Integrated Machine Learning and Optimization Frameworks with Applications in Operations Management

Incorporation of contextual inference in the optimality analysis of operational problems is a canonical characteristic of data-informed decision making that requires interdisciplinary research. In an attempt to achieve individualization in operations management, we design rigorous and yet practical mechanisms that boost efficiency, restrain uncertainty and elevate real-time decision making through integration of ideas from machine learning and operations research literature. In our first study, we investigate the decision of whether to admit a patient to a critical care unit which is a crucial operational problem that has significant influence on both hospital performance and patient outcomes. Hospitals currently lack a methodology to selectively admit patients to these units in a way that patient’s individual health metrics can be incorporated while considering the hospital’s operational constraints. We model the problem as a complex loss queueing network with a stochastic model of how long risk-stratified patients spend time in particular units and how they transition between units. A data-driven optimization methodology then approximates an optimal admission control policy for the network of units. While enforcing low levels of patient blocking, we optimize a monotonic dual-threshold admission policy. Our methodology captures utilization and accessibility in a network model of care pathways while supporting the personalized allocation of scarce care resources to the neediest patients. The interesting benefits of admission thresholds that vary by day of week are also examined. In the second study, we analyze the efficiency of surgical unit operations in the era of big data. The accuracy of surgical case duration predictions is a crucial element in hospital operational performance. We propose a comprehensive methodology that incorporates both structured and unstructured data to generate individualized predictions regarding the overall distribution of surgery durations. Consequently, we investigate methods to incorporate such individualized predictions into operational decision-making. We introduce novel prescriptive models to address optimization under uncertainty in the fundamental surgery appointment scheduling problem by utilizing the multi-dimensional data features available prior to the surgery. Electronic medical records systems provide detailed patient features that enable the prediction of individualized case time distributions; however, existing approaches in this context usually employ only limited, aggregate information, and do not take advantages of these detailed features. We show how the quantile regression forest, can be integrated into three common optimization formulations that capture the stochasticity in addressing this problem, including stochastic optimization, robust optimization and distributionally robust optimization. In the last part of this dissertation, we provide the first study on online learning problems under stochastic constraints that are "soft", i.e., need to be satisfied with high likelihood. Under a Bayesian framework, we propose and analyze a scheme that provides statistical feasibility guarantees throughout the learning horizon, by using posterior Monte Carlo samples to form sampled constraints that generalize the scenario generation approach commonly used in chance-constrained programming. We demonstrate how our scheme can be integrated into Thompson sampling and illustrate it with an application in online advertisement.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145936/1/meisami_1.pd

Optimal Regret Is Achievable With Constant Approximate Inference Error: An Enhanced Bayesian Upper Confidence Bound Framework

Bayesian bandit algorithms with approximate Bayesian inference have been widely used in real-world applications. However, there is a large discrepancy between the superior practical performance of these approaches and their theoretical justification. Previous research only indicates a negative theoretical result: Thompson sampling could have a worst-case linear regret $\Omega(T)$ with a constant threshold on the inference error measured by one $\alpha$-divergence. To bridge this gap, we propose an Enhanced Bayesian Upper Confidence Bound (EBUCB) framework that can efficiently accommodate bandit problems in the presence of approximate inference. Our theoretical analysis demonstrates that for Bernoulli multi-armed bandits, EBUCB can achieve the optimal regret order $O(\log T)$ if the inference error measured by two different $\alpha$-divergences is less than a constant, regardless of how large this constant is. Our study provides the first theoretical regret bound that is better than $o(T)$ in the setting of constant approximate inference error, to our best knowledge. Furthermore, in concordance with the negative results in previous studies, we show that only one bounded $\alpha$-divergence is insufficient to guarantee a sub-linear regret

Mathematical Modelling of the Removal of Basic Blue Dye from Effluent by a Mineral Membrane

Abstract: Water contamination is a major challenge due to the discharging of wastes into the natural resources. In this study, a novel branched pore adsorption model was developed by utilizing external mass transfer coefficients, , effective diffusivity, and lumped microspore diffusion rate parameters. This describes sorption kinetics from long-term adsorption that occurs between an adsorbent and an adsorbate. An investigation of the effects of dye concentration on Basic Blue 9 removal was conducted. Then by considering of initial and boundary conditions the government equations were solved. Using this model, the Basic Blue 9 (or methylene blue is an industrial inhibitor) was removed from a bentonite sample polluted by Basic Blue 9. The maximum adsorption capacity was achieved by using of Freundlich analysis. Based on the experimental data, theoretical concentration - time adjusted models were developed using a FORTRAN computer program to fit the experimental data more precisely and confirm the precision and accuracy of this research