Robust Appointment Scheduling with Heterogeneous Costs

Designing simple appointment systems that under uncertainty in service times, try to achieve both high utilization of expensive medical equipment and personnel as well as short waiting time for patients, has long been an interesting and challenging problem in health care. We consider a robust version of the appointment scheduling problem, introduced by Mittal et al. (2014), with the goal of finding simple and easy-to-use algorithms. Previous work focused on the special case where per-unit costs due to under-utilization of equipment/personnel are homogeneous i.e., costs are linear and identical. We consider the heterogeneous case and devise an LP that has a simple closed-form solution. This solution yields the first constant-factor approximation for the problem. We also find special cases beyond homogeneous costs where the LP leads to closed form optimal schedules. Our approach and results extend more generally to convex piece-wise linear costs. For the case where the order of patients is changeable, we focus on linear costs and show that the problem is strongly NP-hard when the under-utilization costs are heterogeneous. For changeable order with homogeneous under-utilization costs, it was previously shown that an EPTAS exists. We instead find an extremely simple, ratio-based ordering that is 1.0604 approximate

Probabilistic Optimization Techniques in Smart Power System

Uncertainties are the most significant challenges in the smart power system, necessitating the use of precise techniques to deal with them properly. Such problems could be effectively solved using a probabilistic optimization strategy. It is further divided into stochastic, robust, distributionally robust, and chance-constrained optimizations. The topics of probabilistic optimization in smart power systems are covered in this review paper. In order to account for uncertainty in optimization processes, stochastic optimization is essential. Robust optimization is the most advanced approach to optimize a system under uncertainty, in which a deterministic, set-based uncertainty model is used instead of a stochastic one. The computational complexity of stochastic programming and the conservativeness of robust optimization are both reduced by distributionally robust optimization.Chance constrained algorithms help in solving the constraints optimization problems, where finite probability get violated. This review paper discusses microgrid and home energy management, demand-side management, unit commitment, microgrid integration, and economic dispatch as examples of applications of these techniques in smart power systems. Probabilistic mathematical models of different scenarios, for which deterministic approaches have been used in the literature, are also presented. Future research directions in a variety of smart power system domains are also presented.publishedVersio

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

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment

Data-Driven Dynamic Robust Resource Allocation: Application to Efficient Transportation

The transformation to smarter cities brings an array of emerging urbanization challenges. With the development of technologies such as sensor networks, storage devices, and cloud computing, we are able to collect, store, and analyze a large amount of data in real time. Modern cities have brought to life unprecedented opportunities and challenges for allocating limited resources in a data-driven way. Intelligent transportation system is one emerging research area, in which sensing data provides us opportunities for understanding spatial-temporal patterns of demand human and mobility. However, greedy or matching algorithms that only deal with known requests are far from efficient in the long run without considering demand information predicted based on data. In this dissertation, we develop a data-driven robust resource allocation framework to consider spatial-temporally correlated demand and demand uncertainties, motivated by the problem of efficient dispatching of taxi or autonomous vehicles. We first present a receding horizon control (RHC) framework to dispatch taxis towards predicted demand; this framework incorporates both information from historical record data and real-time GPS location and occupancy status data. It also allows us to allocate resource from a globally optimal perspective in a longer time period, besides the local level greedy or matching algorithm for assigning a passenger pick-up location of each vacant vehicle. The objectives include reducing both current and anticipated future total idle driving distance and matching spatial-temporal ratio between demand and supply for service quality. We then present a robust optimization method to consider spatial-temporally correlated demand model uncertainties that can be expressed in closed convex sets. Uncertainty sets of demand vectors are constructed from data based on theories in hypothesis testing, and the sets provide a desired probabilistic guarantee level for the performance of dispatch solutions. To minimize the average resource allocation cost under demand uncertainties, we develop a general data-driven dynamic distributionally robust resource allocation model. An efficient algorithm for building demand uncertainty sets that compatible with various demand prediction methods is developed. We prove equivalent computationally tractable forms of the robust and distributionally robust resource allocation problems using strong duality. The resource allocation problem aims to balance the demand-supply ratio at different nodes of the network with minimum balancing and re-balancing cost, with decision variables on the denominator that has not been covered by previous work. Trace-driven analysis with real taxi operational record data of San Francisco shows that the RHC framework reduces the average total idle distance of taxis by 52%, and evaluations with over 100GB of New York City taxi trip data show that robust and distributionally robust dispatch methods reduce the average total idle distance by 10% more compared with non-robust solutions. Besides increasing the service efficiency by reducing total idle driving distance, the resource allocation methods in this dissertation also reduce the demand-supply ratio mismatch error across the city

