Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach

Aeromedical and ground ambulance services often team up in responding to trauma crashes, especially when the emergency helicopter is unable to land at the crash scene. We propose location-coverage models and a greedy heuristic for their solution to simultaneously locate ground and air ambulances, and landing zones (transfer points). We provide a coverage definition based on both response time and total service time, and consider three coverage options; only ground emergency medical services (EMS) coverage, only air EMS coverage, or joint coverage of ground and air EMS in which the patient is transferred from an ambulance into an emergency helicopter at a transfer point. To analyze this complex coverage situation we develop two sets of models, which are variations of the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). These models address uncertainty in spatial distribution of motor vehicle crash locations by providing coverage to a given set of both crash nodes and paths. The models also consider unavailability of ground ambulances by drawing upon concepts from backup coverage models. We illustrate our results on a case study that uses crash data from the state of New Mexico. The case study shows that crash node and path coverage percentage values decrease when ground ambulances are utilized only within their own jurisdiction.     

Reducing disparities in large-scale emergency medical service systems

Emergency Medical Service (EMS) systems operate under the pressure of knowing that human lives might be directly at stake. In the public eye there is a natural expectation of efficient response. There is abundant literature on the topic of efficient planning of EMS systems (maximizing expected coverage or minimizing response time). Other objectives have been considered but the literature available is very sparse compared to efficiency-based works. Furthermore, while real size EMS systems have been studied, the use of exact models is usually hindered by the amount of computational time required to obtain solutions. We approach the planning of large-scale EMS systems including fairness considerations using a Tabu Search-based heuristic with an embedded approximation procedure for the queuing submodel. This allows for the analysis of large-scale real systems, extending the approach in which strategic decisions (location) and operative decisions (dispatching) are combined to balance efficiency and fairness.     

Covering models and optimization techniques for emergency response facility location and planning: a review

With emergencies being, unfortunately, part of our lives, it is crucial to efficiently plan and allocate emergency response facilities that deliver effective and timely relief to people most in need. Emergency Medical Services (EMS) allocation problems deal with locating EMS facilities among potential sites to provide efficient and effective services over a wide area with spatially distributed demands. It is often problematic due to the intrinsic complexity of these problems. This paper reviews covering models and optimization techniques for emergency response facility location and planning in the literature from the past few decades, while emphasizing recent developments. We introduce several typical covering models and their extensions ordered from simple to complex, including Location Set Covering Problem (LSCP), Maximal Covering Location Problem (MCLP), Double Standard Model (DSM), Maximum Expected Covering Location Problem (MEXCLP), and Maximum Availability Location Problem (MALP) models. In addition, recent developments on hypercube queuing models, dynamic allocation models, gradual covering models, and cooperative covering models are also presented in this paper. The corresponding optimization techniques to solve these models, including heuristic algorithms, simulation, and exact methods, are summarized.     

Supporting decision making to improve the performance of an Italian Emergency Medical Service

An Emergency Medical Service (EMS) plays a fundamental role in providing good quality health care services to citizens, as it provides the first answer in distressing situations. Early response, one of the key factors in a successful treatment of an injury, is strongly influenced by the performance of ambulances, which are sent to rescue the patient. Here we report the research carried on by the authors on the ambulance location and management in the Milano area (Italy), as a part of a wider research project in collaboration with the EMS of Milano and funded by Regione Lombardia. The question posed by the EMS managers was clear and, at the same time, tricky: could decision making tools be applied, based on the currently available data, to provide suggestions for decision makers? To answer such a question, three different studies have been carried on: first the evaluation of the current EMS system performance through statistical analysis; then the study of operational policies which can improve the system performance through a simulation model; and finally the definition of an alternative set of posts through an optimization model. This paper describes the methodologies underlying such studies and reports on how their main findings were crucial to help the EMS in changing its organization model.     

Improving emergency service in rural areas: a bi-objective covering location model for EMS systems

Emergency medical service (EMS) systems are public services that often provide the first line of response to urgent health care needs within a community. Unfortunately, it has been widely documented that large disparities in access to care exist between rural and urban communities. While rural EMS is provided through a variety of resources (e.g. air ambulances, volunteer corps, etc.), in this paper we focus on ground ambulatory care. In particular our goal is to balance the level of first-response ambulatory service provided to patients in urban and rural areas by locating ambulances at appropriate stations. In traditional covering location models the objective is to maximize demand that can be covered; consequently, these models favor locating ambulances in more densely populated areas, resulting in longer response times for patients in more rural areas. To address the issue of fairness in semi-rural/semi-urban communities, we propose three bi-objective covering location models that directly consider fairness via a secondary objective. Results are discussed and compared which provide a menu of alternatives to policy makers.     

