Convex Nonlinear and Integer Programming Approaches for Distributionally Robust Optimization of Complex Systems

The primary focus of the dissertation is to develop distributionally robust optimization (DRO) models and related solution approaches for decision making in energy and healthcare service systems with uncertainties, which often involves nonlinear constraints and discrete decision variables. Without assuming specific distributions, DRO techniques solve for solutions against the worst-case distribution of system uncertainties. In the DRO framework, we consider both risk-neutral (e.g., expectation) and risk-averse (e.g., chance constraint and Conditional Value-at-Risk (CVaR)) measures. The aim is twofold: i) developing efficient solution algorithms for DRO models with integer and/or binary variables, sometimes nonlinear structures and ii) revealing managerial insights of DRO models for specific applications. We mainly focus on DRO models of power system operations, appointment scheduling, and resource allocation in healthcare. Specifically, we first study stochastic optimal power flow (OPF), where (uncertain) renewable integration and load control are implemented to balance supply and (uncertain) demand in power grids. We propose a chance-constrained OPF (CC-OPF) model and investigate its DRO variant which is reformulated as a semidefinite programming (SDP) problem. We compare the DRO model with two benchmark models, in the IEEE 9-bus, 39-bus, and 118-bus systems with different flow congestion levels. The DRO approach yields a higher probability of satisfying the chance constraints and shorter solution time. It also better utilizes reserves at both generators and loads when the system has congested flows. Then we consider appointment scheduling under random service durations with given (fixed) appointment arrival order. We propose a DRO formulation and derive a conservative SDP reformulation. Furthermore, we study a scheduling variant under random no-shows of appointments and derive tractable reformulations for certain beliefs of no-show patterns. One preceding problem of appointment scheduling in the healthcare service operations is the surgery block allocation problem that assigns surgeries to operating rooms. We derive an equivalent 0-1 SDP reformulation and a less conservative 0-1 second-order cone programming (SOCP) reformulation for its DRO model. Finally, we study distributionally robust chance-constrained binary programs (DCBP) for limiting the probability of undesirable events, under mean-covariance information. We reformulate DCBPs as equivalent 0-1 SOCP formulations under two moment-based ambiguity sets. We further exploit the submodularity of the 0-1 SOCP reformulations under diagonal and non-diagonal matrices. We derive extended polymatroid inequalities via submodularity and lifting, which are incorporated into a branch-and-cut algorithm incorporated for efficiently solving DCBPs. We demonstrate the computational efficacy and solution performance with diverse instances of a chance-constrained bin packing problem.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149946/1/zyiling_1.pd

Robust Optimization With Applications In Healthcare Operations Management

Ph.DDOCTOR OF PHILOSOPH

Solving Multi-objective Integer Programs using Convex Preference Cones

Esta encuesta tiene dos objetivos: en primer lugar, identificar a los individuos que fueron víctimas de algún tipo de delito y la manera en que ocurrió el mismo. En segundo lugar, medir la eficacia de las distintas autoridades competentes una vez que los individuos denunciaron el delito que sufrieron. Adicionalmente la ENVEI busca indagar las percepciones que los ciudadanos tienen sobre las instituciones de justicia y el estado de derecho en Méxic

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes