Sally C. Brailsford

Constraint satisfaction problems: algorithms and applications

A constraint satisfaction problem requires a value, selected from a given finite domain, to be assigned to each variable in the problem, so that all constraints relating the variables are satisfied. Many combinatorial problems in operational research, such as schedulling and timetabling, can be formulated as constraint satisfaction problems. Researchers in artificial intelligence usually adopt a constaint satisfaction approach as their prefererd method when tackling such problems. However constraint satisfaction approches are not widely known amongst operational researchers. The aim of this paper is to introduce constraint statisfaction to the operational researchers.

An analysis of the academic literature on simulation and modelling in health care

This article describes a multi-dimensional approach to the classification of the research literature on simulation and modelling in health care. The aim of the study was to analyse the relative frequency of use of a range of operational research modelling approaches in health care, along with the specific domains of application and the level of implementation. Given the vast scale of the health care modelling literature, a novel review methodology was adopted, similar in concept to the approach of stratified sampling. The results provide new insights into the level of activity across many areas of application, highlighting important relationships and pointing to key areas of omission and neglect in the literature. In addition, the approach presented in this article provides a systematic and generic methodology that can be extended to other application domains as well as other types of information source in health-care modelling.

Using industrial processes to improve patient care

Might industrial processes improve quality, reduce waiting times, and enhance the working environment?

Emergency and on-demand health care: modelling a large complex system

This paper describes how system dynamics was used as a central part of a whole-system review of emergency and on-demand health care in Nottingham, England. Based on interviews with 30 key individuals across health and social care, a ‘conceptual map’ of the system was developed, showing potential patient pathways through the system. This was used to construct a stock-flow model, populated with current activity data, in order to simulate patient flows and to identify system bottle-necks. Without intervention, assuming current trends continue, Nottingham hospitals are unlikely to reach elective admission targets or achieve the government target of 82% bed occupancy. Admissions from general practice had the greatest influence on occupancy rates. Preventing a small number of emergency admissions in elderly patients showed a substantial effect, reducing bed occupancy by 1% per annum over 5 years. Modelling indicated a range of undesirable outcomes associated with continued growth in demand for emergency care, but also considerable potential to intervene to alleviate these problems, in particular by increasing the care options available in the community.

Using Simulation to Improve the Blood Supply Chain

This case study is concerned with analysing policies for managing the blood inventory system in a typical UK hospital supplied by a regional blood centre. The objective of the project is to improve procedures and outcomes by modelling the entire supply chain for that hospital, from donor to recipient. The supply chain of blood products is broken down into material flows and information flows. Discrete-event simulation is used to determine ordering policies leading to reductions in shortages and wastage, increased service levels, improved safety procedures and reduced costs, by employing better system coordination. In this paper we describe the model and present results for a representative medium-sized hospital. The model can be used by both the National Blood Service and by hospital managers as a decision support tool to investigate different procedures and policies.

The Progressive Party Problem: Integer Linear Programming and Constraint Programming Compared

Many discrete optimization problems can be formulated as either integer linear programming problems or constraint satisfaction problems. Although ILP methods appear to be more powerful, sometimes constraint programming can solve these problems more quickly. This paper describes a problem in which the difference in performance between the two approaches was particularly marked, since a solution could not be found using ILP.The problem arose in the context of organizing a “progressive party” at a yachting rally. Some yachts were to be designated hosts; the crews of the remaining yachts would then visit the hosts for six successive half-hour periods. A guest crew could not revisit the same host, and two guest crews could not meet more than once. Additional constraints were imposed by the capacities of the host yachts and the crew sizes of the guests.Integer linear programming formulations which included all the constraints resulted in very large models, and despite trying several different strategies, all attempts to find a solution failed. Constraint programming was tried instead and solved the problem very quickly, with a little manual assistance. Reasons for the success of constraint programming in this problem are identified and discussed.

Tutorial: Advances and challenges in healthcare simulation modeling

Simulation has been used for modeling healthcare systems for over forty years. In many respects it is the ideal approach for addressing healthcare issues, yet the relatively small number of successful implementations would suggest that (outside academia) it has been underused in the health sector, compared with manufacturing industry or defense. In this paper we present a review of applications of simulation in healthcare, focusing on successful implementations, and we discuss some possible reasons why simulation has arguably failed to fulfill its potential. We describe recent advances in the area and identify opportunities for further research and new developments.

Towards the holy grail: combining system dynamics and discrete-event simulation in healthcare

The idea of combining discrete-event simulation and system dynamics has been a topic of debate in the operations research community for over a decade. Many authors have considered the potential benefits of such an approach from a methodological or practical standpoint. However, despite numerous examples of models with both discrete and continuous parameters in the computer science and engineering literature, nobody in the OR field has yet succeeded in developing a genuinely hybrid approach which truly integrates the philosophical approach and technical merits of both DES and SD in a single model. In this paper we consider some of the reasons for this and describe two practical healthcare examples of combined DES/SD models, which nevertheless fall short of the “holy grail” which has been so widely discussed in the literature over the past decade.

Towards incorporating human behaviour in models of health care systems: An approach using discrete event simulation

Operational Research models are well established as an effective tool for tackling a vast range of health care problems. Many of these models involve parameters which depend on human behaviour, and thus individuals’ characteristics or personality traits should be included. In this paper we describe a discrete event simulation model of attendance for screening for diabetic retinopathy, a sight-threatening complication of diabetes. This model takes into account the physical states, emotions, cognitions and social status of the persons involved. The model also uses some ideas from the discipline of health psychology. We believe that this approach provides what is potentially a far more accurate method of modelling patients’ attendance behaviour, compared with the standard approach of simple random sampling of patients. However, further empirical work is required, firstly to derive and validate more realistic forms of the model equations, secondly to select the appropriate psychological variables, and thirdly and inevitably to collect data.

Reviewing emergency care systems I: insights from system dynamics modelling.

Objectives: To describe the components of an emergency and urgent care system within one health authority and to investigate ways in which patient flows and system capacity could be improved. Methods: Using a qualitative system dynamics (SD) approach, data from interviews were used to build a conceptual map of the system illustrating patient pathways from entry to discharge. The map was used to construct a quantitative SD model populated with demographic and activity data to simulate patterns of demand, activity, contingencies, and system bottlenecks. Using simulation experiments, a range of scenarios were tested to determine their likely effectiveness in meeting future objectives and targets. Results: Emergency hospital admissions grew at a faster annual rate than the national average for 1998–2001. Without intervention, and assuming this trend continued, acute hospitals were likely to have difficulty sustaining levels of elective work, in reaching elective admission targets and in achieving bed occupancy targets. General practice admissions exerted the greatest influence on occupancy rates. Prevention of emergency admissions for older people (3%–6% each year) reduced bed occupancy in both hospitals by 1% per annum over five years. Prevention of emergency admissions for patients with chronic respiratory disease affected occupancy less noticeably, but because of the seasonal pattern of admissions, had an effect on peak winter occupancy. Conclusions: Modelling showed the potential consequences of continued growth in demand for emergency care, but also considerable scope to intervene to ameliorate the worst case scenarios, in particular by increasing the care management options available in the community.