Three Essays on Data-Driven Optimization for Scheduling in Manufacturing and Healthcare

This dissertation consists of three essays on data-driven optimization for scheduling in manufacturing and healthcare. In Chapter 1, we briefly introduce the optimization problems tackled in these essays. The first of these essays deals with machine scheduling problems. In Chapter 2, we compare the effectiveness of direct positional variables against relative positional variables computationally in a variety of machine scheduling problems and we present our results. The second essay deals with a scheduling problem in healthcare: the team primary care practice. In Chapter 3, we build upon the two-stage stochastic integer programming model introduced by Alvarez Oh (2015) to solve this challenging scheduling problem of determining patient appointment times to minimize a weighted combination of patient wait and provider idle times for the team practice. To overcome the computational complexity associated with solving the problem under the large set of scenarios required to accurately capture uncertainty in this setting, our approach relies on a lower bounding technique based on solving an exhaustive and mutually exclusive group of scenario subsets. Our computational results identify the structure of optimal schedules and quantify the impact of nurse flexibility, patient crossovers and no-shows. We conclude with practical scheduling guidelines for team primary care practices. The third essay deals with another scheduling problem observed in a manufacturing setting similar to first essay, this time in aerospace industry. In Chapter 4, we propose mathematical models to optimize scheduling at a tactical and operational level in a job shop at an aerospace parts manufacturer and implement our methods using real-life data collected from this company. We generalize the Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) from the literature and use novel computational techniques that depend on the data structure observed to reduce the size of the problem and solve realistically-sized instances in this chapter. We also provide a sensitivity analysis of different modeling techniques and objective functions using key performance indicators (KPIs) important for the manufacturer. Chapter 5 proposes extensions of models and techniques that are introduced in Chapters 2, 3 and 4 and outlines future research directions. Chapter 6 summarizes our findings and concludes the dissertation

Multicommodity network flow problem with substitution

Multicommodity network flow problems are generalizations of single commodity network flow problems, where a number of commodities flow through the network often sharing common resources such as arc capacities. While the single commodity problem can be solved in polynomial time even when the flow quantities are imposed as integer values only, the integer multicommodity version of the problem with arc capacities is NPhard. We introduce a generalization of the multicommodity network flow problem where substitution is possible amongst commodities. We develop mathematical models as the linear integer programming formulations of two-commodity and three-commodity problems with both commodity-specific and overall arc capacities. We prove that constraint matrices are totally unimodular in the mathematical programming formulations for the uncapacitated versions. We investigate the empirical computational difficulty of capacitated versions of the problem formulations through a computational study with randomly generated problems and statistical analysis with hypothesis testing. In particular, we explore the effect of capacities and the problem size on solution time. Our results show that solution time significantly increases for both two-commodity and three-commodity problems when both overall and commodity-specific capacities exist. Solution time significantly increases when problem size is increased. Finally, we generalized the two and three-commodity models for the multicommodity problem