Selecting genetic operators to maximise preference satisfaction in a workforce scheduling and routing problem

The Workforce Scheduling and Routing Problem (WSRP) is a combinatorial optimisation problem that involves scheduling and routing of workforce. Tackling this type of problem often requires handling a considerable number of requirements, including customers and workers preferences while minimising both operational costs and travelling distance. This study seeks to determine effective combinations of genetic operators combined with heuristics that help to find good solutions for this constrained combinatorial optimisation problem. In particular, it aims to identify the best set of operators that help to maximise customers and workers preferences satisfaction. This paper advances the understanding of how to effectively employ different operators within two variants of genetic algorithms to tackle WSRPs. To tackle infeasibility, an initialisation heuristic is used to generate a conflict-free initial plan and a repair heuristic is used to ensure the satisfaction of constraints. Experiments are conducted using three sets of real-world Home Health Care (HHC) planning problem instances

Adaptive multiple crossover genetic algorithm to solve workforce scheduling and routing problem

The Workforce Scheduling and Routing Problem refers to the assignment of personnel to visits, across various geographical locations. Solving this problem demands tackling numerous scheduling and routing constraints while aiming to minimise the operational cost. One of the main obstacles in designing a genetic algorithm for this problem is selecting the best set of operators that enable better performance in a Genetic Algorithm (GA). This paper presents an adaptive multiple crossover genetic algorithm to tackle the combined setting of scheduling and routing problems. A mix of problem-specific and traditional crossovers are evaluated by using an online learning process to measure the operator's effectiveness. Best performing operators are given high application rates and low rates are given to the worse performing ones. Application rates are dynamically adjusted according to the learning outcomes in a non-stationary environment. Experimental results show that the combined performances of all the operators works better than using one operator in isolation. This study makes a contribution to advance our understanding of how to make effective use of crossover operators on this highly-constrained optimisation problem

Holistic, data-driven, service and supply chain optimisation: linked optimisation.

The intensity of competition and technological advancements in the business environment has made companies collaborate and cooperate together as a means of survival. This creates a chain of companies and business components with unified business objectives. However, managing the decision-making process (like scheduling, ordering, delivering and allocating) at the various business components and maintaining a holistic objective is a huge business challenge, as these operations are complex and dynamic. This is because the overall chain of business processes is widely distributed across all the supply chain participants; therefore, no individual collaborator has a complete overview of the processes. Increasingly, such decisions are automated and are strongly supported by optimisation algorithms - manufacturing optimisation, B2B ordering, financial trading, transportation scheduling and allocation. However, most of these algorithms do not incorporate the complexity associated with interacting decision-making systems like supply chains. It is well-known that decisions made at one point in supply chains can have significant consequences that ripple through linked production and transportation systems. Recently, global shocks to supply chains (COVID-19, climate change, blockage of the Suez Canal) have demonstrated the importance of these interdependencies, and the need to create supply chains that are more resilient and have significantly reduced impact on the environment. Such interacting decision-making systems need to be considered through an optimisation process. However, the interactions between such decision-making systems are not modelled. We therefore believe that modelling such interactions is an opportunity to provide computational extensions to current optimisation paradigms. This research study aims to develop a general framework for formulating and solving holistic, data-driven optimisation problems in service and supply chains. This research achieved this aim and contributes to scholarship by firstly considering the complexities of supply chain problems from a linked problem perspective. This leads to developing a formalism for characterising linked optimisation problems as a model for supply chains. Secondly, the research adopts a method for creating a linked optimisation problem benchmark by linking existing classical benchmark sets. This involves using a mix of classical optimisation problems, typically relating to supply chain decision problems, to describe different modes of linkages in linked optimisation problems. Thirdly, several techniques for linking supply chain fragmented data have been proposed in the literature to identify data relationships. Therefore, this thesis explores some of these techniques and combines them in specific ways to improve the data discovery process. Lastly, many state-of-the-art algorithms have been explored in the literature and these algorithms have been used to tackle problems relating to supply chain problems. This research therefore investigates the resilient state-of-the-art optimisation algorithms presented in the literature, and then designs suitable algorithmic approaches inspired by the existing algorithms and the nature of problem linkages to address different problem linkages in supply chains. Considering research findings and future perspectives, the study demonstrates the suitability of algorithms to different linked structures involving two sub-problems, which suggests further investigations on issues like the suitability of algorithms on more complex structures, benchmark methodologies, holistic goals and evaluation, processmining, game theory and dependency analysis

