A taxonomy for emergency service station location problem

The emergency service station (ESS) location problem has been widely studied in the literature since 1970s. There has been a growing interest in the subject especially after 1990s. Various models with different objective functions and constraints have been proposed in the academic literature and efficient solution techniques have been developed to provide good solutions in reasonable times. However, there is not any study that systematically classifies different problem types and methodologies to address them. This paper presents a taxonomic framework for the ESS location problem using an operations research perspective. In this framework, we basically consider the type of the emergency, the objective function, constraints, model assumptions, modeling, and solution techniques. We also analyze a variety of papers related to the literature in order to demonstrate the effectiveness of the taxonomy and to get insights for possible research directions

STRATEGIES TO IMPROVE THE EFFICIENCY OF EMERGENCY MEDICAL SERVICE (EMS) SYSTEMS UNDER MORE REALISTIC CONDITIONS

Emergency medical service (EMS) systems provide medical care to pre-hospital patients who need rapid response and transportation. This dissertation proposes a new realistic approach for EMS systems in two major focuses: multiple unit dispatching and relocation strategies. This work makes recommendations for multiple-unit dispatch to multiple call priorities based on simulation optimization and heuristics. The objective is to maximize the expected survival rate. Simulation models are proposed to determine the optimization. A heuristic algorithm is developed for large-scale problems. Numerical results show that dispatching while considering call priorities, rather than always dispatching the closest medical units, could improve the effectiveness of EMS systems. Additionally, we extend the model of multiple-unit dispatch to examine fairness between call priorities. We consider the potentially-life-threatening calls which could be upgraded to life-threatening. We formulate the fairness problem as an integer programming model solved using simulation optimization. Taking into account fairness between priorities improves the performance of EMS systems while still operating at high efficiency. As another focus, we consider dynamic relocation strategy using a nested-compliance table policy. For each state of the EMS systems, a decision must be made regarding exactly which ambulances will be allocated to which stations. We determine the optimal nested-compliance table in order to maximize the expected coverage, in the binary sense, as will be later discussed. We formulate the nested-compliance table model as an integer program, for which we approximate the steady-state probabilities of EMS system to use as parameters to our model. Simulation is used to investigate the performance of the model and to compare the results to a static policy based on the adjusted maximum expected covering location problem (AMEXCLP). Additionally, we extend the nested-compliance table model to consider an upper bound on relocation time. We analyze the decision regarding how to partition the service area into smaller sub-areas (districts) in which each sub-area operates independently under separate relocation strategies. We embed the nested-compliance table model into a tabu search heuristic algorithm. Iteration is used to search for a near-optimal solution. The performance of the tabu search heuristic and AMEXCLP are compared in terms of the realized expected coverage of EMS systems

A generic method to develop simulation models for ambulance systems

In this paper, we address the question of generic simulation models and their role in improving emergency care around the world. After reviewing the development of ambulance models and the contexts in which they have been applied, we report the construction of a reusable model for ambulance systems. Further, we describe the associated parameters, data sources, and performance measures, and report on the collection of information, as well as the use of optimisation to configure the service to best effect. Having developed the model, we have validated it using real data from the emergency medical system in a Brazilian city, Belo Horizonte. To illustrate the benefits of standardisation and reusability we apply the model to a UK context by exploring how different rules of engagement would change the performance of the system. Finally, we consider the impact that one might observe if such rules were adopted by the Brazilian system

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

Models for ambulance planning on the strategic and the tactical level

Ambulance planning involves decisions to be made on different levels. The decision for choosing base locations is usually made for a very long time (strategic level), but the number and location of used ambulances can be changed within a shorter time period (tactical level). We present possible formulations for the planning problems on these two levels and discuss solution approaches that solve both levels either simultaneously or separately. The models are set up such that different types of coverage constraints can be incorporated. Therefore, the models and approaches can be applied to different emergency medical services systems occurring all over the world. The approaches are tested on data based on the situation in the Netherlands and compared based on computation time and solution quality. The results show that the solution approach that solves both levels separately performs better when considering minimizing the number of bases. However, the solution approach that solves both levels simultaneously performs better when considering minimizing the number of ambulances. In addition, with the latter solution approach it is easier to make a good trade-off between minimizing the number of bases and ambulances because it considers a weighted objective function. However, the computation time of this approach increases exponentially with the input size whereas the computation time of the approach that solves both levels separately follows a more linear trend

Joint Location and Dispatching Decisions for Emergency Medical Service Systems

Emergency Medical Service (EMS) systems are a service that provides acute care and transportation to a place for definitive care, to people experiencing a medical emergency. The ultimate goal of EMS systems is to save lives. The ability of EMS systems to do this effectively is impacted by several resource allocation decisions including location of servers (ambulances), districting of demand zones and dispatching rules for the servers. The location decision is strategic while the dispatching decision is operational. Those two decisions are usually made separately although both affect typical EMS performance measures. The service from an ambulance is usually time sensitive (patients generally want the ambulances to be available as soon as possible), and the demand for service is stochastic. Regulators also impose availability constraints, the most generally accepted being that 90\% of high priority calls (such as those related to cardiac arrest events) should be attended to within 8 minutes and 59 seconds. In the case of minimizing the mean response time as the only objective, previous works have shown that there are cases in which it might not be optimal to send the closest available server to achieve the minimum overall response time. Some researchers have proposed integrated models in which the two decisions are made sequentially. The main contribution of this work is precisely in developing the integration of location and dispatching decisions made simultaneously. Combining those decisions leads to complex optimization models in which even the formulation is not straightforward. In addition, given the stochastic nature of the EMS systems the models need to have a way to represent their probabilistic nature. Several researchers agree that the use of queuing theory elements in combination with location, districting and dispatching models is the best way to represent EMS systems. Often heuristic/approximate solution procedures have been proposed and used since the use of exact methods is only suitable for small instances. Performance indicators other than Response Time can be affected negatively when the dispatching rule is sending the closest server. For instance, there are previous works claiming that when the workload of the servers is taken into account, the nearest dispatching policy can cause workload imbalances. Therefore, researchers mentioned as a potential research direction to develop solution approaches in which location, districting and dispatching could be handled in parallel, due to the effect that all those decisions have on key performance measures for an EMS system. In this work the aim is precisely the development of an optimization framework for the joint problem of location and dispatching in the context of EMS systems. The optimization framework is based on meta heuristics. Fairness performance indicators are also considered, taking into account different points of view about the system, in addition to the standard efficiency criteria. Initially we cover general aspects related to EMS systems, including an overall description of main characteristics being modeled as well as an initial overview of related literature. We also include an overall description and literature review with focus on solution methodologies for real instances, of two related problems: the $p$-median problem and the maximal covering location problem (MCLP). Those two problems provide much of the basic structure upon which the main mathematical model integrating location and dispatching decisions is built later. Next we introduce the mathematical model (mixed-integer non-linear problem) which has embedded a queuing component describing the service nature of the system. Given the nature of the resulting model it was necessary to develop a solution algorithm. It was done based on Genetic Algorithms. We have found no benefit on using the joint approach regarding mean Response Time minimization or Expected Coverage maximization. We concluded that minimizing Response Time is a better approach than maximizing Expected Coverage, in terms of the trade-off between those two criteria. Once the optimization framework was developed we introduced fairness ideas to the location/allocation of servers for EMS systems. Unlike the case of Response Time, we found that the joint approach finds better solutions for the fairness criteria, both from the point of view of internal and external costumers. The importance of that result lies in the fact that people not only expect the service from ambulances to be quick, but also expect it to be fair, at least in the sense that any costumer in the system should have the same chances of receiving quick attention. From the point of view of service providers, balancing ambulance workloads is also desirable. Equity and efficiency criteria are often in conflict with each other, hence analyzing trade-offs is a first step to attempt balancing different points of view from different stakeholders. The initial modeling and solution approach solve the problem by using a heuristic method for the overall location/allocation decisions and an exact solution to the embedded queuing model. The problem of such an approach is that the embedded queuing model increases its size exponentially with relation to the number of ambulances in the system. Thus the approach is not practical for large scale real systems, say having 10+ ambulances. Therefore we addressed the scalability problem by introducing approximation procedures to solve the embedded queuing model. The approximation procedures are faster than the exact solution method for the embedded sub-problem. Previous works mentioned that the approximated solutions are only marginally apart from the exact solution (1 to 2\%). The mathematical model also changed allowing for several ambulances to be assigned to a single station, which is a typical characteristic of real world large scale EMS systems. To be able to solve bigger instances we also changed the solution procedure, using a Tabu Search based algorithm, with random initialization and dynamic size of the tabu list. The conclusions in terms of benefits of the joint approach are true for bigger systems, i.e. the joint approach allows for finding the best solutions from the point of view of several fairness criteria

