Mathematical analysis of emergency ambulance location

Proper ambulance location is crucial in saving lives and reducing injury. To determine efficient and effective locations, it is necessary to evaluate both the spatial and temporal distributions of demand. Because of the complex nature of the ambulance response and transport activities, the problem is subdivided into a facility location problem and a vehicle allocation problem. A set covering model is modified to solve the location problem while a simulation is used to solve the allocation problem. Combining these two models provides a powerful methodology for systematically finding a satisfactory solution to the ambulance location problem.     

Ambulance response time in a Brazilian emergency medical service

Research efforts on ambulance response times for Emergency Medical Services (EMS) calls have been made for decades, especially in developed countries, using different techniques and with varying objectives. In Brazil, a developing country, the scarce scientific production on this vital indicator prioritizes scenarios for EMS in cities with more than one million inhabitants. This shows the importance of extending research to the reality of small and medium-sized cities. This paper presents SAMU, the Brazilian EMS that follows the Franco-German emergency medicine model, compiling numbers related to service at the national level. The use of quantile regression allows the identification of the RT for the EMS and helps to explain the effects of factors at the system level, at the patient level, and specific factors on response time intervals of Southwest Paraná SAMU. This specific EMS, characterized as an inter-municipal consortium of prehospital services, is responsible for prehospital emergency care for an approximate population of 635,000 inhabitants in 42 small towns in the State of Paraná in southern Brazil. From the analysis of the records of 12,050 ambulance dispatches, it was possible to identify the average ambulance response time of 14 min and 25 s. The regression model was able to explain the influence of the independent variables at the system level (presumed severity of the emergency, ambulance dispatch time, and ambulance travel time), at the patient level (age, gender, and characteristic of the emergency) and specific variables of the emergency (day of the week and time of day) on the dependent variable response time over the quantiles, showing that the dispatch time, travel time, time of day, service to male patients and critical cases influence the ambulance response time. This work contributes to deepening the understanding of the management of EMS operations in a developing country, allows the comparison of the RT identified in relation to other countries, and identifies factors that impact the RT for other actors directly or indirectly involved. The practical implications are also presented, as well as how the study impacts the decision-making and management process of the EMS in the short, medium and long term.     

Bracing for demand shocks: An experimental investigation

We investigate inventory ordering decisions when decision makers anticipated a demand shock. Decision makers anticipating an event have been shown to brace for an uncertain negative outcome by overestimating the likelihood of that event. Decision makers faced with a spike in demand may incur increased holding costs because they may brace, exhibiting a judgment bias, and consequently a decision bias by over-ordering inventory. Three studies span conditions of uncertainty regarding the timing and magnitude of a demand shock: Employing three between-subjects experiments, Study 1 investigates behavior when decision makers were faced with uncertainty in timing and in magnitude of demand at the most elemental level, manipulating holding and stock out costs. The three experimental tasks feature uncertainty about the magnitude of demand (Experiment 1.1), uncertainty about the timing of demand (Experiment 1.2), and uncertainty about both the magnitude and timing of demand (Experiment 1.3). Study 2 uses a dynamic, multi-period replenishment task and a between-subjects manipulation regarding the uncertainty of timing and magnitude of a demand shock. Study 3 also employs a multi-period decision environment, but compares behavior under a demand shock condition with that in a condition featuring only random variability. The collective results from the three studies identify a bias toward over-ordering in response to a demand shock, relative to the optimal orders. The between-subjects manipulations in Study 2 points toward a possible remedy as we found that providing information concerning the timing and magnitude of a shock ameliorated the bias. The primary revelation was that decision makers had more difficulty dealing with uncertain timing than with uncertain magnitude of demand. One implication is that it is particularly critical for retailers to carefully plan and manage how they share information with upstream supply chain partners regarding when they plan to introduce store-level promotions.     

