Modelling nationwide hospital length of stay: opening the black box

Hospital length of stay is considered to be a reliable and valid proxy for measuring the consumption of hospital resources. Average length of stay, however, albeit easy to quantify and calculate, does not suitably reflect the nature of such underlying distributions and may therefore mask the effects that the different streams of patients have on the system. This paper uses routinely collected and readily available nationwide data on stroke-related patients, aged 65 years and over, who were discharged from English hospitals over a 1-year period. This will be the basis for a running example illustrating the alternative methods of analysis and models of patients' length of stay. The methods include statistical methods: survival analysis, mixed exponential and phase-type distributions; and decision modelling techniques: compartmental and simulation models. The paper concludes by summarizing these various modelling techniques and by highlighting the similarity of the estimated parameters of patient flow as calculated by the phase-type distribution and compartmental modelling techniques.     

Introducing competition in healthcare services: The role of private care and increased patient mobility

We study the operational implications from competition in the provision of healthcare services, in the context of national public healthcare systems in Europe. Specifically, we study the potential impact of two alternative ways through which policy makers have introduced such competition: (i) via the introduction of private hospitals to operate alongside public hospitals and (ii) via the introduction of increased patient choice to grant European patients the freedom to choose the country they receive treatment at. We use a game-theoretic framework with a queueing component to capture the interactions among the patients, the hospitals and the healthcare funders. Specifically, we analyze two different sequential games and obtain closed form expressions for the patients’ waiting time and the funders’ reimbursement cost in equilibrium. We show that the presence of a private provider can be beneficial to the public system: the patients’ waiting time will decrease and the funders’ cost can decrease under certain conditions. Also, we show that the cross-border healthcare policy, which increases patient mobility, can also be beneficial to the public systems: when welfare requirements across countries are sufficiently close, all funders can reduce their costs without increasing the patients’ waiting time. Our analysis implies that in border regions, where the cost of crossing the border is low, “outsourcing” the high-cost country’s elective care services to the low-cost country is a viable strategy from which both countries’ systems can benefit.     

Fleet Structures Model: Predictive Modelling of the UK Sea-Fishing Fleet

The Fleet Structures Model is a predictive computer model under development by the Sea Fish Industry Authority. Its purpose is to simulate aspects of the structure and operation of the UK sea-fishing fleet in order to make comparative appraisals of fleet-management policy scenarios under varying assumptions about the behavioural environment. The model operates in yearly incremental steps, providing feedback between the fleet operation, the expected changes in fleet structure, fish prices and the state of fish stocks. It is an analytic model, and is mainly deterministic with stochastic elements. Implementation is in programs written in Pascal. This paper presents an overview of the model, and highlights aspects of its development and implementation.     

On the length of simplex paths: The assignment case

This paper reports on an experimental study of the distribution of the length of simplex paths for the Optimal Assignment Problem. We study the distribution of the pivot counts for a version of the simplex method that with essentially equal probabilities introduces any variable with negative reduced cost into the basis. In this situation the distribution of the pivot counts turns out to be normally distributed and independent of the actual cost coefficients, provided these are sufficiently spread out. Further, the mean and standard deviation grow only moderately with the size of the problem, namely asd ^1.8, andd ^1.5 respectively for ad×d problem, implying in particular that the pivot counts concentrate around the mean with growingd. The usual simplex method on the other hand gives a growth ofd ^1.6. Hence a large part of the favourable polynomial growth experienced on practical problems may be attributed to the fact that the simplex paths are rather short on the average, at least for assignment problems.     

Crosslinking of an unsaturated polyester resin in the mould: Modelling and heat transfer studies

The crosslinking of unsaturated polyester was studied by using an experiment and a mathematical model of the process. Temperature–time profiles were recorded in the centre of the sample inside the mould at the outer wall of the cylindrical copper mould, and in the bulk of the heated air bath. A numerical model was constructed by taking into account the heat transferred by convection from the air to the mould surface and the heat transferred by conduction through the resin, as well as the heat generated by the crosslinking reaction. The convection heat transfer coefficient was determined in independent experiments with the empty copper mould. Introduction of the carbon base filler reduced the amount of heat generated in the composite due to the less reactive component in the composite. As a result, it lowered the temperature of the resin. By recording the temperature-time and the degree of crosslinking time profiles developed within the sample extensive knowledge of the process can be obtained. The effects of the convection heat transfer on the rate of mould heating, and the conduction heat transfer through the mould as well as the internal heat generated by the crosslinking reaction are visibly shown, despite a complexity of the process.     

