A Selective Scheduling Problem with Sequence-dependent Setup Times: A Risk-averse Approach

This paper addresses a scheduling problem with parallel identical machines and sequence-dependent setup times in which the setup and the processing times are random parameters. The model aims at minimizing the total completion time while the total revenue gained by the processed jobs satisfies the manufacturer’s threshold. To handle the uncertainty of random parameters, we adopt a risk-averse distributionally robust approach developed based on the Conditional Value-at-Risk measure hedging against the worst-case performance. The proposed model is tested via extensive experimental results performed on a set of benchmark instances. We also show the efficiency of the deterministic counterpart of our model, in comparison with the state-of-the-art model proposed for a similar problem in a deterministic context

Nature-inspired Methods for Stochastic, Robust and Dynamic Optimization

Nature-inspired algorithms have a great popularity in the current scientific community, being the focused scope of many research contributions in the literature year by year. The rationale behind the acquired momentum by this broad family of methods lies on their outstanding performance evinced in hundreds of research fields and problem instances. This book gravitates on the development of nature-inspired methods and their application to stochastic, dynamic and robust optimization. Topics covered by this book include the design and development of evolutionary algorithms, bio-inspired metaheuristics, or memetic methods, with empirical, innovative findings when used in different subfields of mathematical optimization, such as stochastic, dynamic, multimodal and robust optimization, as well as noisy optimization and dynamic and constraint satisfaction problems

Secure and cost-effective operation of low carbon power systems under multiple uncertainties

Power system decarbonisation is driving the rapid deployment of renewable energy sources (RES) like wind and solar at the transmission and distribution level. Their differences from the synchronous thermal plants they are displacing make secure and efficient grid operation challenging. Frequency stability is of particular concern due to the current lack of provision of frequency ancillary services like inertia or response from RES generators. Furthermore, the weather dependency of RES generation coupled with the proliferation of distributed energy resources (DER) like small-scale solar or electric vehicles permeates future low-carbon systems with uncertainty under which legacy scheduling methods are inadequate. Overly cautious approaches to this uncertainty can lead to inefficient and expensive systems, whilst naive methods jeopardise system security. This thesis significantly advances the frequency-constrained scheduling literature by developing frameworks that explicitly account for multiple new uncertainties. This is in addition to RES forecast uncertainty which is the exclusive focus of most previous works. The frameworks take the form of convex constraints that are useful in many market and scheduling problems. The constraints equip system operators with tools to explicitly guarantee their preferred level of system security whilst unlocking substantial value from emerging and abundant DERs. A major contribution is to address the exclusion of DERs from the provision of ancillary services due to their intrinsic uncertainty from aggregation. This is done by incorporating the uncertainty into the system frequency dynamics, from which deterministic convex constraints are derived. In addition to managing uncertainty to facilitate emerging DERs to provide legacy frequency services, a novel frequency containment service is designed. The framework allows a small amount of load shedding to assist with frequency containment during high RES low inertia periods. The expected cost of this service is probabilistic as it is proportional to the probability of a contingency occurring. The framework optimally balances the potentially higher expected costs of an outage against the operational cost benefits of lower ancillary service requirements day-to-day. The developed frameworks are applied extensively to several case studies. These validate their security and demonstrate their significant economic and emission-saving benefits.Open Acces

Routing and scheduling optimisation under uncertainty for engineering applications

The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits.The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits

RISK-AVERSE AND AMBIGUITY-AVERSE MARKOV DECISION PROCESSES

Ph.DDOCTOR OF PHILOSOPH

Stochastic Optimization Approaches for Outpatient Appointment Scheduling under Uncertainty

