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

Bi-objective Evolutionary Heuristics for Bus Drivers

The Bus Driver Rostering Problem refers to the assignment of drivers to the daily schedules of the company's buses, during a planning period of a given duration. The drivers' schedules must comply with legal and institutional rules, namely the Labour Law, labour agreements and the company's specific regulations. This paper presents a bi-objective model for the problem and two evolutionary heuristics differing as to the strategies adopted to approach the Pareto frontier. The first one, the utopian strategy, extends elitism to include an unfeasible solution in the population, and the second one is an adapted version of the well known SPEA2 (Strength Pareto Evolutionary Algorithm). The heuristics' empirical performance is studied with computational tests on a set of instances generated from vehicle and crew schedules. This research shows that both methodologies are adequate to tackle the instances of the Bus Driver Rostering Problem. In fact, in short computing times, they provide the planning department, with several feasible solutions, rosters that are very difficult to obtain manually and, in addition, identify among them the efficient solutions of the bi-objective model

A Memetic Algorithm for a Bi-objective Bus Driver Rostering Problem

The Bus Driver Rostering Problem (DRP) consists of assigning bus drivers to daily duties during a planning period. The problem considers hard constraints imposed by institutional and legal requirements. Solutions should as much as possible satisfy soft constraints that qualify rosters according to either the company's or the drivers' interests. A bi-objective version of the DRP is considered and two models are presented. Due to the high computational complexity of DRP, this paper proposes the Strength Pareto Utopic Memetic Algorithm (SPUMA) a new heuristic algorithm specially devised to tackle the problem. SPUMA genetic component combines utopic elitism with a strength Pareto fitness evaluation and includes an improvement procedure. Computational results show that SPUMA outperforms an adaptation of one of the state-of-the-art most competitive multi-objective evolutionary algorithms, SPEA2

A decomposition approach to the integrated vehicle-crew-rostering problem

The problem addressed in this paper is the integrated vehicle-crew-rostering problem (VCRP) aiming to define the schedules for the buses and the rosters for the drivers of a public transit company. The VCRP is described by a bi-objective mixed binary linear programming model with one objective function aggregating vehicle and crew scheduling costs and the other the rostering features. The VCRP is solved by a heuristic approach based on Benders decomposition where the master problem is partitioned into daily integrated vehicle-crew scheduling problems and the sub-problem is a rostering problem. Computational experience with data from a bus company in Lisbon shows the ability of the decomposition approach for producing a variety of potentially efficient solutions for the VCRP within low computing times

Solving Public Transit Scheduling Problems

Operational planning within public transit companies has been extensively tackled but still remains a challenging area for operations research models and techniques. This phase of the planning process comprises vehicle scheduling, crew scheduling and rostering problems. In this paper, a new integer mathematical formulation to describe the integrated vehicle-crew-rostering problem is presented. The method proposed to solve this multi-objective problem is a sequential algorithm considered within a preemptive goal programming framework that starts from the solution of an integrated vehicle and crew scheduling problem and ends with the solution of a driver rostering problem. Feasible solutions for the vehicle and crew scheduling problem are obtained by combining a column generation scheme with a branch-and-bound method. These solutions are the input of the rostering problem, which is tackled through a mixed binary linear programming approach. An application to real data of a Portuguese bus company is reported and shows the importance of integrating the three scheduling problems

Um sistema para o planeamento e gestão das escalas de pessoal de enfermagem de uma unidade hospitalar

Instituto Superior de Economia e Gestão.Neste trabalho apresenta-se um sistema desenvolvido para o planeamento mensal e para a gestão diária das escalas do pessoal de enfermagem de um serviço de clínica cirúrgica de um hospital Estas tarefas são actualmente fertas manualmente, pela responsável do serviço, com base em procedimentos de rotina decorrentes da experiência O sistema automatizado é composto por dois subsistemas e foi implementado em computador pessoal do tipo IBM - compatível O subsistema de planeamento mensal baseia-se na formulação do problema de planeamento como uma sequência de problemas de transporte O subsistema de gestão diária das escalas tem por base a formulação do problema de determinação de uma solução para uma falta inesperada como um problema de determinação do caminho mais curto num grafo Com o novo sistema pretende-se libertar a responsável do serviço de uma tarefa morosa e desinteressante e eventualmente melhorar a qualidade das soluções obtidas respeitando as preferências do pessoal de enfermagem São apresentados resultados computacionais obtidos num conjunto de testes efectuados em que se consideraram diferentes alternativas de funcionamento do serviço.N/

Técnicas de investigação operacional aplicadas a um problema de escalonamento de pessoal em contexto hospitalar

