Solving a Bi-objective Nurse Rerostering Problem by Using a Utopic Pareto Genetic Heuristic

Nurse rerostering arises when at least one nurse announces that she will be unable to undertake the tasks previously assigned to her. The problem amounts to building a new roster that satisfies the hard constraints already met by the current one and, as much as possible, fulfils two groups of soft constraints which define the two objectives to be attained. A bi-objective genetic heuristic was designed on the basis of a population of individuals characterised by pairs of chromosomes, whose fitness complies with the Pareto ranking of the respective decoded solution. It includes an elitist policy, as well as a new utopic strategy, introduced for purposes of diversification. The computational experiments produced promising results for the practical application of this approach to real life instances arising from a public hospital in Lisbon

Approximate Algorithms for the Combined arrival-Departure Aircraft Sequencing and Reactive Scheduling Problems on Multiple Runways

The problem addressed in this dissertation is the Aircraft Sequencing Problem (ASP) in which a schedule must be developed to determine the assignment of each aircraft to a runway, the appropriate sequence of aircraft on each runway, and their departing or landing times. The dissertation examines the ASP over multiple runways, under mixed mode operations with the objective of minimizing the total weighted tardiness of aircraft landings and departures simultaneously. To prevent the dangers associated with wake-vortex effects, separation times enforced by Aviation Administrations (e.g., FAA) are considered, adding another level of complexity given that such times are sequence-dependent. Due to the problem being NP-hard, it is computationally difficult to solve large scale instances in a reasonable amount of time. Therefore, three greedy algorithms, namely the Adapted Apparent Tardiness Cost with Separation and Ready Times (AATCSR), the Earliest Ready Time (ERT) and the Fast Priority Index (FPI) are proposed. Moreover, metaheuristics including Simulated Annealing (SA) and the Metaheuristic for Randomized Priority Search (Meta-RaPS) are introduced to improve solutions initially constructed by the proposed greedy algorithms. The performance (solution quality and computational time) of the various algorithms is compared to the optimal solutions and to each other. The dissertation also addresses the Aircraft Reactive Scheduling Problem (ARSP) as air traffic systems frequently encounter various disruptions due to unexpected events such as inclement weather, aircraft failures or personnel shortages rendering the initial plan suboptimal or even obsolete in some cases. This research considers disruptions including the arrival of new aircraft, flight cancellations and aircraft delays. ARSP is formulated as a multi-objective optimization problem in which both the schedule\u27s quality and stability are of interest. The objectives consist of the total weighted start times (solution quality), total weighted start time deviation, and total weighted runway deviation (instability measures). Repair and complete regeneration approximate algorithms are developed for each type of disruptive events. The algorithms are tested against difficult benchmark problems and the solutions are compared to optimal solutions in terms of solution quality, schedule stability and computational time

Optimization Models and Approximate Algorithms for the Aerial Refueling Scheduling and Rescheduling Problems

The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with release times and due date-to-deadline window. ARSP assumes that the jobs have different release times, due dates, and due date-to-deadline windows between the refueling due date and a deadline to return without refueling. The Aerial Refueling Rescheduling Problem (ARRP), on the other hand, can be defined as updating the existing AR schedule after being disrupted by job related events including the arrival of new aircrafts, departure of an existing aircrafts, and changes in aircraft priorities. ARRP is formulated as a multiobjective optimization problem by minimizing the total weighted tardiness (schedule quality) and schedule instability. Both ARSP and ARRP are formulated as mixed integer programming models. The objective function in ARSP is a piecewise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, four approximate algorithms are proposed to obtain solutions in reasonable computational times, namely (1) apparent piecewise tardiness cost with release time rule (APTCR), (2) simulated annealing starting from random solution (SArandom ), (3) SA improving the initial solution constructed by APTCR (SAAPTCR), and (4) Metaheuristic for Randomized Priority Search (MetaRaPS). Additionally, five regeneration and partial repair algorithms (MetaRE, BestINSERT, SEPRE, LSHIFT, and SHUFFLE) were developed for ARRP to update instantly the current schedule at the disruption time. The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with randomly generated data to represent AR operations and disruptions. Effectiveness of the scheduling and rescheduling algorithms are compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, APTCR is more likely to outperform SArandom especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of APTCR is significantly better than SA in both cases. MetaRaPS is more likely to outperform SAAPTCR in terms of average error from optimal solutions for both small and large size problems. Results for small size problems show that MetaRaPS algorithm is more robust compared to SAAPTCR. However, CPU time performance of SA is significantly better than MetaRaPS in both cases. ARRP experiments were conducted with various values of objective weighting factor for extended analysis. In the job arrival case, MetaRE and BestINSERT have significantly performed better than SEPRE in terms of average relative error for small size problems. In the case of job priority disruption, there is no significant difference between MetaRE, BestINSERT, and SHUFFLE algorithms. MetaRE has significantly performed better than LSHIFT to repair job departure disruptions and significantly superior to the BestINSERT algorithm in terms of both relative error and computational time for large size problems

Minimizing the waiting time for emergency surgery

Hospitals aim to deliver the highest quality of care. One key priority is to schedule emergency surgeries as quickly as possible, because postponing them generally increases a patient’s risk of complications and even death. In this paper, we consider the case that emergency surgeries are scheduled in one of the elective Operating Rooms (ORs). In this situation, emergency patients are operated once an going elective surgery has finished. We denote these completion times of the elective surgeries by ‘break-in-moments’ (BIMs). The waiting time for emergency surgeries can be reduced by spreading these BIMs as evenly as possible over the day. This can be achieved by sequencing the surgeries in their assigned OR, such that the maximum interval between two consecutive BIMs is minimized. In this paper, we discuss several exact and heuristic solution methods for this new type of scheduling problem. However, in practice, emergency surgeries arising throughout the day and the uncertainty of the durations of elective surgeries, may disrupt the initial schedule. As a result, the completion times of the elective surgeries, and therefore, the BIMs change, leading also to a change of the maximum distance between two BIMs. To estimate this effect and investigate the robustness of the created schedules, we conduct a simulation study. Computational results show that the best approaches reduce the waiting time of emergency surgeries by approximately 10%

Decision support systems for task scheduling: applications in manufacturing and healthcare

Esta Tesis se centra en el problema de la programación de tareas. Aunque pueden encontrarse diferentes definiciones de la programación de tareas en la literatura, aquí se define como la asignación de un número de tareas – acciones individuales que deben realizarse para completar un determinado proceso-, a un conjunto de recursos, en momentos de tiempo específicos. Pueden encontrarse ejemplos de programación de tareas en muchos contextos, como por ejemplo, el orden en el que deben fabricarse las diferentes partes de un coche, la asignación de quirófanos y cirujanos a intervenciones quirúrgicas en un hospital, o el orden en el que deben ser servidos los clientes de un restaurante. La programación de tareas supone un elemento clave en muchas compañías, en el campo de los servicios y en el de la fabricación, ya que es esencial para la coordinación del trabajo entre los diferentes actores involucrados, tales como departamentos, recursos (físicos y humanos) o entidades externas. En la mayoría de los casos, la programación de tareas conlleva trabajar con grandes cantidades de datos relacionados con el proceso y gestionar correctamente el conjunto de restricciones que controlan el proceso. Como consecuencia de esto, la programación de tareas suele hacerse con ayuda de herramientas informáticas que ofrecen algún tipo de soporte para el decisor. A este respecto, el auge de las Tecnologías de la Información (TI) en las últimas décadas ha ayudado enormemente al desarrollo de sistemas computarizados que ofrecen soporte a la toma de decisiones – Sistemas de Soporte a la Decisión (SSD) – en muchos ámbitos, incluyendo la programación de tareas. Además, ha habido un notable aumento en la capacidad computacional que ha hecho posible afrontar problemas de programación de tareas que se consideraban irresolubles hace algunos años. A pesar de estos avances, se ha detectado un gap entre teoría y práctica al llevar estas nuevas condiciones a la práctica, que puede ser demostrado por el limitado número de sistemas que se han implementado y aceptado por los usuarios satisfactoriamente. La hipótesis de trabajo de esta Tesis es que, para reducir este gap entre teoría y práctica, estos sistemas deberían considerar un conjunto de aspectos que se han estudiado en la literatura pero que no se han tenido en cuenta en el proceso de implementación, tales como el rol del decisor en el sistema, el contexto organizacional donde se toman las decisiones para la programación o la consideración de la programación como un proceso dinámico. Normalmente, cada vez que una empresa necesita implementar un SSD para la programación de tareas (SSDPT), es posible elegir entre dos opciones: adquirir una solución off-the-shelf, o diseñar y desarrollar una herramienta personalizada. Cuando se elige la primera opción, normalmente la solución no se adapta perfectamente a las actividades de la empresa, y considerando que la programación de tareas es muy dependiente del contexto, esta opción puede resultar en una situación muy documentada en la literatura en la que se consigue una implementación muy limitada en la que hay diferentes sistemas de información trabajando en paralelo para tener en cuenta las diferentes especificidades de la empresa. Por otro lado, si se opta por la segunda opción, esta suele derivar en largos tiempos de implementación con resultados pobres, ya que el equipo de desarrollo podría no tener en cuenta los errores y aciertos de otras implementaciones, tales como las funcionalidades que un sistema debería tener o los perfiles que se debería dar a los diferentes usuarios. Como resumen podríamos decir que el diseño y la implementación de SSDPT tienen un conjunto de problemas que constituyes una de las principales causas del gap existente entre la teoría de la programación de tareas y su implementación en la práctica. Para mejorar la actividad de diseño y desarrollo de SSDPT, el objetivo de esta tesis es proponer un framework común para el desarrollo de SSDPT. Para asegurar su validez y analizar su rango de aplicación, se analiza su factibilidad en dos sectores de aplicación, fabricación y salud, y se llevan a cabo dos casos de estudio en estos sectores. Para conseguir el objetivo general de la Tesis, se consideran un conjunto de objetivos específicos: 1. Proponer un framework para el diseño y desarrollo de SSDPT. • El framework tiene en cuenta todos los problemas detectados en la literatura que tienen que ver con los fallo a la hora de implementar este tipo de sistemas. Este framework se detalla mediante un conjunto de perspectivas. 2. Analizar las implementaciones existentes de SSDPT para analizar la alineación del framework propuesto con las implementaciones existentes de este tipo de sistemas en los dos campos de aplicación. • Se lleva a cabo una revisión sistemática de la literatura en SSDPT en fabricación. Las contribuciones revisadas se clasifican de acuerdo a las funcionalidades que presentan. Se analizan y discuten una serie de resultados y conclusiones de los mismos. Además se realiza una revisión de SSDPT comerciales para la programación de quirófanos. Estas contribuciones también se clasifican según sus funcionalidades y se presentan y discuten una serie de resultados y conclusiones. 3. Levar a cabo el diseño e implementación de dos SSDPT de acuerdo con el framework propuesto para demostrar su validez. • Basándonos en el framework un SSDPT para fabricación y un SSDPT para la programación de quirófanos han sido propuestos: i. El SSDPT para fabricación se implementó para una empresa de fabricación situada en Sevilla. Primero se describe el contexto en el que el sistema actúa y el problema considerado. Después se estudian los principales casos de uso del sistema y se relacionan con el framework propuesto. Más tarde, se proponen una serie de métodos de resolución eficientes para el problema analizado. Finalmente, se realiza una breve discusión sobre los principales resultados de implementación del sistema. ii. El SSDPT para programación de quirófanos se implementó en un hospital situado en Sevilla. Primero se describe el contexto en el que el sistema actúa y el problema considerado. Después se estudian los principales casos de uso del sistema y se relacionan con el framework propuesto. Más tarde, se proponen una serie de métodos de resolución eficientes para el problema analizado. Finalmente, se realiza una breve discusión sobre los principales resultados de implementación del sistema.This thesis focuses on the problem of task scheduling. Although slightly different definitions of task scheduling can be found in the literature, here it is defined as the allocation of a number of tasks - single actions that must be performed to complete a specific process-, to a set of resources, at specific moments in time. Examples of task scheduling can be found in many settings, as for example, the order in which the different parts of a car have to be manufactured in a set of machines, the allocation of operating rooms and surgeons to the surgical interventions in a hospital, or the order in which the customers of a restaurant should be served. Clearly, task scheduling is a core activity of many companies, both in manufacturing and in services, as it is essential for the coordination of the work between the different involved actors, such as departments, resources (human and physical) or external entities. In most settings, task scheduling involves treating large amounts of data related to the process and properly handling the set of constraints controlling this process. As a consequence, task scheduling is usually carried out with the help of computer tools that offer some type of support to the decision maker. In this regard, the rising of Information Technologies (ITs) in the last decades has helped enormously to develop computer systems providing support for decision making - i.e. Decision Support Systems (DSSs) - for many decisions, including task scheduling. At the same time, there has been a notable increase in computer capacity that has made possible facing task scheduling problems that were considered unsolvable some years ago. Despite these advances, an important gap between theory and practice has been found when translating these new conditions into practice, as it can be proven by the relatively short number of documented systems that have been correctly implemented and accepted by users. The working hypothesis in this Thesis is that, in order to reduce this gap between theory and practice, these tools should consider a number of aspects that have been studied in the literature but that have not been taken into account in practice during the implementation process, such as the role of the decision makers in these tools, the organisational context where scheduling decisions take place or the consideration of scheduling as a dynamic process. Typically, each time a company requires to implement of a DSS for task scheduling, in the following DSSTS, it faces two different options: either acquiring an off-the-shelf solution, or designing and developing an in-house tool. If the former option is chosen, the acquired solution may not fit perfectly into the activities of the company, and, since task scheduling is company-specific, this approach may result in a situation widely documented in the literature where there exist limited implementations that needs information systems working in parallel to deal with the specificities of the company. On the contrary, the second option usually derives in large implementation times with poor results, as the development team may not take into account errors or successes from former implementations, such as the functionalities that the system should include or the profiles required for the decision makers among others. As a summary, the design and implementation of DSSTS suffer a number of problems which constitute a root cause for the existing gap between the scheduling theory and its implementation into practice. In order to improve the activity of designing and developing DSSTS, the aim of this thesis is to propose a common framework for the development of DSSTS. In order to ensure the validity and range of application of this framework, its feasibility is analysed within two specific fields of applications, namely manufacturing and healthcare, and two implementation case studies are conducted within these fields. In order to fullfil this general objective, a number of specific objectives can be detailed: 1. To propose a framework for the design and development of DSSTS. • This framework address all the issues found in literature regarding the common failures when implementing this type of systems. A number of perspectives of the framework are given in order to properly detail it. 2. To analyse existing implementations of DSSTS in order to check the alignment of the framework proposed with the task scheduling systems implemented in the two sectors chosen for the evaluation of the framework. • A systematic literature review on manufacturing DSSTS is carried out. The reviewed contributions are classified according to their functionalities. A number of findings and conclusions about these findings are discussed. Additionally, a review on commercial operating room DSSTS is done. These contributions are also classified according to their functionality and a number of findings and conclusions about these findings are discussed. 3. To conduct the design and implementation of two DSSTS according to the proposed framework in order to demonstrate its applicability. • Based on the proposed framework, a manufacturing DSSTS and an operating room DSSTS are implemented: i. The manufacturing DSSTS is applied to a real manufacturing company in Sevilla. First, we describe the context where the DSSTS is deployed and the problem addressed, i.e. the hybrid flowshop scheduling problem with missing operations. Then, the main use cases of the DSSTS are discussed and related to the framework. Next, a set of efficient solution procedures for the problem under study are proposed. And finally, a brief discussion on the main results of the implementation of the DSSTS is carried out. ii. The operating room DSSTS is applied to a real hospital in Sevilla. First, we describe the context where the DSSTS is deployed and the problem addressed, i.e. the the operating room scheduling problem. Then, the main use cases of the DSSTS are discussed and related to the framework. Next, a set of efficient solution procedures for the problem under study are proposed. And finally, a brief discussion on the main results of the implementation of the DSSTS is carried out