Alternate risk measures for emergency medical service system design

The stochastic nature of emergency service requests and the unavailability of emergency vehicles when requested to serve demands are critical issues in constructing valid models representing real life emergency medical service (EMS) systems. We consider an EMS system design problem with stochastic demand and locate the emergency response facilities and vehicles in order to ensure target levels of coverage, which are quantified using risk measures on random unmet demand. The target service levels for each demand site and also for the entire service area are specified. In order to increase the possibility of representing a wider range of risk preferences we develop two types of stochastic optimization models involving alternate risk measures. The first type of the model includes integrated chance constraints (ICCs ), whereas the second type incorporates ICCs  and a stochastic dominance constraint. We develop solution methods for the proposed single-stage stochastic optimization problems and present extensive numerical results demonstrating their computational effectiveness.     

Recent optimization models and trends in location,relocation, and dispatching of emergency medical vehicles

Over the past 10 years, a considerable amount of research has been devoted to the development of models to support decision making in the particular yet important context of Emergency Medical Services (EMS). More specifically, the need for advanced strategies to take into account the uncertainty and dynamism inherent to EMS, as well as the pertinence of socially oriented objectives, such as equity, and patient medical outcomes, have brought new and exciting challenges to the field. In this context, this paper summarizes and discusses modern modeling approaches to address problems related to ambulance fleet management, particularly those related to vehicle location and relocation, as well as dispatching decisions. Although it reviews early works on static ambulance location problems, this review concentrates on recent approaches to address tactical and operational decisions, and the interaction between these two types of decisions. Finally, it concludes on the current state of the art and identifies promising research avenues in the field.     

Alternative metrics to measure EMS system performance

In the development of strategy for the response to emergent incidents, emergency medical services (EMS) organizations must properly manage their resources while also adhering to response time mandates established by contractual agreements. Performance of an EMS system is typically measured by focusing on the response time of its first responders. However, given that some incidents require the response of multiple emergency vehicles, investigating only the initial response to incidents is inadequate. In this research, we propose two new metrics, in addition to the first response metric, to evaluate the performance of EMS operations: total response time and last responder response time. We develop three mixed integer programming formulations, each one focused on minimizing one of the three metrics, to model the assignment of emergency vehicles to incidents. We also propose a fourth model that combines the metrics via a weighted objective function. This model allows for the simultaneous consideration of the response metrics when evaluating the effectiveness of an emergency response dispatch policy. Experimental results, from comparisons of the models against a greedy dispatch policy, suggest the consideration of multiple response metrics leads to a more robust and effective dispatch policy. Finally, analysis using the models has potential to shape improved strategic and operational policies of EMS organizations. Journal of the Operational Research Society advance online publication, 29 June 2016; doi:10.1057/jors.2016.39     

A robust counterpart approach to the bi-objective emergency medical service design problem

The paper presents a bi-objective robust program to design a cost-responsiveness efficient emergency medical services (EMS) system under uncertainty. The proposed model simultaneously determines the location of EMS stations, the assignment of demand areas to EMS stations, and the number of EMS vehicles at each station to balance cost and responsiveness. We develop a robust counterpart approach to cope with the uncertain parameters in the EMS system. Extensive numerical studies are performed to demonstrate the benefits of our robust optimization approach.     

Alternative targets for data envelopment analysis through multi-objective linear programming: Rio de Janeiro Odontological Public Health System Case Study

In the last 10 years much has been written about the drawbacks of radial projection. During this time, many authors proposed methods to explore, interactively or not, the efficient frontier via non-radial projections. This paper compares three families of data envelopment analysis (DEA) models: the traditional radial, the preference structure and the multi-objective models. We use the efficiency analysis of Rio de Janeiro Odontological Public Health System as a background for comparing the three methods through a real case with one integer and one exogenous variable. The objectives of the study case are (i) to compare the applicability of the three approaches for efficiency analysis with exogenous and integer variables, (ii) to present the main advantages and drawbacks for each approach, (iii) to prove the impossibility to project in some regions and its implications, (iv) to present the approximate CPU time for the models, when this time is not negligible. We find that the multi-objective approach, although mathematically equivalent to its preference structure peer, allows projections that are not present in the latter. Furthermore, we find that, for our case study, the traditional radial projection model provides useless targets, as expected. Furthermore, for some parts of the frontier, none of the models provide suitable targets. Other interesting result is that the CPU-time for the multi-objective formulation, although its endogenous high complexity, is acceptable for DEA applications, due to its compact nature.     