Metaheuristics For Solving Real World Employee Rostering and Shift Scheduling Problems

Optimising resources and making considerate decisions are central concerns in any responsible organisation aiming to succeed in efficiently achieving their goals. Careful use of resources can have positive outcomes in the form of fiscal savings, improved service levels, better quality products, improved awareness of diminishing returns and general output efficiency, regardless of field. Operational research techniques are advanced analytical tools used to improve managerial decision-making. There have been a variety of case studies where operational research techniques have been successfully applied to save millions of pounds. Operational research techniques have been successfully applied to a multitude of fields, including agriculture, policing, defence, conservation, air traffic control, and many more. In particular, management of resources in the form of employees is a challenging problem --- but one with the potential for huge improvements in efficiency. The problem this thesis tackles can be divided into two sub-problems; the personalised shift scheduling & employee rostering problem, and the roster pattern problem. The personalised shift scheduling & employee rostering problem involves the direct scheduling of employees to hours and days of week. This allows the creation of schedules which are tailored to individuals and allows a fine level over control over the results, but with at the cost of a large and challenging search space. The roster pattern problem instead takes existing patterns employees currently work, and uses these as a pool of potential schedules to be used. This reduces the search space but minimises the number of changes to existing employee schedules, which is preferable for personnel satisfaction. Existing research has shown that a variety of algorithms suit different problems and hybrid methods are found to typically outperform standalone ones in real-world contexts. Several algorithmic approaches for solving variations of the employee scheduling problem are considered in this thesis. Initially a VNS approach was used with a Metropolis-Hastings acceptance criterion. The second approach utilises ER&SR controlled by the EMCAC, which has only been used in the field of exam timetabling, and has not before been used within the domain of employee scheduling and rostering. ER&SR was then hybridised with our initial approach, producing ER&SR with VNS. Finally, ER&SR was hybridised into a matheuristic with Integer Programming and compared to the hybrid's individual components. A contribution of this thesis is evidence that the algorithm ER&SR has merit outside of the original sub-field of exam scheduling, and can be applied to shift scheduling and employee rostering. Further, ER&SR was hybridised and schedules produced by the hybridisations were found to be of higher quality than the standalone algorithm. In the literature review it was found that hybrid algorithms have become more popular in real-world problems in recent years, and this body of work has explored and continued this trend. Problem formulations in this thesis provide insight into creating constraints which satisfy the need for minimising employee dissatisfaction, particularly in regards to abrupt change. The research presented in this thesis has positively impacted a multinational and multibillion dollar field service operations company. This has been achieved by implementing a variety of techniques, including metaheuristics and a matheuristic, to schedule shifts and roster employees over a period of several months. This thesis showcases the research outputs by this project, and highlights the real-world impact of this research

Novel heuristic and metaheuristic approaches to the automated scheduling of healthcare personnel

This thesis is concerned with automated personnel scheduling in healthcare organisations; in particular, nurse rostering. Over the past forty years the nurse rostering problem has received a large amount of research. This can be mostly attributed to its practical applications and the scientific challenges of solving such a complex problem. The benefits of automating the rostering process include reducing the planner’s workload and associated costs and being able to create higher quality and more flexible schedules. This has become more important recently in order to retain nurses and attract more people into the profession. Better quality rosters also reduce fatigue and stress due to overwork and poor scheduling and help to maximise the use of leisure time by satisfying more requests. A more contented workforce will lead to higher productivity, increased quality of patient service and a better level of healthcare. Basically stated, the nurse rostering problem requires the assignment of shifts to personnel to ensure that sufficient employees are present to perform the duties required. There are usually a number of constraints such as working regulations and legal requirements and a number of objectives such as maximising the nurses working preferences. When formulated mathematically this problem can be shown to belong to a class of problems which are considered intractable. The work presented in this thesis expands upon the research that has already been conducted to try and provide higher quality solutions to these challenging problems in shorter computation times. The thesis is broadly structured into three sections. 1) An investigation into a nurse rostering problem provided by an industrial collaborator. 2) A framework to aid research in nurse rostering. 3) The development of a number of advanced algorithms for solving highly complex, real world problems

An Optimisation-based Framework for Complex Business Process: Healthcare Application

