The decathlon consists of ten events with scores which are then aggregated to determine the final ranking. We develop a decathlon scoring method which is far simpler than the existing standard (IAAF1984) tables, as there are only 9 parameters instead of 30 which have an impact on the overall rank. We first identify athletes who are on the Pareto-efficient frontier i.e. those who are not dominated by anyone else. We then remove these frontier athletes and again pick all non-dominated athletes to obtain a second dominating group/Pareto frontier and iterate this procedure for the decathlon data from 1986 to 2020. Each of these groups are then characterized by their set of ten median performances. Improving from the last to the top group can then be seen as a path of progress, leading from the lowest to the highest set of median performances. Every event should have the same importance, so we normalize the data such that the path of progress follows as much as possible a space diagonal of a ten dimensional hypercube. Furthermore, any adjustment of a benchmark does not change any actual decathlon performance, hence there cannot be any unwanted rank reversals. This allows a smooth adjustment of these tables in the future, if for instance a new type of javelin needs to be introduced to reduce the range. We normalize such that current performances between 7000 and 9000 points still fall into the same range with our point tables.

This study seeks to identify the most effective forecasting period and methods for predicting demand in an Accident & Emergency (A&E) department at a mid-sized hospital in England. Utilizing the National Hospital Episode Statistics (HES) dataset, that covers a 36-month period from February 2010 to January 2013, the research evaluates four commonly used forecasting methods: Autoregressive Integrated Moving Average (ARIMA), exponential smoothing, stepwise linear regression (SLR), and Seasonal and Trend decomposition using Loess (STLF). Forecast accuracy is assessed using the Mean Absolute Scaled Error (MASE). The MASE values for the best forecasting methods across different periods were 0.7834 for daily, 0.9354 for weekly, and 0.5259 for monthly estimates. The study found that the SLR model was the most effective predictive method, with monthly estimation emerging as the optimal period. Contrary to past studies that favoured daily estimates, this research indicated that daily A&E demand forecasts might not be the most accurate.

We consider the problem of fitting a relationship (e.g., a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according to which variable is chosen as being dependent, and the dependent variable is unrealistically assumed to be the only variable which has any measurement error (noise). We present a very general method for estimating a linear functional relationship between multiple noisy variables, which are treated impartially, i.e., no distinction between dependent and independent variables. The data are not assumed to follow any distribution, but all variables are treated as being equally reliable. Our approach extends the geometric mean functional relationship to multiple dimensions. This is especially useful with variables measured in different units, as it is naturally scale invariant, whereas orthogonal regression is not. This is because our approach is not based on minimizing distances, but on the symmetric concept of correlation. The estimated coefficients are easily obtained from the covariances or correlations, and correspond to geometric means of associated least squares coefficients. The ease of calculation will hopefully allow widespread application of impartial fitting to estimate relationships in a neutral way.

There has been a growing trend for public accountability of those who represent or act on behalf of the general public. Whilst politicians are forever appearing in the media to justify their actions, what has been lacking has been a broad objective measure of the amount of activity that they perform whilst in Parliament itself.We present a first attempt at a multi-dimensional scoring and ranking of British Members of Parliament. Three criteria are included in the score: the number of speeches made, the number of votes attended, and the number of written questions submitted. We use the resulting scores to place MPs into four quartiles and then show how the political parties are distributed amongst these four ‘divisions’. We also present the ‘Top 30 MPs’ according to our aggregate performance measure.

The difficulty that hospital management has been experiencing over the past decade in balancing demand and capacity needs is unprecedented in the United Kingdom. Due to a shortage of capacity, hospitals cannot treat all patients. We developed a whole hospital-level decision support system to assess and respond to the needs of local populations. We integrated a comparative forecasting approach and discrete event simulation modelling using Hospital Episode Statistics and local datasets. It is clear from the literature that this level of whole hospital simulation model has never been developed before (an innovative decision support system). First, the demands of all hospital specialties were forecasted, and the forecasts were embedded into the simulation model as input. Secondly, a simulation model was developed to capture the patient pathway of all specialties. The model integrates every component of a hospital to aid with efficient and effective use of scarce resources (e.g., staff and beds). As a result, the hospital can meet the increasing demand with its current resources. According to the scenario analysis, the hospital bed occupancy rate will reach the national target (i.e., 85%), and the total hospital revenue will increase by approximately 13%, with a 10% increase in A&E and outpatient and a 20% increase in inpatient demand. In conclusion, the hospital-level simulation model can become a crucial instrument for decision-makers to provide an efficient service for hospitals in England and other parts of the world.

When comparing performance (of products, services, entities, etc.), multiple attributes are involved. This paper deals with a way of weighting these attributes when one is seeking an overall score. It presents an objective approach to generating the weights in a scoring formula which avoids personal judgement. The first step is to find the maximum possible score for each assessed entity. These upper bound scores are found using Data Envelopment Analysis. In the second step the weights in the scoring formula are found by regressing the unique DEA scores on the attribute data. Reasons for using least squares and avoiding other distance measures are given. The method is tested on data where the true scores and weights are known. The method enables the construction of an objective scoring formula which has been generated from the data arising from all assessed entities and is, in that sense, democratic.

The increasing pressures on the healthcare system in the UK are well documented. The solution lies in making best use of existing resources (e.g. beds), as additional funding is not available. Increasing demand and capacity shortages are experienced across all specialties and services in hospitals. Modelling at this level of detail is a necessity, as all the services are interconnected, and cannot be assumed to be independent of each other. Our review of the literature revealed two facts; First an entire hospital model is rare, and second, use of multiple OR techniques are applied more frequently in recent years. Hybrid models which combine forecasting, simulation and optimization are becoming more popular. We developed a model that linked each and every service and specialty including A&E, and outpatient and inpatient services, with the aim of, (1) forecasting demand for all the specialties, (2) capturing all the uncertainties of patient pathway within a hospital setting using discrete event simulation, and (3) developing a linear optimization model to estimate the required bed capacity and staff needs of a mid-size hospital in England (using essential outputs from simulation). These results will bring a different perspective to key decision makers with a decision support tool for short and long term strategic planning to make rational and realistic plans, and highlight the benefits of hybrid models.

Hastanelerdeki insan kaynakları ve bütçe gibi kısıtlı kaynaklar, artan hastane taleplerini karşılamak için yetersiz kalabilmekte ve bu durum hastanelerdeki sağlık hizmeti sağlayıcıları için yoğun iş yüküne neden olabilmektedir. Travma ve ortopedi poliklinikleri İngiltere’deki hastanelerde en yüksek hasta aktivitesine ve takipli tedavi sayısına sahiptir. Bu çalışma, tam teşekküllü bir İngiliz hastanesinde travma ve ortopedi polikliniğinin projeksiyonu için klinik kullanım oranlarının hesaplanmasında Ulusal İstatistik Ofisi ile entegre simülasyon tabanlı bir karar destek sisteminin geliştirilmesi amaçlanmıştır. Hastanenin hizmet verdiği yerleşim bölgesinin yıllar itibari ile büyüme projeksiyonları göz önünde bulundurularak, hastanenin gelecekteki üç yıllık talebi ele alınmıştır. Senaryo analizinde, klinik kullanım oranını etkileyen üç parametre (Talep, klinik zaman dilimi ve hasta takip sayısı) içeren deneysel bir analiz dikkate alınmıştır. En düşük, ortalama ve en yüksek olmak üzere üç farklı klinik kullanım oranları, öngörülen her bir yıl için toplam 8 deneyden oluşan senaryo analizi yoluyla travma ve ortopedi polikliniği için hesaplanmıştır. Bu çalışma da ayrıca tedavi süreleri ve doktorların yıllık tam zamanlı çalışma süreleri dikkate alınarak öngörülen her bir yıl için ihtiyaç duyulan doktor sayıları belirlenmiştir. Geliştirilen bu karar destek sistemi, klinik kullanım oranlarının polikliniklerde daha iyi anlaşılması ve gelecekte ihtiyaç duyulacak personel, yeterli bütçe ve ekipman gibi kaynak ihtiyaçlarının önceden tespit edilmesi ve daha iyi kaynak planlamalarının yapılabilmesi için hastane yönetimine bir öngörü sunmaktadır.

The World Happiness Report is published by the United Nations Sustainable Development Solutions Network and contains an international ranking of national average happiness, as measured by surveys of personal life evaluations. It also contains an analysis which tries to explain the happiness figures from more than 150 countries using data on six key variables. That analysis assumes the factors combine in an additive manner and therefore operate independently of each other. By contrast, we explore a multiplicative model, which allows for interactivity or synergy between factors, as well as the possibility of diminishing marginal benefit at higher levels of achievement. We find that this model provides a better fit to the data and is therefore superior in its explanatory power. The implication for policy-makers is that they should focus on improving those factors which are the lowest for their nation as this will provide greater relative benefits to subjective well-being. At an individual level this means focusing on improving conditions for those who are experiencing the lowest levels of well-being.

Accident and emergency (A&E) departments in England have been struggling against severe capacity constraints. In addition, A&E demands have been increasing year on year. In this study, our aim was to develop a decision support system combining discrete event simulation and comparative forecasting techniques for the better management of the Princess Alexandra Hospital in England. We used the national hospital episodes statistics data-set including period April, 2009 - January, 2013. Two demand conditions are considered: the expected demand condition is based on A&E demands estimated by comparing forecasting methods, and the unexpected demand is based on the closure of a nearby A&E department due to budgeting constraints. We developed a discrete event simulation model to measure a number of key performance metrics. This paper presents a crucial study which will enable service managers and directors of hospitals to foresee their activities in future and form a strategic plan well in advance.

BACKGROUND Because of increasing demand, hospitals in England are currently under intense pressure resulting in shortages of beds, nurses, clinicians, and equipment. To be able to effectively cope with this demand, the management needs to accurately find out how many patients are expected to use their services in the future. This applies not just to one service but for all hospital services. PURPOSE A forecasting modelling framework is developed for all hospital's acute services, including all specialties within outpatient and inpatient settings and the accident and emergency (A&E) department. The objective is to support the management to better deal with demand and plan ahead effectively. METHODOLOGY/APPROACH Having established a theoretical framework, we used the national episodes statistics dataset to systematically capture demand for all specialties. Three popular forecasting methodologies, namely, autoregressive integrated moving average (ARIMA), exponential smoothing, and multiple linear regression were used. A fourth technique known as the seasonal and trend decomposition using loess function (STLF) was applied for the first time within the context of health-care forecasting. RESULTS According to goodness of fit and forecast accuracy measures, 64 best forecasting models and periods (daily, weekly, or monthly forecasts) were selected out of 760 developed models; ie, demand was forecasted for 38 outpatient specialties (first referrals and follow-ups), 25 inpatient specialties (elective and non-elective admissions), and for A&E. CONCLUSION This study has confirmed that the best demand estimates arise from different forecasting methods and forecasting periods (ie, one size does not fit all). Despite the fact that the STLF method was applied for the first time, it outperformed traditional time series forecasting methods (ie, ARIMA and exponential smoothing) for a number of specialties. PRACTISE IMPLICATIONS Knowing the peaks and troughs of demand for an entire hospital will enable the management to (a) effectively plan ahead; (b) ensure necessary resources are in place (eg, beds and staff); (c) better manage budgets, ensuring enough cash is available; and (d) reduce risk.

Abstract—Over the past decade, the non-elective admissions in the UK have increased significantly. Taking into account limited resources (i.e. beds), the related service managers are obliged to manage their resources effectively due to the non-elective admissions which are mostly admitted to inpatient specialities via A&E departments. Geriatric medicine is one of specialities that have long length of stay for the non-elective admissions. This study aims to develop a discrete event simulation model to understand how possible increases on non-elective demand over the next 12 months affect the bed occupancy rate and to determine required number of beds in a geriatric medicine speciality in a UK hospital. In our validated simulation model, we take into account observed frequency distributions which are derived from a big data covering the period April, 2009 to January, 2013, for the non-elective admission and the length of stay. An experimental analysis, which consists of 16 experiments, is carried out to better understand possible effects of case studies and scenarios related to increase on demand and number of bed. As a result, the speciality does not achieve the target level in the base model although the bed occupancy rate decreases from 125.94% to 96.41% by increasing the number of beds by 30%. In addition, the number of required beds is more than the number of beds considered in the scenario analysis in order to meet the bed requirement. This paper sheds light on bed management for service managers in geriatric medicine specialities.