Predicting ambulance demand using singular spectrum analysis

This paper demonstrates techniques to generate accurate predictions of demand exerted upon the Emergency Medical Services (EMS) using data provided by the Welsh Ambulance Service Trust (WAST). The aim is to explore new methods to produce accurate forecasts that can be subsequently embedded into current OR methodologies to optimise resource allocation of vehicles and staff, and allow rapid response to potentially life-threatening emergencies. Our analysis explores a relatively new non-parametric technique for time series analysis known as Singular Spectrum Analysis (SSA). We explain the theory of SSA and evaluate the performance of this approach by comparing the results with those produced by conventional time series methods. We show that in addition to being more flexible in approach, SSA produces superior longer-term forecasts (which are especially helpful for EMS planning), and comparable shorter-term forecasts to well established methods.     

On the identification of sales forecasting models in the presence of promotions

Shorter product life cycles and aggressive marketing, among other factors, have increased the complexity of sales forecasting. Forecasts are often produced using a Forecasting Support System that integrates univariate statistical forecasting with managerial judgment. Forecasting sales under promotional activity is one of the main reasons to use expert judgment. Alternatively, one can replace expert adjustments by regression models whose exogenous inputs are promotion features (price, display, etc). However, these regression models may have large dimensionality as well as multicollinearity issues. We propose a novel promotional model that overcomes these limitations. It combines Principal Component Analysis to reduce the dimensionality of the problem and automatically identifies the demand dynamics. For items with limited history, the proposed model is capable of providing promotional forecasts by selectively pooling information across established products. The performance of the model is compared against forecasts provided by experts and statistical benchmarks, on weekly data; outperforming both substantially.     

Modelling and long-term simulation of a heat recovery steam generator

Developing accurate non-linear dynamical models for heat recovery steam generator (HRSG) units is presented in this article. The common non-linear autoregressive with exogenous input (NARX) system topology was employed to develop the neuro-fuzzy models based on the experimental data taken during field experiments. In this structure, the non-linear behaviours of the HRSG unit can be characterized through interpolation of local linear models associated with different operating regions via fuzzy inference mechanism. The operating regimes were recognized by applying a genetic algorithm-based fuzzy clustering technique to the prepared data sets. The structures of the fuzzy models are defined with respect to the obtained optimal cluster centres and the corresponding membership functions. The parameters of fuzzy rules were adjusted by recursive least-squares estimation method to fit the model responses to real data. The performances of developed models were evaluated by performing a comparison between the model responses and the responses of the real plant. In addition, the stability of the developed models was assessed by perturbing the model inputs from the nominal values. This guarantees the long-term simulation capabilities of the developed models. A comparison between the responses of the corresponding models and the models obtained from some recent modelling approaches was performed to show the advantages of the developed models. The results show the accuracy and reliability of the developed models at transient and steady-state conditions.     

基于贝叶斯向量自回归的区域经济预测模型:以青海为例

由于缺乏足够的观测数据等原因,常规的区域经济预测模型在我国难以获得预期的预测效果,而贝叶斯向量自回归(BVAR)模型将变量的统计性质作为参数的先验分布引入到传统的VAR模型中,能够克服自由度过少的问题,以青海为例,本文建立了一个BVAR模型,并引入了全国GDP和中央政府转移支付作为外生变量以描述国民经济与区域经济的联系...     

Strong consistency of the empirical martingale simulation option price estimator

A simulation technique known as empirical martingale simulation （EMS） was proposed to improve simulation accuracy. By an adjustment to the standard Monte Carlo simulation, EMS ensures that the simulated price satisfies the rational option pricing bounds and that the estimated derivative contract price is strongly consistent with payoffs that satisfy Lipschitz condition. However, for some currently used contracts such as self-quanto options and asymmetric or symmetric power options, it is open whether the above asymptotic result holds. In this paper, we prove that the strong consistency of the EMS option price estimator holds for a wider class of univariate payoffs than those restricted by Lipschitz condition. Numerical experiments demonstrate that EMS can also substantially increase simulation accuracy in the extended setting.     

Elementary mathematics specialists in “departmentalized” teaching assignments: Affordances and constraints

In this article, we describe the experiences of three Elementary Mathematics Specialists (EMS) who were part of a larger project investigating the impact of EMS certification and assignment (self-contained or “departmentalized”) on teaching practices and student achievement outcomes. All three of the teachers were “departmentalized,” in the sense that each was responsible for teaching mathematics to at least two groups of students, and accordingly, did not teach all subjects as would a typical self-contained elementary teacher. Each teacher had recently earned an Elementary Mathematics Specialist certificate through completion of a 24-credit, graduate-level program designed to build pedagogical content knowledge and leadership capacity in mathematics. Through a series of observations and interviews over the course of one school year, we examined how the teachers described and navigated specific affordances and constraints they encountered in their particular contexts. Common affordances included opportunities to revise and learn from instruction, and constraints included reduced flexibility introduced by the need to schedule multiple classes of mathematics. Despite these common features, we found important differences between the three models of departmentalization, which we describe as team approach, class swap, and grade-level mathematics teacher. For example, some of the models provided more opportunities for collaboration while others made it difficult for teachers to address potential inequities in learning opportunities across sections. Despite the constraints of their respective models, we found evidence of the EMS-certified teachers drawing on professional expertise in mathematics to meet student needs.     

Nonlinear Least Squares Estimation of Log-ACD Models

This paper studies a nonlinear least squares estimation method for the logarithmic autoregressive conditional duration (Log-ACD) model. We establish the strong consistency and asymptotic normality for our estimator under weak moment conditions suitable for applications involving heavy-tailed distributions. We also discuss inference for the Log-ACD model and Log-ACD models with exogenous variables. Our results can be easily translated to study Log-GARCH models. Both simulation study and real data analysis are conducted to show the usefulness of our results.     

Padé Approximation in Economics

In economics, the systematic treatment of data to obtain specific properties from long (or short) data series is a main objective. The use of rational models and related numerical methods can be useful to help to predict the behaviour of relevant economic variables with a certain degree of certainty. This paper is concerned with illustrating the application of several numerical methods, in particular, the corner method, epsilon-algorithm, rs-algorithm and qd-algorithm, to the problem of model identification in time series analysis. These methods, closely related to theoretical research in Padé Approximation, are proposed to identify some type of rational structure associated with economic data in different contexts (financial, marketing, farming). Moreover, they incorporate the expectations of exogenous economic variables to improve the fit and forecasting of classic time series models.     

The effects of exogenous variables in efficiency measurement—A monte carlo study

A Monte Carlo study is conducted to compare the stochastic frontier method and the data envelopment analysis (DEA) method in measuring efficiency in situations where firms are subject to the effects of factors which are beyond managerial control. In making efficiency measurements and comparisons, one must separate the effects of the environment (the exogenous factors) and the effects of the productive efficiency. There are two basic approaches to account for the effects of exogenous variables: (1) an one-step procedure which includes the exogenous variables directly in estimating the efficiency measures, and (2) a two-step procedure which first estimates the relative ‘gross’ efficiencies using inputs and outputs, then analyzes the effects of the exogenous variables on the ‘gross’ efficiency. The results show that the magnitude of exogenous variables does not appear to have any significant effect on the performance of the one-step stochastic frontier method as long as the exogenous variables are correctly identified and accounted for. However, the effects of exogenous variables are significant for the two-step approach, especially for the DEA methods.     

Monte Carlo scenario generation for retail loan portfolios

Monte Carlo simulation is a common method for studying the volatility of market traded instruments. It is less employed in retail lending, because of the inherent nonlinearities in consumer behaviour. In this paper, we use the approach of Dual-time Dynamics to separate loan performance dynamics into three components: a maturation function of months-on-books, an exogenous function of calendar date, and a quality function of vintage origination date. The exogenous function captures the impacts from the macroeconomic environment. Therefore, we want to generate scenarios for the possible futures of these environmental impacts. To generate such scenarios, we must go beyond the random walk methods most commonly applied in the analysis of market-traded instruments. Retail portfolios exhibit autocorrelation structure and variance growth with time that requires more complex modelling. This paper is aimed at practical application and describes work using ARMA and ARIMA models for scenario generation, rules for selecting the correct model form given the input data, and validation methods on the scenario generation. We find when the goal is capturing the future volatility via Monte Carlo scenario generation, that model selection does not follow the same rules as for forecasting. Consequently, tests more appropriate to reproducing volatility are proposed, which assure that distributions of scenarios have the proper statistical characteristics. These results are supported by studies of the variance growth properties of macroeconomic variables and theoretical calculations of the variance growth properties of various models. We also provide studies on historical data showing the impact of training length on model accuracy and the existence of differences between macroeconomic epochs.