震后模糊道路破损率条件下应急物资调配研究

应急物资调配是应急物流系统重要研究问题之一,直接关系到应急物流活动的成败。考虑到灾后运输道路破损率不能立即确定,构建了道路破损率与物资需求量为梯形模糊数的多目标应急物资调配模型。通过将其转化为具有确定系数的多目标规划模型来进行求解,并提出了求得该模型满意解的算法。最后通过算例分析说明该方法的有效性。     

不确定OD需求下混合交通网络设计的鲁棒优化模型

假定OD需求是不确定的,但它属于一个有界多面体,应用鲁棒优化的方法对不确定OD需求下混合网络设计问题进行了研究,建立了基于用户均衡的混合网络设计的极小极大模型,并采用需求生成的算法求解不确定OD需求下混合网络设计的鲁棒对应模型。数值算例的结果表明应用鲁棒优化方法得到的混合网络设计方案不仅更加符合实际,而且较传统确定性的混合网络设计方案具有更高的可靠性。     

Data-driven forecasting for operational planning of emergency medical services

Emergency medical services (EMS) play a vital role in delivering pre-hospital care. The operational efficiency of such services is critical and adequate demand forecasts can contribute to such a goal. But for that, the available data need to be well characterized before being used. Previous studies have failed to address some important aspects of this need, such as exploring a comprehensive list of contextual data to decide which are relevant to explain the EMS demand behavior. Moreover, modern forecasting techniques have been explored in the EMS context, including neural networks, but the computational complexity inherent to the methods and their use was not discussed. Finally, it is also unclear how different demand patterns can be when predicting the volume of emergency calls considering the priority level and the number of dispatches according to vehicle type. This study proposes a generic data-driven forecasting method to address these shortcomings and to support operational decisions. The results obtained with the proposed method indicate that each priority call and vehicle type shows different patterns, which suggests that such differentiation should contribute to better resource allocation. At the same time, the operational impact of the demand shared by neighboring zones proved to be significant at bases near the border. The models developed resulted in important decision tools that can be used to predict the dynamic demand of EMS on an hourly or shift basis. Additionally, the method adds value for decision-makers that want to plan not only when and how many but also where resources are demanded, avoiding assumptions that impact the operational performance.     

The use of spectral analysis to validate peanning models

Statistical fit of model predictions to empirical evidence is found to be an insufficient condition for establishing the validity of a planning model where the dynamic behavior is of particular importance. The paper describes a spectral analysis statistical test that can be used to validate the structure of a planning model by comparing the time series generated by the model with the actual time series of events for the real system under study. Validation of an ambulance simulation model is reported in which the model apparently was valid based on classical goodness of fit tests of aggregate data. However, following a spectral analysis of the simulation results, an entirely new method of generating incidents was found to be necessary. The resulting model then was able to duplicate realistically the essential cyclical nature of hourly demand for emergency care observed in the real system which periodically created excessive busy and idle periods not realized in the structure of the original model.     

The investment decision of a Multinational Firm under uncertain quantity restrictions

In this paper we analyze the allocative investment decisions of a Multinational Firm (MNF) when it faces uncertain quantity restrictions such as a voluntary export restraint or a quota imposed by the host government. The model with uncertain quantity restrictions is analyzed further by introducing additional uncertainties such as a foreign tax rate, transfer prices, foreign exchange rates and foreign demand. The MNF invests more in the host country due to uncertain quantity restrictions. The risk averse MNF invests more in the host country despite its uncertain tax rate if the transfer price is less than the expected marginal revenue loss due to the uncertain quantity restriction. The uncertain transfer price leads the MNF to invest more in the foreign country if the tax rates are dissimilar between the two countries. Foreign demand uncertainty and foreign exchange rates uncertainty have the same effects on capital allocation between the host country and home country. In particular, we derive the condition under which the direction of investment is unambiguous.     

A goal programming model for the siting of multilevel EMS systems.

