Margarida Vaz Pato

A genetic algorithm approach to a nurse rerostering problem

Abstract The nurse rerostering problem occurs when one or more nurses cannot work in shifts that were previously assigned to her or them. If no pool of reserve nurses exists to replace those absent, then the current roster must be rebuilt. This new roster must comply with the labour rules and institutional constraints. Moreover, it must be as similar as possible to the current one. The present paper describes constructive heuristics, besides several versions of genetic algorithms based on specific encoding and operators for sequencing problems applied to the nurse rerostering problem, defined with hard constraints. In the genetic algorithms described, each individual in the population is associated with a pair of chromosomes, representing permutations of tasks and nurses. Those permutations are used as input to a procedure that generates rosters. The fitness of individuals is given by the similarity between the roster generated from the permutations and the current one. The authors developed several versions of the genetic algorithm, whose difference lay in the encoding of permutations and in the genetic operators used for each encoding. These heuristics were tested with real data from a Lisbon hospital and yielded good quality solutions. Scope and purpose The research reported is part of a project designed to develop a system for the management of nurse schedules for implementation in Portuguese public hospitals. The specific problem of rebuilding nurse schedules is addressed when unexpected staff absences arise. The complexity of the problem led the authors to design heuristic procedures. The tests performed so far with real data have shown that the algorithms attain good quality solutions at a computing time within the bounds stipulated by the hospital.

SHIP ASSIGNMENT WITH HUB AND SPOKE CONSTRAINTS

As the shipping industry enters the future, an increasing number of technological developments are being introduced into this market. This has led to a significant change in business operations, such as the innovative design of hub and spoke systems, resulting in cargo consolidation and a better use of the ships capacity. In the light of this new scenario, the authors present a successful application of integer linear programming to support the decision-making process of assigning ships to previously defined voyages — the rosters. The tool used to build the final models was the MS-Excel Solver (Microsoft® Excel 97 SR-2, 1997), a package that enabled the real case studies addressed to be solved. The results of the experiment prompted the authors to favour the assignment of very small fleets, as opposed to the existing high number of ships employed in such real trades,

An integer programming approach to elective surgery scheduling

The scope of this work covers a real case of elective surgery planning in a Lisbon hospital. The aim is to employ more efficiently the resources installed in the surgical suite of the hospital in question besides improving the functioning of its surgical service. Such a planning sets out to schedule elective surgeries from the waiting list on a weekly time horizon with the objective of maximizing the use of the surgical suite. For this purpose, the authors develop an integer linear programming model. The model is tested using real data obtained from the hospital’s record. The non-optimal solutions are further improved by developing a custom-made, simple and efficient improvement heuristic. Application of this heuristic effectively improves almost all non-optimal solutions. The results are analyzed and compared with the actual performance of the surgical suite. This analysis reveals that the solutions obtained using this approach comply with the conditions imposed by the hospital and improve the use of the surgical suite. It also shows that in this case study the plans obtained from the proposed approach may be implemented in real life.

Solving the Problem of Rerostering Nurse Schedules with Hard Constraints: New Multicommodity Flow Models

The problem of rerostering nurse schedules arises in hospitals when at least one nurse informs that she will be unable to perform the shifts assigned to her on one or more future work days. As a result, the current roster must be rebuilt in accordance with labour contract rules and institutional requirements. All such restraints are regarded as hard constraints. However, major alterations in the previously assigned nurse schedules must be avoided. This paper is based on a case study of a public hospital in Portugal. It presents two new integer multicommodity flow formulations for the rerostering problem, besides a computational experiment performed using real data. The first model is based on a directed multilevel acyclic network. The aggregation of nodes in this network led to the second model. The results obtained show that the second integer multicommodity flow formulation outperforms the first, both in terms of solution quality, as well as in computational time.

