An optimization approach for ambulance location and the districting of the response segments on highways

In this paper we present a method to optimize the configuration and operation of emergency medical systems on highways. Different from the approaches studied in the previous papers, the present method can support two combined configuration decisions: the location of ambulance bases along the highway and the districting of the response segments. For example, this method can be used to make decisions regarding the optimal location and coverage areas of ambulances in order to minimize mean user response time or remedy an imbalance in ambulance workloads within the system. The approach is based on embedding a well-known spatially distributed queueing model (hypercube model) into a hybrid genetic algorithm to optimize the decisions involved. To illustrate the application of the proposed method, we utilize two case studies on Brazilian highways and validate the findings via a discrete event simulation model.     

The capacitated maximal covering location problem with backup service

The maximal covering location problem has been shown to be a useful tool in siting emergency services. In this paper we expand the model along two dimensions — workload capacities on facilities and the allocation of multiple levels of backup or prioritized service for all demand points. In emergency service facility location decisions such as ambulance sitting, when all of a facility's resources are needed to meet each call for service and the demand cannot be queued, the need for a backup unit may be required. This need is especially significant in areas of high demand. These areas also will often result in excessive workload for some facilities. Effective siting decisions, therefore, must address both the need for a backup response facility for each demand point and a reasonable limit on each facility's workload. In this paper, we develop a model which captures these concerns as well as present an efficient solution procedure using Lagrangian relaxation. Results of extensive computational experiments are presented to demonstrate the viability of the approach.     

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.     

A Non-linear Multi-criteria Programming Approach for Determining County Emergency Medical Service Ambulance Allocations

In this paper an integer, non-linear mathematical programming model is developed to allocate emergency medical service (EMS) ambulances to sectors within a county in order to meet a government-mandated response-time criterion. However, in addition to the response-time criterion, the model also reflects criteria for budget and work-load, and, since ambulance response is best described within the context of a queueing system, several of the model system constraints are based on queueing formulations adapted to a mathematical programming format. The model is developed and demonstrated within the context of an example of a county encompassing rural, urban and mixed sectors which exhibit different demand and geographic characteristics. The example model is solved using an integer, non-linear goal-programming technique. The solution results provide ambulance allocations to sectors within the county, the probability of an ambulance exceeding a prespecified response time, and the utilization factor for ambulances per sector.     

Methods for solving nonlinear equations used in evaluating emergency vehicle busy probabilities

In this paper we present two iterative methods for solving a model to evaluate busy probabilities for Emergency Medical Service (EMS) vehicles. The model considers location dependent service times and is an alternative to the mean service calibration method; a procedure, used with the Hypercube Model, to accommodate travel times and location-dependent service times. We use monotonicity arguments to prove that one iterative method always converges to a solution. A large computational experiment suggests that both methods work satisfactorily in EMS systems with low ambulance busy probabilities and the method that always converges to a solution performs significantly better in EMS systems with high busy probabilities.     

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.     

Research, practice, uncertainty and responsibility

Three issues concerning the relationship between research and practice are addressed. (1) A certain ‘prototype mathematics classroom’ seems to dominate the research field, which in many cases seems selective with respect to what practices to address. I suggest challenging the dominance of the discourse created around the prototype mathematics classroom. (2) I find it important to broaden the school-centred discourse on mathematics education and to address the very different out-of-school practices that include mathematics. Many of these practices are relevant for interpreting what is taking place in a school context. That brings us to (3) socio-political issues of mathematics education. When the different school-sites for learning mathematics as well as the many different practices that include mathematics are related, we enter the socio-political dimension of mathematics education.On the one hand we must consider questions like: Could socio-political discrimination be acted out through mathematics education? Could mathematics education exercise a regimentation and disciplining of students? Could it include discrimination in terms of language? Could it include sexism and racism? On the other hand: Could mathematics education bring about competencies which can be described as empowering, and as supporting the development of mathematical literary or a ‘mathemacy’, important for the development of critical citizenship?However, there is no hope for identifying a one-way route to mathemacy. More generally: There is no simple way of identifying the socio-political functions of mathematics education. Mathematics education has to face uncertainty, and this challenge brings us to the notion of responsibility.     

Multicriteria decision aid in financial management

The financial decisions of an organization are usually included in the context of optimization. Concerning a long-term period, there are decisions related to the optimal allocation of funds, and decisions related to the optimal financial structure. In the short-term case, the decisions are related to the optimization of stocks, cash, accounts receivable, current liabilities, etc. The financial theory analyzes these decisions, mainly from an optimal point of view. The optimal character of such decisions has led researchers to propose operations research techniques to solve the problems that are inherent in such decisions. This paper examines the contribution of multicriteria analysis in solving financial decision problems in a realistic context. The paper also includes an extensive bibliography on the subject.     

