IDEA: Integrated Decomposition for Enterprise Analysis

这个项目确定了一类新的随机程序，称为“分布式随机程序”，并为它们的解开发了计算方法。所研究的方法论涉及Guignard和Kim的“拉格朗日分解”方法与Higle和Sen.的“随机分解”方法的结合。主要动机是研究不确定条件下基于企业的决策的集成模型和求解方法。基于企业的模型是将与企业内不同实体相关联的各种组件问题结合在一起的模型。当然，这些组件问题通常会反映操作方面的问题，并进行了详细的说明。他们各自的解决方案通常需要高度专业化的计算方法，以挑战现有的计算资源。因此，将它们直接合并到基于企业的模型中可能会导致一个大大超出当前计算能力的模型。为了纠正这种情况，该项目提倡使用反映与日常业务相关的不确定性的组成部分问题的替代模型，并以能够指导战略决策的方式组合在一起。这个项目的一个主要目标是开发基于分解方案的解决方案，以解决由此产生的一类问题，这些分解方案利用了企业模型的一般结构。在过去的几年中，将不确定性纳入复杂商业环境的需求变得越来越明显。许多公司已经投入了大量的时间和资源来开发可用于辅助运营决策的模型。例如，航空公司通常使用食道化的模型来帮助他们进行机队分配、机组人员安排、维护计划等。除了这些类型的运营决策外，公司还进行战略或长期决策，例如当航空公司确定它将服务于什么市场时。一般而言，这些战略决策影响了业务决策，尽管这种影响或与日常业务决策相关的不确定性通常都不在企业的战略决策模型中。本项目是对不确定环境下基于企业的决策集成模型和求解方法的探索。

This project identifies a new class of stochastic programs referred to as"Distributed Stochastic Programs," and develops computational approachesfor their solution. The methodology to be studied involves a marriage of the"Lagrangean Decomposition" method of Guignard and Kim with the "StochasticDecomposition" methods of Higle and Sen. The primary motivation is the study ofintegrated models and solution methods for enterprise-based decision making under uncertainty. An enterprise-based model is one that couples a variety of component problems that are associated with different entities within the enterprise. Of necessity these component problems, which will typically reflect operational concerns,are finely detailed. Their individual solutions often require highly specialized computational approaches that challenge current computing resources. As a result, their direct incorporation within anenterprise-based model would likely lead to a model that greatly exceedscurrent computational capabilities. To remedy this situation, thisproject advocates the use of surrogate models of the component problemsthat reflect the uncertainty associated with the day-to-day operations,and are combined in a manner that permits guidance for strategic decisions. A primary goal of this project is the development of solution methods for the resulting class of problems based on decomposition schemes that exploit the general structure of the enterprise model.Over the past few years, the need to incorporate uncertaintywithin complex business environments has become increasinglyobvious. Many firms have invested a great deal of time andresources in developing models that can be used to assist withoperational decision making. For example, airlines typically usesophisticated models to assist with their air fleet assignments, crewscheduling, maintenance schedules, etc. In addition to thesetypes of operational decisions, firms also undertake strategic, orlong-term, decisions, such as when an airline determineswhat markets it will serve. In general, these strategic decisionsimpact the operational decisions, although neither this impact nor the uncertainty associated with day-to-day operational decisions istypically captured within the enterprise's strategic decision model. This project involves an exploration of integrated models and solution methods for enterprise-based decision making under uncertainty.