Novel mathematical models for optimal screening and multicriteria scheduling problems

点击翻译按钮获取中文摘要

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.