Comparative performance measurement in regulation: the case of English and Welsh sewerage services

This paper discusses the use of comparative performance measurement by means of Data Envelopment Analysis in the context of the regulation of English and Welsh water companies. Specifically, the use of Data Envelopment Analysis to estimate potential cost savings in sewerage is discussed as it fed into the price review of water companies carried out by the regulator of water companies in 1994. The application is used as a vehicle for highlighting generic issues in terms of assessing the impact of factors on the ranking of units on performance, the insights gained from using alternative methods to assess comparative performance, and the issue of assessing comparative performance when few in number but highly complex entities are involved. The paper should prove of interest to those interested in regulation and, more generally, in the use of methods of comparative performance measurement.     

On well-posedness of incompressible two-phase flows with phase transitions: the case of non-equal densities

The basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics is studied. The latter means that the total energy is conserved and the total entropy is nondecreasing. We consider the case of constant but non-equal densities of the phases, complementing our previous paper (Prüss et?al. in Evol Equ Control Theory 1:171–194, 2012) where the case of equal densities is analyzed. The local well-posedness of such problems is proved by means of the technique of maximal L _p -regularity, in a configuration where the interface is nearly flat and initial data are small.     

Modelling the cost of poor quality in a five-state part manufacturing operation: a case study

The quality history of individual parts from a critical operation can be modeled by a five-state Markov chain involving factory rework operation, customer inspection and field test, parts scrapped, parts defective but used-as-is by concession or re-graded for alternative applications, and defect-free parts satisfying customer requirements. We estimate total failure cost by a five-state Markov chain model and present a case study to demonstrate relationship of the total failure cost to appraisal and prevention costs.     

Fifty years of probabilistic decision analysis: a view from the UK

In 1959, LJ Savage attended a statistics seminar held in his honour at the University of London, confronting those present with a radically different approach to reasoning about uncertainty. Britain was well placed to respond to Savage, as very similar ideas had been laid out in Britain a full generation earlier, and in the next few decades, British and British-based practitioners and researchers championed a collection of techniques for thinking quantitatively about uncertainty (which we call ‘Probabilistic Decision Analysis’), developing practice, and contributing to theoretic knowledge about the underlying psychology and mathematics. This effectively turned a collection of purely theoretical ideas into a practical modelling technology. In the first decade of the 21st century, some 50 years on, these ideas have made a noticeable influence on practice and thinking in various domains, but numerous challenges still remain.     

Modelling the Epidemiological Consequences of HIV Infection and AIDS: A Contribution from Operational Research

As part of the worldwide effort involved in modelling the spread of AIDS, nothing has been heard from the operational research community. Yet OR, with its client-oriented modelling philosophy, patently has a role to play in assisting clinicians, epidemiologists and health planners to obtain greater understanding of this staggering threat to public health. Using the methods of system dynamics, a model of the spread of AIDS in the UK homosexual population has been developed. It is implemented on a personal computer, and possesses the capability to capture complex virological and behavioural features of the epidemic whilst portraying the consequences in an easily digested graphical form. Some examples of these results are presented. The model's structure and parameters are also fully described, together with sensitivity tests on the crucial incubation time distribution.     

Bifurcation of the essential dynamics of Lorenz maps and applications to Lorenz-like flows: Contributions to the study of the expanding case

In this article we provide, by using kneadings sequences, the combinatorial bifurcation diagramme associated to a typical two parameter of Lorenz maps on the real line. We apply these results to two parameter families of geometric Lorenz-like flows.Partially supported by Fondecyt grants #1970720, #1990903, DICYT-USACH-Chile and PRONEX on Dynamical Systems. Brazil.     

Putting soft OR methods to work: the case of IS strategy development for the UK Parliament

In 1999 a project was undertaken to develop an information systems strategy (ISS) for the UK Parliament. This was the first time that both Houses of Parliament, the Lords and the Commons, had collaborated in such a venture. The paper describes the attempt to apply soft OR in the project. Because of the inherent interest of the context of the intervention, the paper describes the project in some detail. In the event the formal soft OR methods were not used but a soft approach was taken. The experience complements earlier studies in the retail, mining and electricity supply industries. The paper is the last in a series of published case studies, which describe attempts to apply soft methods in practice. Together the cases articulate the ‘strand of practice’ of one practitioner.     

Modelling in the absence of data: a case study of fleet maintenance in a developing country

Adequate and relevant objective data for modelling maintenance decision problems are often incomplete or not readily accessible. This is particularly true in developing countries. In this paper the experience gained between 1991–95 in conducting a maintenance study of an inter-city express bus fleet in a developing country is presented. The lack of available maintenance records and operating data rendered the study the most data-starved maintenance modelling exercise the authors have met before or since. The study required the use of subjective methods to both define the problem and to estimate parameters, and the application of recently developed concepts in maintenance modelling along with snapshot analysis and delay time modelling. This imposed a structured approach to problem recognition and problem solution. The study contributed both directly and indirectly to a change in work culture and to a reduction in bus breakdown rate. The company was re-visited 5?years later specifically to seek evidence of lasting impact. Some evidence existed and is reported in the paper.     