The Irish healthcare system is currently facing major pressures due to rising demand, caused by population growth, ageing and high expectations of service quality. This pressure on the Irish healthcare system creates a need for support from research institutions in dealing with decision areas such as resource allocation and performance measurement. While approaches such as modelling, simulation, multi-criteria decision analysis, performance management, and optimisation can – when applied skilfully – improve healthcare performance, they represent just one part of the solution. Accordingly, to achieve significant and sustainable performance, this research aims to develop a practical, yet effective, optimisation-based framework for managing complex processes in the healthcare domain. Through an extensive review of the literature on the aforementioned solution techniques, limitations of using each technique on its own are identified in order to define a practical integrated approach toward developing the proposed framework. During the framework validation phase, real-time strategies have to be optimised to solve Emergency Department performance issues in a major hospital. Results show a potential of significant reduction in patients average length of stay (i.e. 48% of average patient throughput time) whilst reducing the over-reliance on overstretched nursing resources, that resulted in an increase of staff utilisation between 7% and 10%. Given the high uncertainty in healthcare service demand, using the integrated framework allows decision makers to find optimal staff schedules that improve emergency department performance. The proposed optimum staff schedule reduces the average waiting time of patients by 57% and also contributes to reduce number of patients left without treatment to 8% instead of 17%. The developed framework has been implemented by the hospital partner with a high level of success

Novel heuristic and metaheuristic approaches to the automated scheduling of healthcare personnel

This thesis is concerned with automated personnel scheduling in healthcare organisations; in particular, nurse rostering. Over the past forty years the nurse rostering problem has received a large amount of research. This can be mostly attributed to its practical applications and the scientific challenges of solving such a complex problem. The benefits of automating the rostering process include reducing the planner’s workload and associated costs and being able to create higher quality and more flexible schedules. This has become more important recently in order to retain nurses and attract more people into the profession. Better quality rosters also reduce fatigue and stress due to overwork and poor scheduling and help to maximise the use of leisure time by satisfying more requests. A more contented workforce will lead to higher productivity, increased quality of patient service and a better level of healthcare. Basically stated, the nurse rostering problem requires the assignment of shifts to personnel to ensure that sufficient employees are present to perform the duties required. There are usually a number of constraints such as working regulations and legal requirements and a number of objectives such as maximising the nurses working preferences. When formulated mathematically this problem can be shown to belong to a class of problems which are considered intractable. The work presented in this thesis expands upon the research that has already been conducted to try and provide higher quality solutions to these challenging problems in shorter computation times. The thesis is broadly structured into three sections. 1) An investigation into a nurse rostering problem provided by an industrial collaborator. 2) A framework to aid research in nurse rostering. 3) The development of a number of advanced algorithms for solving highly complex, real world problems

Optimisation heuristics for solving technician and task scheduling problems

Motivated by an underlying industrial demand, solving intractable technician and task scheduling problems through the use of heuristic and metaheuristic approaches have long been an active research area within the academic community. Many solution methodologies, proposed in the literature, have either been developed to solve a particular variant of the technician and task scheduling problem or are only appropriate for a specific scale of the problem. The motivation of this research is to find general-purpose heuristic approaches that can solve variants of technician and task scheduling problems, at scale, balancing time efficiency and solution quality. The unique challenges include finding heuristics that are robust, easily adapted to deal with extra constraints, and scalable, to solve problems that are indicative of the real world. The research presented in this thesis describes three heuristic methodologies that have been designed and implemented: (1) the intelligent decision heuristic (which considers multiple team configuration scenarios and job allocations simultaneously), (2) the look ahead heuristic (characterised by its ability to consider the impact of allocation decisions on subsequent stages of the scheduling process), and (3) the greedy randomized heuristic (which has a flexible allocation approach and is computationally efficient). Datasets used to test the three heuristic methodologies include real world problem instances, instances from the literature, problem instances extended from the literature to include extra constraints, and, finally, instances created using a data generator. The datasets used include a broad array of real world constraints (skill requirements, teaming, priority, precedence, unavailable days, outsourcing, time windows, and location) on a range of problem sizes (5-2500 jobs) to thoroughly investigate the scalability and robustness of the heuristics. The key findings presented are that the constraints a problem features and the size of the problem heavily influence the design and behaviour of the solution approach used. The contributions of this research are; benchmark datasets indicative of the real world in terms of both constraints included and problem size, the data generators developed which enable the creation of data to investigate certain problem aspects, mathematical formulation of the multi period technician routing and scheduling problem, and, finally, the heuristics developed which have proved to be robust and scalable solution methodologies

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