A review and classification of heuristics for permutation flow-shop scheduling with makespan objective

Makespan minimization in permutation flow-shop scheduling is an operations research topic that has been intensively addressed during the last 40 years. Since the problem is known to be NP-hard for more than two machines, most of the research effort has been devoted to the development of heuristic procedures in order to provide good approximate solutions to the problem. However, little attention has been devoted to establish a common framework for these heuristics so that they can be effectively combined or extended. In this paper, we review and classify the main contributions regarding this topic and discuss future research issues.Ministerio de Ciencia y Tecnología DPI-2001-311

The dynamic, resource-constrained shortest path problem on an acyclic graph with application in column generation and literature review on sequence-dependent scheduling

This dissertation discusses two independent topics: a resource-constrained shortest-path problem (RCSP) and a literature review on scheduling problems involving sequence-dependent setup (SDS) times (costs). RCSP is often used as a subproblem in column generation because it can be used to solve many practical problems. This dissertation studies RCSP with multiple resource constraints on an acyclic graph, because many applications involve this configuration, especially in column genetation formulations. In particular, this research focuses on a dynamic RCSP since, as a subproblem in column generation, objective function coefficients are updated using new values of dual variables at each iteration. This dissertation proposes a pseudo-polynomial solution method for solving the dynamic RCSP by exploiting the special structure of an acyclic graph with the goal of effectively reoptimizing RCSP in the context of column generation. This method uses a one-time âÂÂpreliminaryâ phase to transform RCSP into an unconstrained shortest path problem (SPP) and then solves the resulting SPP after new values of dual variables are used to update objective function coefficients (i.e., reduced costs) at each iteration. Network reduction techniques are considered to remove some nodes and/or arcs permanently in the preliminary phase. Specified techniques are explored to reoptimize when only several coefficients change and for dealing with forbidden and prescribed arcs in the context of a column generation/branch-and-bound approach. As a benchmark method, a label-setting algorithm is also proposed. Computational tests are designed to show the effectiveness of the proposed algorithms and procedures. This dissertation also gives a literature review related to the class of scheduling problems that involve SDS times (costs), an important consideration in many practical applications. It focuses on papers published within the last decade, addressing a variety of machine configurations - single machine, parallel machine, flow shop, and job shop - reviewing both optimizing and heuristic solution methods in each category. Since lot-sizing is so intimately related to scheduling, this dissertation reviews work that integrates these issues in relationship to each configuration. This dissertation provides a perspective of this line of research, gives conclusions, and discusses fertile research opportunities posed by this class of scheduling problems. since, as a subproblem in column generation, objective function coefficients are updated using new values of dual variables at each iteration. This dissertation proposes a pseudo-polynomial solution method for solving the dynamic RCSP by exploiting the special structure of an acyclic graph with the goal of effectively reoptimizing RCSP in the context of column generation. This method uses a one-tim