A longitudinal view of mathematics achievement of primary students: case studies from Japan, Singapore, and the United States

This paper shares results from a secondary analysis of data from the participation of Japanese, Singaporean, and U.S. students in the International Project on Mathematical Attainment (IPMA). IPMA was a longitudinal study to assess the mathematics achievement of primary students from their first year of schooling through the end of fifth grade. Tests were constructed to enable achievement on the same items to be assessed over multiple years, thus permitting the assessment of growth in achievement throughout primary school. Achievement is compared to the grade at which the content is introduced so that achievement can be related to students’ opportunity to learn.     

Multicriteria decision support methodologies for auditing decisions: The case of qualified audit reports in the UK

All UK companies are required by company law to prepare financial statements that must comply with law and accounting standards. With the exception of very small companies, financial accounts must then be audited by UK registered auditors who must express an opinion on whether these statements are free from material misstatements, and have been prepared in accordance with legislation and relevant accounting standards (unqualified opinion) or not (qualified opinion). The objective of the present study is to explore the potentials of developing multicriteria decision aid models for reproducing, as accurately as possible, the auditors’ opinion on the financial statements of the firms. A sample of 625 company audited years with qualified statements and 625 ones with unqualified financial statements over the period 1998–2003 from 823 manufacturing private and public companies is being used in contrast to most of the previous works in the UK that have mainly focused on very small or very large public companies. Furthermore, the models are being developed and tested using the walk-forward approach as opposed to previous studies that employ simple holdout tests or resampling techniques. Discriminant analysis and logit analysis are also used for comparison purposes. The out-of-time and out-of-sample testing results indicate that the two multicriteria decision aid techniques achieve almost equal classification accuracies and are both more efficient than discriminant and logit analysis.     

A flexible adaptive memory-based algorithm for real-life transportation operations: Two case studies from dairy and construction sector

Effective routing of vehicles remains a focal goal of all modern enterprises, thriving for excellence in project management with minimal investment and operational costs. This paper proposes a metaheuristic methodology for solving a practical variant of the well-known Vehicle Routing Problem, called Heterogeneous Fixed Fleet VRP (HFFVRP). Using a two-phase construction heuristic, called GEneralized ROute Construction Algorithm (GEROCA), the proposed metaheuristic approach enhances its flexibility to easily adopt various operational constraints. Via this approach, two real-life distribution problems faced by a dairy and a construction company were tackled and formulated as HFFVRP. Computational results on the aforementioned case studies show that the proposed metaheuristic approach (a) consistently outperforms previous published metaheuristic approaches we have developed to solve the HFFVRP, and (b) substantially improves upon the current practice of the company. The key result that impressed both companies’ management was the improvement over the bi-objective character of their problems: the minimization of the total distribution cost as well as the minimization of the number of the given heterogeneous number of vehicles used.     

Towards the integration of system modelling with scenario planning to support strategy: the case of the UK energy industry

A key aspect of strategy is sense-making of the unfolding uncertainty in the business environment and responding appropriately to achieve organisational objectives. However, uncertainty means that there is more than one future open to an organisation. Sense-making is therefore problematic. Scenario planning is one approach to sense-making that helps to explore and understand uncertainty, aiming for the identification of potential predetermined elements in the business environment. In this paper we propose the integration of systems modelling with scenario planning to support the exploration of uncertainty, identify knowledge gaps that set a (subsequent) research agenda, understand the role and usefulness of historical data, and model research outcomes to help reveal potential predetermined elements. Specifically, scenario planning identifies potential predetermined elements in the business environment; system modelling in the form of behaviour-over-time graphs, causal mapping and feedback loops helps in structuring and linking variables and their interaction to provide an understanding of the systemic drivers of these predetermined elements. Methodological integration of this type enhances modellers’ ability to support strategy in organisations.     

Ratio and Frontier Analysis for Assessing Corporate Performance: Evidence from the Grocery Industry in the UK

This paper considers the use of alternative methodologies for assessing corporate performance of industrial sectors within the economy. It is argued that the use of ratio analysis in itself is insufficient for assessing performance, and that more advanced tools like data envelopment analysis should be used to complement ratio analysis. Data envelopment analysis is used in the paper to address a series of issues concerning the measurement of corporate performance, which includes an assessment of sales' efficiency, the effects of economies of scale, benchmarking of a firm's performance and the association between industry groups and performance. The paper uses data drawn from the grocery industry in the UK.