Facility siting models known as location covering techniques have proven to be useful particularly for emergency medical services (EMS) planning, given the importance of ambulances responding to demand within some maximum time constraint. These models represent a set of methods which focus the health planner's attention on the access of people to health care, since they attempt to “cover” people in need of service within some specified time standard.This research develops a technique for the locational planning of sophisticated EMS systems, characterized by multiple levels of emergency health services. Specifically, a two-tiered system with “basic life support” and “advanced life support” capabilities is modeled as a goal program.By applying location covering techniques within a goal programming framework, this study develops a method for the siting of multilevel EMS systems so that (1) each service level maximizes coverage of its own demand population, and (2) “back-up” coordination between levels is assured. The usefulness of this goal program as a health planning tool is evidenced in the model's explicit articulation of EMS policy objectives and its ability to link system levels in terms of “goal-directed behavior”. The working of this multilevel covering model is demonstrated by reference to EMS planning scenarios and related numerical examples.     

Strategic compensation in South Korea's publicly traded firms

This strategic compensation model based on contingency theory of organizations proposes that a fit between the organization's business environment and compensation system will affect the firm's performance (Rockmore, 1991; Rockmore and Scarpello, 1994). This proposition was tested with a set of Korean sample data of seventy-five publicly traded companies within thirty-four three-digit Standard Industrial Classification codes.

The cluster analysis applied to the 7-item task environment uncertainty components resulted in two group classifications that face relatively ‘more certain’ and ‘more uncertain’ environments. Principal component factor analysis of the 8-item compensation system components resulted in three compensation system factors and subsequent cluster analysis classified firm pay plans into two clusters, which we labelled ‘more traditional’ and ‘more innovative’. Discriminant analysis confirmed the resulting classifications of both task environment and compensation system types. With both ROA and EPS measures, significantly more ‘fits’ (firms in stable environment that use traditional compensation system or firms in uncertain environment that use innovative compensation system) showed financial gains compared with ‘nonfits’. This financial impact of the contingency was more salient for those firms that face uncertain environment. The same results were obtained when ANOVA was performed.     

A two-period newsvendor model for prepositioning with a post-disaster replenishment using Bayesian demand update

Humanitarian aid agencies usually resort to inventory prepositioning to mitigate the impact of disasters by sending emergency supplies to the affected area as quickly as possible. However, a lack of replenishment opportunity after a disaster can greatly hamper the effectiveness of the relief operation due to uncertainty in demand. In this paper, a prepositioning problem is formulated as a two-period newsvendor model where the response phase is divided into two periods. The model acknowledges the demand to be uncertain even after the disaster and utilises the Bayesian approach to revise the demand of the second period. Based on the revised demand, an order is placed at the beginning of the second period to be replenished instantaneously. A two-stage solution methodology is proposed to find the prepositioning quantity and post-disaster replenishment quantity, which minimise the total expected costs of relief operations. A numerical example is presented to demonstrate the solution methodology, and sensitivity analysis is performed to examine the effect of model parameters. The results highlight the indifferent characteristics shown by the replenishment quantity with the variation in model parameters.     

An application of a spatially distributed queuing model to an ambulance system

An application of a spatially distributed queuing model to an ambulance system is presented. The purpose of this research was to assess the usefulness of a variation of the “hypercube” queuing model developed specifically for modeling an ambulance system. The model was applied to the emergency medical system of Greenville County, South Carolina using historical data. Results indicate that the model provides reasonably accurate estimates of system performance measures when the input parameters can be accurately specified.     

Minimising emergency response time of ambulances through pre-positioning in Dhaka city,Bangladesh

This study conducted a large-scale survey in Dhaka, Bangladesh; the survey involved 95 major hospitals, more than 3000 emergency room patients, and 2 of the largest ambulance operators. Currently, most ambulances are parked within the vicinity of hospitals and are either dispatched or fetched by the acquaintances of the patient on demand, resulting in lengthy round trips. Reducing the response time of ambulances would certainly improve the emergency service, and pre-positioning of the ambulances could be a solution to reducing the response time. This study used two approaches to address the problem. First, the location-allocation problem was solved to find the optimal number of ambulance locations by maximising the demand coverage. Second, separate location-allocation for the peak and off-peaks, using K-means clustering, was applied to systematically optimise the ambulance positioning in small clusters near demand points. These approaches could substantially improve the existing emergency response time. Distributing ambulances near demand points yielded greater improvements in response time than when the ambulances are stationed near hospitals.     

