development of a theory on the trade-off between data gathering, model specification, and decision-making. The results from this research should advance knowledge in that area.