Outpatient clinics (OPCs) are quickly growing as a central component of the healthcare system. OPCs offer a variety of medical services, with benefits such as avoiding inpatient hospitalization, improving patient safety, and reducing costs of care. However, they also introduce new challenges for appointment planning and scheduling, primarily due to the heterogeneity and variability in patient characteristics, multiple competing performance criteria, and the need to deliver care within a tight time window. Ignoring uncertainty, especially when designing appointment schedules, may have adverse outcomes such as patient delays and clinic overtime. Conversely, accounting for uncertainty when scheduling has the potential to create more efficient schedules that mitigate these adverse outcomes. However, many challenges arise when attempting to account for uncertainty in appointment scheduling problems. In this dissertation, we propose new stochastic optimization models and approaches to address some of these challenges. Specifically, we study three stochastic outpatient scheduling problems with broader applications within and outside of healthcare and propose models and methods for solving them. We first consider the problem of sequencing a set of outpatient procedures for a single provider (where each procedure has a known type and a random duration that follows a known probability distribution), minimizing a weighted sum of waiting, idle time, and overtime. We elaborate on the challenges of solving this complex stochastic, combinatorial, and multi-criteria optimization problem and propose a new stochastic mixed-integer programming model that overcomes these challenges in contrast to the existing models in the literature. In doing so, we show the art of, and the practical need for, good mathematical formulations in solving real-world scheduling problems. Second, we study a stochastic adaptive outpatient scheduling problem which incorporates the patients’ random arrival and service times. Finding a provably-optimal solution to this problem requires solving a MSMIP, which in turn must optimize a scheduling problem over each random arrival and service time for each stage. Given that this MSMIP is intractable, we present two approximation based on two-stage stochastic mixed-integer models and a Monte Carlo Optimization approach. In a series of numerical experiments, we demonstrate the near-optimality of the appointment order (AO) rescheduling policy, which requires that patients are served in the order of their scheduled appointments, in many parameter settings. We also identify parameter settings under which the AO policy is suboptimal. Accordingly, we propose an alternative swap-based policy that improves the solution of such instances. Finally, we consider the outpatient colonoscopy scheduling problem, recognizing the impact of pre-procedure bowel preparation (prep) quality on the variability of colonoscopy duration. Data from a large OPC indicates that colonoscopy durations are bimodal, i.e., depending on the prep quality they can follow two different probability distributions, one for those with adequate prep and the other for those with inadequate prep. We define a distributionally robust outpatient colonoscopy scheduling (DRCOS) problem that seeks optimal appointment sequence and schedule to minimize the worst-case weighted expected sum of patient waiting, provider idling, and provider overtime, where the worst-case is taken over an ambiguity set characterized through the known mean and support of the prep quality and durations. We derive an equivalent mixed-integer linear programming formulation to solve DRCOS. Finally, we present a case study based on extensive numerical experiments in which we draw several managerial insights into colonoscopy scheduling.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/151727/1/ksheha_1.pdfDescription of ksheha_1.pdf : Restricted to UM users only

Personalized Data-Driven Learning and Optimization: Theory and Applications to Healthcare

This dissertation is broadly about developing new personalized data-driven learning and optimization methods with theoretical performance guarantees for three important applications in healthcare operations management and medical decision-making. In these research problems, we are dealing with longitudinal settings, where the decision-maker needs to make multi-stage personalized decisions while collecting data in-between stages. In each stage, the decision-maker incorporates the newly observed data in order to update his current system's model or belief, thereby making better decisions next. This new class of data-driven learning and optimization methods indeed learns from data over time so as to make efficient and effective decisions for each individual in real-time under dynamic, uncertain environments. The theoretical contributions lie in the design and analysis of these new predictive and prescriptive learning and optimization methods and proving theoretical performance guarantees for them. The practical contributions are to apply these methods to resolve unmet real-world needs in healthcare operations management and medical decision-making so as to yield managerial and practical insights and new functionality.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/167949/1/keyvan_1.pd

Robust Local Search for Solving RCPSP/max with Durational Uncertainty

Scheduling problems in manufacturing, logistics and project management have frequently been modeled using the framework of Resource Constrained Project Scheduling Problems with minimum and maximum time lags (RCPSP/max). Due to the importance of these problems, providing scalable solution schedules for RCPSP/max problems is a topic of extensive research. However, all existing methods for solving RCPSP/max assume that durations of activities are known with certainty, an assumption that does not hold in real world scheduling problems where unexpected external events such as manpower availability, weather changes, etc. lead to delays or advances in completion of activities. Thus, in this paper, our focus is on providing a scalable method for solving RCPSP/max problems with durational uncertainty. To that end, we introduce the robust local searc

Digital twin-driven real-time planning, monitoring, and controlling in food supply chains

There needs to be more clarity about when and how the digital twin approach could benefit the food supply chains. In this study, we develop and solve an integrated problem of procurement, production, and distribution strategies (PPDs) in a medium-scale food processing company. Using the digital twin approach, the model considers the industrial symbiosis opportunities between the supplier, manufacturer, and customer using interval and sequence variables operating in a constrained environment using mixed-integer linear programming (MILP) and agent-based simulation (ABS) methodology. The study optimizes the make-span and lead time, simultaneously achieving a higher level of digitalization. The analysis demonstrates how digital twin accelerates supply chain productivity by improving makespan time, data redundancy (DR), optimal scheduling plan (OSP), overall operations effectiveness (OOE), overall equipment effectiveness (OEE), and capacity utilization. Our findings provide compelling evidence that the seamless integration PPDs enormously enhance production flexibility, resulting in an excellent service level of 94 %. Managers leverage real-time simulation to accurately estimate the replenishment point with minimal lead time, ensuring optimized operations. Furthermore, our results demonstrate that implementing PPDs has yielded considerable benefits. Specifically, we observed a remarkable 65 % utilization of the pasteurizer and aging vessel and an impressive 97 % utilization of the freezer. Moreover, by applying the DT model, the present model found a notable 6 % reduction in backlog, further streamlining operations and enhancing efficiency