Novel mathematical models for optimal screening and multicriteria scheduling problems

拟议的研究包括两个相关的研究路线。我们的第一个研究流探讨了确定系统的最佳筛选时间表的问题，随机恶化走向失败。筛选提供了关于系统当前恶化程度的不完善信息，基于该信息，最佳预防措施（即，更换、修复）。这个问题对于包括疾病筛查在内的各种实际应用是非常重要的。特别是，为这个问题开发的建模框架可以用于优化预防性癌症筛查，这可能对社会产生重大影响。在这方面，我们探索新的建模框架的最佳筛选问题的基础上马尔可夫决策过程和控制理论。我们将分析这些复杂的模型，以证明某些结构属性的存在。我们将使用这些属性来开发更快的解决方案算法来解决这个问题。此外，我们开发了一个多目标最优筛选问题的解决方法，确定帕累托最优解支配其他可行的解决方案。拟议的研究还将解决人口的最佳筛查问题，以确定如何将有限的筛查资源分配给人口中的个人。

The proposed research consists of two related lines of research. Our first research stream explores the problem of determining the optimal screening schedule of a system that stochastically deteriorates towards failure. Screenings provide imperfect information about the current deterioration level of the system, based on which optimal preventative actions (i.e., replacement, repair) are determined. This problem is of great importance for various practical applications including disease screening. In particular, the modeling framework developed for this problem can be used in optimizing preventative cancer screening, which may have a significant impact on the society. In this context, we explore novel modeling frameworks for the optimal screening problem based on Markov decision processes and control theory. We will analyze these complex models to prove the existence of certain structural properties. We will use such properties to develop faster solution algorithms to solve this problem. In addition, we develop a solution method for multi-objective optimal screening problems which determine the Pareto-optimal solutions dominating the other feasible solutions. The proposed research will also address the optimal screening problem for a population, in order to determine how limited screening resources should be allocated to the individuals within the population.