Power System Operations with Probabilistic Guarantees

This study is motivated by the fact that uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electrical grids. Among various tools for decision making in uncertain environments, this study focuses on chance-constrained optimization, which provides explicit probabilistic guarantees on the feasibility of optimal solutions. Although quite a few methods have been proposed to solve chance-constrained optimization problems, there is a lack of comprehensive review and comparative analysis of the proposed methods. In this work, we provide a detailed tutorial on existing algorithms and a survey of major theoretical results of chance-constrained optimization theory. Data-driven methods, which are not constrained by any specific distributions of the underlying uncertainties, are of particular interest. Built upon chance-constrained optimization, we propose a three-stage power system operation framework with probabilistic guarantees: (1) the optimal unit commitment in the operational planning stage; (2) the optimal reactive power dispatch to address the voltage security issue in the hours-ahead adjustment period; and (3) the secure and reliable power system operation under uncertainties in real time. In the day-ahead operational planning stage, we propose a chance-constrained SCUC (c-SCUC) framework, which ensures that the risk of violating constraints is within an acceptable threshold. Using the scenario approach, c-SCUC is reformulated to the scenario-based SCUC (s-SCUC) problem. By choosing an appropriate number of scenarios, we provide theoretical guarantees on the posterior risk level of the solution to s-SCUC. Inspired by the latest progress of the scenario approach on non-convex problems, we demonstrate the structural properties of general scenario problems and analyze the specific characteristics of s-SCUC. Those characteristics were exploited to benefit the scalability and computational performance of s-SCUC. In the adjustment period, this work first investigates the benefits of look-ahead coordination of both continuous-state and discrete-state reactive power support devices across multiple control areas. The conventional static optimal reactive power dispatch is extended to a “moving-horizon” type formulation for the consideration of spatial and temporal variations. The optimal reactive power dispatch problem is further enhanced with chance constraints by considering the uncertainties from both renewables and contingencies. This chance-constrained optimal reactive power dispatch (c-ORPD) formulation offers system operators an effective tool to schedule voltage support devices such that the system voltage security can be ensured with quantifiable level of risk. Security-constrained Economic Dispatch (SCED) lies at the center of real-time operation of power systems and modern electricity markets. It determines the most cost-efficient output levels of generators while keeping the real-time balance between supply and demand. In this study, we formulate and solve chance-constrained SCED (c-SCED), which ensures system security under uncertainties from renewables. The c-SCED problem also serves as a benchmark problem for a critical comparison of existing algorithms to solve chance-constrained optimization problems

Situation Awareness for Smart Distribution Systems

In recent years, the global climate has become variable due to intensification of the greenhouse effect, and natural disasters are frequently occurring, which poses challenges to the situation awareness of intelligent distribution networks. Aside from the continuous grid connection of distributed generation, energy storage and new energy generation not only reduces the power supply pressure of distribution network to a certain extent but also brings new consumption pressure and load impact. Situation awareness is a technology based on the overall dynamic insight of environment and covering perception, understanding, and prediction. Such means have been widely used in security, intelligence, justice, intelligent transportation, and other fields and gradually become the research direction of digitization and informatization in the future. We hope this Special Issue represents a useful contribution. We present 10 interesting papers that cover a wide range of topics all focused on problems and solutions related to situation awareness for smart distribution systems. We sincerely hope the papers included in this Special Issue will inspire more researchers to further develop situation awareness for smart distribution systems. We strongly believe that there is a need for more work to be carried out, and we hope this issue provides a useful open-access platform for the dissemination of new ideas

RISK-AVERSE AND AMBIGUITY-AVERSE MARKOV DECISION PROCESSES

Ph.DDOCTOR OF PHILOSOPH