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。 作为研究的第二个流，我们将开发最佳和近似的解决方法的多目标调度问题的最小化的延迟（晚）的工作和加权流时间，以确定帕累托最优的特定任务的时间表。为这个问题开发一个建模和解决方案框架是一个重大的贡献，因为它在几个领域的实际重要性。例如，在医院中，该问题表征了医生的观点，其目标是增加在预定义的时间间隔内服务的患者的数量，并减少患者在医院中花费的时间。我们使用MIP和分支&界来建模和求解这个多目标调度问题。我们还开发了基于波束搜索和遗传算法的近似解方法。

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. As a secondary stream of research, we will develop optimal and approximate solution methods for the multicriteria scheduling problem of minimizing the number of tardy (late) jobs and weighted flow-time in order to determine Pareto-optimal schedules of particular tasks. Developing a modeling and solution framework for this problem is a significant contribution because of its practical importance in several fields. For example, in a hospital, this problem characterizes the perspective of a doctor whose objective is to increase the number of patients served within predefined time intervals and decrease the time that the patients spent in the hospital. We model and solve this multicriteria scheduling problem using MIP and Branch & Bound. We also develop approximate solution methods based on beam-search and genetic algorithms.