Doutoramento em Matemática Aplicada à Economia e à GestãoO objectivo desta dissertação é resolver um problema de escalonamento de pessoal em contexto hospitalar - o problema de substituição de pessoal em falta a escalas de serviço, aplicando técnicas de Investigação Operacional. Este problema consiste em reconstruir os planos de escalas quando acontecimentos inesperados impedem que uma ou mais enfermeiras executem tarefas que lhes estavam atribuídas. O novo plano de esclas tem de satisfazer os requisitos mínimos exigidos para o funcionamento do serviço, as normas instituídas pela administração e a legislação laboral. Deverá ainda alterar o menos possível as escalas das restantes enfermeiras. A situação foi modelizada como problema de caminhos numa rede multinível e como problema de fluxo inteiro multimercadorias, tendo sido também formalizada em programação linear inteira e estudadas prioridades destas formalizações. Propõem-se métodos heurísticos para a sua resolução, designadamente diferentes versões de uma heurística construtiva e de um algorítmo genético. Apresentam-se os resultados de testes computacionais correspondentes, a um conjunto de instâncias geradas com dados reais de dois serviços hospitalares, obtidos quer com a implementação computacional em Delphi dos diferentes métodos heurísticos, quer com a resolução de problemas de programação linear inteira, usando o CPLEX. Consideram-se de muito boa qualidade as soluções encontradas, em pouco tempo computacional.The objective of this dissertation is to solve a scheduling problem in a hospital context - the rerostering of nurse schedules, with the support of Operations Research. The rerostering problem occurs, when nurses are absent from shifts that cannot operate below a minimum number of personnel stipulated by the organisation. In this case the nurse schedules must be rebuilt from the first day of absences to the last day of the planning period, by altering the schedules of other nurses. These changes should not conflict with the rules laid down by the administration and employment contracts, and should affect the previous schedules as little as possible. The problem is formulated in the context of network optimisation paths and integer multicommodity flow and also in integer linear programming. Properties of those formulations were analysed. Heuristics methods are proposed to solve the problem, namely versions of a constructive heuristic and of a genetic algorithm. Computational experiments were carried out on a set of test instances generated with data from real rosters. Good results were obtained within accetable computational times for all instances tested, either by using CPLEX integer optimiser to solve the resultant integer linear programming problems, or the implemented versions of the heuristics, coded with Delphi programming language

Bi-objective evolutionary heuristics for bus driver rostering

The Bus Driver Rostering Problem (BRP) refers to the assignment of drivers to the daily crew duties that cover a set of schedules for buses of a company during a planning period of a given duration, e.g., a month. An assignment such as this, denoted as roster, must comply with legal and institutional rules, namely Labour Law, labour agreements and the company’s regulations. This paper presents a new bi-objective model for the BRP, assuming a non-cyclic rostering context. One such model is appropriate to deal with the specific and diverse requirements of individual drivers, e.g. absences. Two evolutionary heuristics, differing as to the strategies adopted to approach the Pareto frontier, are described for the BRP. The first one, following a utopian strategy, extends elitism to include an infeasible (utopic) and two potential lexicographic individuals in the population, and the second one is an adapted version of the well known SPEA2 (Strength Pareto Evolutionary Algorithm). The heuristics’ empirical performance was studied through computational tests on BRP instances generated from the solution of integrated vehicle-crew scheduling problems, along with the rules of a public transit company operating in Portugal. This research shows that both methodologies are adequate to tackle these instances. However, the second one is, in general, the more favourable. In reasonable computation times they provide the company’s planning department with several rosters that satisfy all the constraints, an achievement which is very difficult to obtain manually. In addition, among these rosters they identify the potentially efficient ones with respect to the BRP model’s two objectives, one concerning the interests of administration, the other the interests of the workers. Both heuristics have advantages and drawbacks. This suggests that they should be used complementarily. On the other hand, the heuristics can, with little effort, be adapted to a wide variety of rostering rules

A computational application for multi-skill nurse staffing in hospital units

Abstract Background Approaches to nurse staffing are commonly concerned with determining the minimum number of care hours according to the illness severity of patients. However, there is a gap in the literature considering multi-skill and multi-shift nurse staffing. This study addresses nurse staffing per skill category, at a strategical decision level, by considering the organization of work in shifts and coping with variability in demand. Methods We developed a method to determine the nursing staff levels in a hospital, given the required patient assistance. This method relies on a new mathematical model for complying with the legislation and guidelines while minimizing salary costs. A spreadsheet-based tool was developed to embed the model and to allow simulating different scenarios and evaluating the impact of demand fluctuations, thus supporting decision-making on staff dimensioning. Results Experiments were carried out considering real data from a Brazilian hospital unit. The results obtained by the model support the current total staff level in the unit under study. However, the distribution of staff among different skill categories revealed that the current real situation can be improved. Conclusions The method allows the determining of staff level per shift and skill depending on the mix of patients’ illness severity. Hospital management is offered the possibility of optimizing the staff level using a spreadsheet, a tool most managers are familiar with. In addition, it is possible to evaluate the implications of decisions on workforce dimensioning by simulating different demand scenarios. This tool can be easily adapted to other hospitals, using local rules and legislation

Additional file 1: of A computational application for multi-skill nurse staffing in hospital units

Optimization model. The mathematical model used to represent the problem and to implement in the computational tool. (PDF 193 kb