A Multiobjective Genetic Algorithm for the Class/Teacher Timetabling Problem

The drawing up of school timetables is a slow, laborious task, performed by people working on the strength of their knowledge of resources and constraints of a specific institution. This paper begins by presenting the timetabling problems that emerge in the context of educational institutions. This is followed by a description of the basic characteristics of the class/teacher timetabling problem. Timetables are considered feasible provided the so-called hard constraints are respected. However, to obtain high-quality timetabling solutions, other conditions should be satisfied in this case - those of soft constraints - which impose satisfaction of a set of desirable conditions for classes and teachers. A multiobjective genetic algorithm was proposed for this timetabling problem, incorporating two distinct objectives. They concern precisely the minimization of the violations of both types of constraints, hard and soft, while respecting the two competing aspects - teachers and classes. A brief description of the characteristics of a genetic multiobjective metaheuristic is presented, followed by the nondominated sorting genetic algorithm, using a standard fitness-sharing scheme improved with an elitist secondary population. This approach represents each timetabling solution with a matrix-type chromosome and is based on special-purpose genetic operators of crossover and mutation developed to act over a secondary population and a fixed-dimension main population of chromosomes. The paper concludes with a discussion of the favorable results obtained through an application of the algorithm to a real instance taken from a university establishment in Portugal.

Search strategies for the feeder bus network design problem

This paper reports on computing solutions for a specific problem arising in public transport systems - the Feeder Bus Network Design Problem (FBDP). The problem requires the design of a set of feeder bus routes and the definition of their service frequencies to satisfy both the resource constraints and the demand for transportation: passengers located at any of the bus stops wish to go to any of the stations of a rail transit line in order to access a common destination identified as the central station. The objective is to minimize a cost function, where both passenger and operator interests are considered. This problem may be formulated as a difficult, nonlinear and nonconvex mixed integer problem, classified as NP-hard. The study focuses on a combined building plus improving heuristic procedure, partially taken from literature. The starting module builds up a solution through a sequential savings or a two-phase method, and for the last module the method includes local search, as well as tabu search heuristics with different strategies. Additionally, computational results from a set of problems simulating real life situations are given. Through this experiment the authors conclude that the simplest short-term version of tabu search is one of most promising heuristics.

A Comparison of Discrete and Continuous Neural Network Approaches to Solve the Class/Teacher Timetabling Problem

Abstract This study explores the application of neural network-based heuristics to the class/teacher timetabling problem (CTTP). The paper begins by presenting the problem characteristics in terms of hard and soft constraints and proposing a formulation for the energy function required to map the issue within the artificial neural network model. There follow two distinct approaches to simulating neural network evolution. The first uses a Potts mean-field annealing simulation based on continuous Potts neurons, which has obtained favorable results in various combinatorial optimization problems. Afterwards, a discrete neural network simulation, with discrete winner-takes-all neurons, is proposed. The paper concludes with a comparison of the computational results taken from the application of both heuristics to hard hypothetical and real CTTP instances. This experiment demonstrates that the discrete approach performs better, in terms of solution quality as well as execution time. By extending the comparison, the neural discrete solutions are also compared with those obtained from a multiobjective genetic algorithm, which is already being successfully used for this problem within a timetabling software application.

Solving a bi-objective nurse rerostering problem by using a utopic Pareto genetic heuristic

Abstract 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.

An Integer Multicommodity Flow Model Applied to the Rerostering of Nurse Schedules

The problem of rerostering service schedules is very common in organizations that work shifts around the clock every day of the year with a set number of employees. Whenever one or more workers announce that they will not be able to attend to tasks previously assigned in their schedule, those tasks must be performed at the expense of alterations in the schedules of other workers. 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. This is a difficult real problem calling for a computational tool to cope with it easily. In the paper the issue is described in detail in the context of nurse scheduling and formulated as an integer multicommodity flow problem with additional constraints, in a multi-level acyclical network. A heuristic was implemented as a first approach to solving the problem. Subsequently the integer linear programming formulation of the multicommodity flow model and two linear relaxations were tested using CPLEX [2] optimizers. The computational results reported regard real instances from a Lisbon state hospital. Satisfactory rosters were obtained within acceptable computational times in all instances tested, either with the integer optimizer, or with the heuristic. This being so, refinements will be undertaken to embed these methodologies in a decision support system that may assist the head nurse in her daily rerostering activities.

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.