Fifty years of operational research and emergency response

Over the past 50 years, a wealth of applications has resulted from researchers turning their attention to operations such as fire suppression, law enforcement and ambulance services. The 1970s might even be argued as the ‘golden age’ of this particular effort, producing many of the seminal works in fire station location planning, unit assignment and ambulance queuing models. Such efforts naturally continue through to the present, but with a focus shifting away from earlier contexts of established urban emergency service systems. Simultaneously, current evidence from the field suggests that far more work remains. In this paper, we review the operational research (OR) foundation in emergency response so far, highlighting the fact that most of what has been accomplished addresses the well-structured problems of emergency services. This, in turn, offers an explanation for some paradoxical challenges from the field: most of emergency response itself is semi-structured, at best. While OR has traditionally focused on the management of an organization, emergency response ultimately requires the management of disorganization, suggesting an important OR growth area for the next 50 years.     

A multi-period double coverage approach for locating the emergency medical service stations in Istanbul

We consider the multi-period location planning problem of emergency medical service (EMS) stations. Our objective is to maximize the total population serviced by two distinct stations within two different response time limits over a multi-period planning horizon. Our aim is to provide a backup station in case no ambulance is available in the closer station and to develop a strategic plan that spans multiple periods. In order to solve this problem, we propose a Tabu Search approach. We demonstrate the effectiveness of the proposed approach on randomly generated data. We also implement our approach to the case of Istanbul to determine the locations of EMS stations in the metropolitan area.     

MIP models for production lot sizing problems with distribution costs and cargo arrangement

This study presents mixed integer programming (MIP) models for production lot sizing problems with distribution costs using unit load devices such as pallets and containers. Problems that integrate production lot sizing decisions and loading of the products in vehicles (bins) are also modelled, in which constraints such as weight limits, volume restrictions or the value of the cargo loaded in the bins are considered. In general, these problems involve a trade-off between production, inventory and distribution costs. Lot sizing decisions should take into account production capacity and product demand constraints. Distribution decisions are related to the loading and transport of products in unit load devices. The MIP models are solved by the branch-and-cut method of an optimization package and the results show that these approaches have the potential to address different practical situations.     

Facility location and supply chain management – A review

Facility location decisions play a critical role in the strategic design of supply chain networks. In this paper, a literature review of facility location models in the context of supply chain management is given. We identify basic features that such models must capture to support decision-making involved in strategic supply chain planning. In particular, the integration of location decisions with other decisions relevant to the design of a supply chain network is discussed. Furthermore, aspects related to the structure of the supply chain network, including those specific to reverse logistics, are also addressed. Significant contributions to the current state-of-the-art are surveyed taking into account numerous factors. Supply chain performance measures and optimization techniques are also reviewed. Applications of facility location models to supply chain network design ranging across various industries are presented. Finally, a list of issues requiring further research are highlighted.     

An evidential approach to SLAM,path planning,and active exploration

Probability theory has become the standard framework in the field of mobile robotics because of the inherent uncertainty associated with sensing and acting. In this paper, we show that the theory of belief functions with its ability to distinguish between different types of uncertainty is able to provide significant advantages over probabilistic approaches in the context of robotics. We do so by presenting solutions to the essential problems of simultaneous localization and mapping (SLAM) and planning based on belief functions. For SLAM, we show how the joint belief function over the map and the robot's poses can be factored and efficiently approximated using a Rao-Blackwellized particle filter, resulting in a generalization of the popular probabilistic FastSLAM algorithm. Our SLAM algorithm produces occupancy grid maps where belief functions explicitly represent additional information about missing and conflicting measurements compared to probabilistic grid maps. The basis for this SLAM algorithm are forward and inverse sensor models, and we present general evidential models for range sensors like sonar and laser scanners. Using the generated evidential grid maps, we show how optimal decisions can be made for path planning and active exploration. To demonstrate the effectiveness of our evidential approach, we apply it to two real-world datasets where a mobile robot has to explore unknown environments and solve different planning problems. Finally, we provide a quantitative evaluation and show that the evidential approach outperforms a probabilistic one both in terms of map quality and navigation performance.     

Two-player simultaneous location game: Preferential rights and overbidding

Competitive location problems can be characterized by the fact that the decisions made by others will affect our own payoffs. In this paper, we address a discrete competitive location game in which two decision-makers have to decide simultaneously where to locate their services without knowing the decisions of one another. This problem arises in a franchising environment in which the decision-makers are the franchisees and the franchiser defines the potential sites for locating services and the rules of the game. At most one service can be located at each site, and one of the franchisees has preferential rights over the other. This means that if both franchisees are interested in opening the service in the same site, only the one that has preferential rights will open it. We consider that both franchisees have budget constraints, but the franchisee without preferential rights is allowed to show interest in more sites than the ones she can afford. We are interested in studying the influence of the existence of preferential rights and overbidding on the outcomes for both franchisees and franchiser. A model is presented and an algorithmic approach is developed for the calculation of Nash equilibria. Several computational experiments are defined and their results are analysed, showing that preferential rights give its holder a relative advantage over the other competitor. The possibility of overbidding seems to be advantageous for the franchiser, as well as the inclusion of some level of asymmetry between the two decision-makers.     

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.     

