Mathematical Programming Under Uncertainty: Risk and Recourse Revisited

随着市场竞争的加剧，美国经济的许多部门都认识到改进资源规划的必要性。举例来说，请注意许多制造企业越来越多地接受准时制哲学，电信行业向动态路由能力的转变，以及城市交通规划中的自适应信号控制。在每一个这些领域，资源（例如，生产能力和网络能力）都是在需要之前获得的，并且在确定了精确的系统需求后，通过适应性分配提高了利用。由于在规划时无法获得有关系统运行的精确信息，因此资源规划问题涉及不确定情况下的决策。该项目关注于允许自适应资源分配的系统的规划问题的建模和解决方案。这些方法是基于随机分解的。随机分解的计算经验表明，它非常适合求解不确定条件下涉及最优规划的大规模问题。当系统需求的可变性只能通过模拟场景来评估时，它特别有用。该项目分为三个阶段，包括数学发展和验证这些方法、计算机执行所产生的算法，以及在案例研究的基础上对这些算法进行测试，这些案例研究将与工业合作者共同开发。

With increased competition in the marketplace, many sectors of the American economy are acknowledging the need for improved resource planning. By way of example, note the growing acceptance of the Just-In-Time philosophy in many manufacturing firms, the move toward dynamic routing capabilities within the telecommunication industry and adaptive signal control in urban traffic planning. In each of these areas, resources (e.g., productive capabilities and network capacities) are acquired well in advance of their need, and utilization is improved by adaptive allocation as precise system requirements are identified. Since precise information regarding system operation is not available at the time of planning, the resource planning problem involves decision making under uncertainty. This project focusses on modeling and solution of planning problems for systems that allow adaptive resource allocation. These methodologies are based on stochastic decomposition. Computational experience with stochastic decomposition indicates that it is ideally suited to the solution of large scale problems involving optimal planning under uncertainty. It is particularly useful when the variability of system requirements can only be assessed via simulated scenarios. The project involves three phases, involving the mathematical development and verification of these methods, computer implementation of the resulting algorithms, and testing of these algorithms on models based on case-studies which will be developed in conjunction with industrial collaborators.