基于Stackelberg博弈的连续性生产企业原料采购优化模型

文中以连续性生产企业原料采购为研究对象,选择单个供应商和单个生产商组成的两层供应链子系统,探讨在不确定性环境与信息不对称情形下,采用Stackelberg博弈理论建立采购批量折扣模型,使得供应商利用批量折扣使双方成本达到最优并降低不确定性带来的风险,应用实例表明该方法能够有效地改善供应链的协调性。     

Causal models in plan evaluation

A major purpose of urban planning is solving urban problems. Though a number of planning methods exist to evaluate the effectiveness of alternative plans, few offer specific methods for identifying the causes of urban problems, developing alternative plans that address these causes, and estimating plan effects. Borrowed from the social sciences, causal models may be used to achieve these plan evaluation objectives. Causal models developed from substantive theory of urban processes are used to estimate both direct and indirect plan effects as well as to evaluate plan efficiency, equity and uncertainty. The implications of causal models for planning education, theory and practice are also discussed.     

Modeling emergency medical response to a mass casualty incident using agent based simulation

Emergency managers have to develop plans for responding to disasters within their jurisdiction. This includes coordinating multiple independent agencies participating in the response. While much of this is currently done by use of intuition and expert judgment, models can be used to test assumptions and examine the impact of policies and resource levels. The autonomous nature of responders as well as the rapidly changing information during a disaster suggests that agent based models can be especially suited for examining policy questions. In this work, we built an agent based model of a given urban area to simulate the emergency medical response to a mass casualty incident (MCI) in that area. The model was constructed from publicly available geographic information system and data regarding available response resources (such as ambulances, EMS personnel and hospital beds). Three different agent types are defined to model heterogeneous entities in the system. By simulating various response policies, the model can inform emergency responders on the requirements and response protocols for disaster response and build intuition and understanding in advance of facing actual incidents that are rare in the day-to-day operating experiences.     

A Hybrid model for locating new emergency facilities to improve the coverage of the road crashes

We propose an emergency facility-locating model aimed at increasing the coverage of emergency demand throughout the city. The proposed model takes into account the status and location of the emergency facilities in the network and identifies locations suitable for the construction of new facilities. Here, Data Envelopment Analysis (DEA) and Maximum Coverage Location Problem (MCLP) have been combined in a single model. To do so, design problem and evaluation problem are considered concurrently to maximize the efficiency of services provided by emergency facilities across the city in response to the demand. Moreover, the total emergency demand in each district was considered in relation to the population density, the fatal, injurious, and property damage only (PDO) crashes. The coverage area of each emergency facility was assumed to be proportional to the average ambulance speed in the surrounding road network during rush hours. The available budget was included in the model to let the model function under various fiscal conditions. Model input variables consisted of average number of mortalities, injuries and PDO crashes as well as the population density of each urban district. The output variables of the model included the coverage share of proposed emergency centers and hospitals equipped with ambulances. The model was tested on the network of Tehran (Iran). It is recommended to add the location of some emergency centers and hospitals to the network. Moreover, the results showed that ten urban districts had efficiency problem in provision of emergency services.     

The effect of systematic risk factors on counterparty default and credit risk of interest rate swaps

This research investigates the effect of specific systematic risk factors on credit risk pricing and capital allocation of interest rate swaps. Because of the stochastic nature of uncertain future cash flows and interest rates, practitioners typically employ the Black-Scholes option pricing model in combination with a simulation analysis to establish capital requirements and estimate the shadow price of an interest rate swap. However, this practice of pricing swap risk excludes systematic risk factors that affect the risk shadow price, thereby underestimating the capital allocation required for financial institutions. This research demonstrates the effect of risk mispricing when simulation models ignore systematic risk factors such as model risk, convexity risk, and parameter risk on the pricing of interest rate swaps.