Digital technologies and the challenge of constructing an inclusive school mathematics

This article addresses research related to the use of digital technologies in the teaching and learning of mathematics in Brazil. Its scope is limited to the context of school mathematics and, more specifically, to an ongoing research programme which involves the development of collaborative research partnerships with teachers of mathematics. The paper begins with a brief presentation of the introduction of computers into the Brazilian educational scenario in the 1980s, highlighting how computer technology was heralded as a key to permitting new pedagogical approaches appropriate to the constructivist philosophy of that time. It goes on to consider recent developments in the theoretical frameworks used to interpret mathematics learning in the presence of digital technologies and the importance of focusing on the learning system as a whole, considering epistemological, cognitive and pedagogic dimensions concomitantly. In this vein, it is argued that for any real integration to take place, the mathematical practices afforded by digital tools must be considered legitimate by all the actors in this process and, perhaps most notably, by teachers. The rest of the paper focuses on our approaches to involve teachers in making decisions about technology use in their own classrooms. The strategy used was based on the realisation of research activities underpinned by the idea of the collaborative design of learning situations and the goal of including the wide diversity of learners that characterises Brazilian mathematics classrooms.     

Some statistical challenges in automated driving systems

Automated driving systems are rapidly developing. However, numerous open problems remain to be resolved to ensure this technology progresses before its widespread adoption. A large subset of these problems are, or can be framed as, statistical decision problems. Therefore, we present herein several important statistical challenges that emerge when designing and operating automated driving systems. In particular, we focus on those that relate to request-to-intervene decisions, ethical decision support, operations in heterogeneous traffic, and algorithmic robustification. For each of these problems, earlier solution approaches are reviewed and alternative solutions are provided with accompanying empirical testing. We also highlight open avenues of inquiry for which applied statistical investigation can help ensure the maturation of automated driving systems. In so doing, we showcase the relevance of statistical research and practice within the context of this revolutionary technology.     

Dynamic pricing and inventory control: robust vs. stochastic uncertainty models—a computational study

In this paper, we consider a variety of models for dealing with demand uncertainty for a joint dynamic pricing and inventory control problem in a make-to-stock manufacturing system. We consider a multi-product capacitated, dynamic setting, where demand depends linearly on the price. Our goal is to address demand uncertainty using various robust and stochastic optimization approaches. For each of these approaches, we first introduce closed-loop formulations (adjustable robust and dynamic programming), where decisions for a given time period are made at the beginning of the time period, and uncertainty unfolds as time evolves. We then describe models in an open-loop setting, where decisions for the entire time horizon must be made at time zero. We conclude that the affine adjustable robust approach performs well (when compared to the other approaches such as dynamic programming, stochastic programming and robust open loop approaches) in terms of realized profits and protection against constraint violation while at the same time it is computationally tractable. Furthermore, we compare the complexity of these models and discuss some insights on a numerical example.     

The Study of Human Decision-Making: A Cautionary Tale from the World of Experimental Gaming

In recent years there has been a move within the Operational Research community towards the view that the established methods may be inadequate for dealing with complex problems and that an understanding of human decision-making itself is needed. Recognising the importance of this, however, leaves open the question of how research in this area should best proceed. In this paper we look at the difference between two contrasting approaches; that is, between simply collecting hard data about the overt decisions people make under specified conditions and actually trying to explore the (subjective) reasons for this behaviour. Specifically, these issues are examined within the context of some work done with experimental gaming. The example clearly illustrates how failure to examine a variety of possible explanations for behaviour may lead to fundamentally inaccurate conclusions. Finally, it is concluded that in order to study decision-making effectively, it is vitally important that evidence is taken from as wide a variety of sources as possible.     

Strategic facility location: A review

Facility location decisions are a critical element in strategic planning for a wide range of private and public firms. The ramifications of siting facilities are broadly based and long-lasting, impacting numerous operational and logistical decisions. High costs associated with property acquisition and facility construction make facility location or relocation projects long-term investments. To make such undertakings profitable, firms plan for new facilities to remain in place and in operation for an extended time period. Thus, decision makers must select sites that will not simply perform well according to the current system state, but that will continue to be profitable for the facility's lifetime, even as environmental factors change, populations shift, and market trends evolve. Finding robust facility locations is thus a difficult task, demanding that decision makers account for uncertain future events. The complexity of this problem has limited much of the facility location literature to simplified static and deterministic models. Although a few researchers initiated the study of stochastic and dynamic aspects of facility location many years ago, most of the research dedicated to these issues has been published in recent years. In this review, we report on literature which explicitly addresses the strategic nature of facility location problems by considering either stochastic or dynamic problem characteristics. Dynamic formulations focus on the difficult timing issues involved in locating a facility (or facilities) over an extended horizon. Stochastic formulations attempt to capture the uncertainty in problem input parameters such as forecast demand or distance values. The stochastic literature is divided into two classes: that which explicitly considers the probability distribution of uncertain parameters, and that which captures uncertainty through scenario planning. A wide range of model formulations and solution approaches are discussed, with applications ranging across numerous industries.