The main objective of the study was to identify the factors contributing to the usage of enterprise resource planning systems at the organisational layer, the departmental layer and the end-user layer in Higher Education Institutions (HEIs) in Pakistan. The conceptual framework of this study is based on the Unified Theory of Acceptance and Use of Technology (UTAUT) developed by Venkatesh, Morris, Davis, & Davis (2003). The multi-level conceptual model developed for the study was tested empirically using three distinct questionnaires for analytical layers. Primary data was collected from 18 higher education institutions in Pakistan; 86 responses from the organisational layer, 143 from the departmental layer and 1088 from the enduser layer. Structural equations were formulated to investigate the effect of factors at three layers contributing to the usage of Enterprise Resource Planning Systems (ERPS). Organisational training was found to be the only factor not making a significant contribution to the usage of enterprise resource planning systems while all other factors included in the conceptual framework were proved to be significant. The model formulation and application of SEM techniques to investigate the determinants of usage of ERPS in HEIs in Pakistan is the unique contribution of this study.

We present a simple method for estimating a single relationship between multiple variables, which are all treated symmetrically i.e. there is no distinction between dependent and independent variables. This is of interest when estimating a law from observations in the natural sciences, although workers in the social sciences may also find this of interest when fitting relationships to data. All variables are assumed to have error but no information about the error is assumed. Unlike other symmetric methods, the weights or coefficients can be obtained easily – indeed, these can be expressed in terms of least squares coefficients. The approach has the important properties of providing a functional relationship which is scale invariant and unique.

Surveys show that the mean absolute percentage error (MAPE) is the most widely used measure of prediction accuracy in businesses and organizations. It is, however, biased: when used to select among competing prediction methods it systematically selects those whose predictions are too low. This has not been widely discussed and so is not generally known among practitioners. We explain why this happens. We investigate an alternative relative accuracy measure which avoids this bias: the log of the accuracy ratio, that is, log (prediction/actual). Relative accuracy is particularly relevant if the scatter in the data grows as the value of the variable grows (heteroscedasticity). We demonstrate using simulations that for heteroscedastic data (modelled by a multiplicative error factor) the proposed metric is far superior to MAPE for model selection. Another use for accuracy measures is in fitting parameters to prediction models. Minimum MAPE models do not predict a simple statistic and so theoretical analysis is limited. We prove that when the proposed metric is used instead, the resulting least squares regression model predicts the geometric mean. This important property allows its theoretical properties to be understood.

Simple additive weighting is a well-known method for scoring and ranking alternative options based on multiple attributes. However, the pitfalls associated with this approach are not widely appreciated. For example, the apparently innocuous step of normalizing the various attribute data in order to obtain comparable figures leads to markedly different rankings depending on which normalization is chosen. When the criteria are aggregated using multiplication, such difficulties are avoided because normalization is no longer required. This removes an important source of subjectivity in the analysis because the analyst no longer has to make a choice of normalization type. Moreover, it also permits the modelling of more realistic preference behaviour, such as diminishing marginal utility, which simple additive weighting does not provide. The multiplicative approach also has advantages when aggregating the ratings of panel members. This method is not new but has been ignored for too long by both practitioners and teachers. We aim to present it in a nontechnical way and illustrate its use with data on business schools.

Napoleonic France won a great many of more than 150 battles in which it engaged. There has been much dispute about which, if any, of the many qualitative theories as to why it was so successful is correct; many of them centered on the personal characteristics of Napoleon himself. However, none of these theories appears amenable to statistical analysis. To examine this question quantitatively we take a new direction. We leave aside questions of generalship and instead analyze the sizes of both of the opposing armies in battles of the Napoleonic Wars, analyzing French wins and losses separately. We find the best-fit linear models for these data sets using the Geometric Mean Functional Relationship. The coefficients of determination for both of these results were 71%, implying that our best fits model the data unexpectedly well. The difference between these two models has high statistical significance. Napoleonic France won even though outnumbered on average by 9%, whereas their opposition won only when they outnumbered the French by typically 83%. We conclude that absolute sizes of armies -- and not just their relative size -- are important factors in determining the result of a battle, and that Napoleonic France and its opponents were very different in their ability to win for given army sizes.

Surveys show that the mean absolute percentage error (MAPE) is the most widely used measure of forecast accuracy in businesses and organizations. It is also used to compare accuracy across multiple data sets, e.g. when choosing a forecasting method. Yet this metric systematically favours methods which under-forecast. Thus when MAPE is used for model selection it will be biased. We explain why this happens.