A mathematical programming approach for dispatching and relocating EMS vehicles.

We consider the problem of dispatching and relocating EMS vehicles during a pandemic outbreak. In such a situation, the demand for EMS vehicles increases and in order to better utilize their capacity, the idea of serving more than one patient by an ambulance is introduced. Vehicles transporting high priority patients cannot serve any other patient, but those transporting low priority patients are allowed to be rerouted to serve a second patient. We have considered three separate problems in this research. In the first problem, an integrated model is developed for dispatching and relocating EMS vehicles, where dispatchers determine hospitals for patients. The second problem considers just relocating EMS vehicles. In the third problem only dispatching decisions are made where hospitals are pre-specified by patients not by dispatchers. In the first problem, the objective is to minimize the total travel distance and the penalty of not meeting specific constraints. In order to better utilize the capacity of ambulances, we allow each ambulance to serve a maximum of two patients. Considerations are given to features such as meeting the required response time window for patients, batching non-critical and critical patients when necessary, ensuring balanced coverage for all census tracts. Three models are proposed- two of them are linear integer programing and the other is a non-linear programing model. Numerical examples show that the linear models can be solved using general-purpose solvers efficiently for large sized problems, and thus it is suitable for use in a real time decision support system. In the second problem, the goal is to maximize the coverage for serving future calls in a required time window. A linear programming model is developed for this problem. The objective is to maximize the number of census tracts with single and double coverage, (each with their own weights) and to minimize the travel time for relocating. In order to tune the parameters in this objective function, an event based simulation model is developed to study the movement of vehicles and incidents (911 calls) through a city. The results show that the proposed model can effectively increase the system-wide coverage by EMS vehicles even if we assume that vehicles cannot respond to any incidents while traveling between stations. In addition, the results suggest that the proposed model outperforms one of the well-known real time repositioning models (Gendreau et al. (2001)). In the third problem, the objective is to minimize the total travel distance experienced by all EMS vehicles, while satisfying two types of time window constraints. One requires the EMS vehicle to arrive at the patients\u27 scene within a pre-specified time, the other requires the EMS vehicle to transport patients to their hospitals within a given time window. Similar to the first problem, each vehicle can transport maximum two patients. A mixed integer program (MIP) model is developed for the EMS dispatching problem. The problem is proved to be NP-hard, and a simulated annealing (SA) method is developed for its efficient solution. Additionally, to obtain lower bound, a column generation method is developed. Our numerical results show that the proposed SA provides high quality solutions whose objective is close to the obtained lower bound with much less CPU time. Thus, the SA method is suitable for implementation in a real-time decision support system

AGENT-BASED DISCRETE EVENT SIMULATION MODELING AND EVOLUTIONARY REAL-TIME DECISION MAKING FOR LARGE-SCALE SYSTEMS

Computer simulations are routines programmed to imitate detailed system operations. They are utilized to evaluate system performance and/or predict future behaviors under certain settings. In complex cases where system operations cannot be formulated explicitly by analytical models, simulations become the dominant mode of analysis as they can model systems without relying on unrealistic or limiting assumptions and represent actual systems more faithfully. Two main streams exist in current simulation research and practice: discrete event simulation and agent-based simulation. This dissertation facilitates the marriage of the two. By integrating the agent-based modeling concepts into the discrete event simulation framework, we can take advantage of and eliminate the disadvantages of both methods.Although simulation can represent complex systems realistically, it is a descriptive tool without the capability of making decisions. However, it can be complemented by incorporating optimization routines. The most challenging problem is that large-scale simulation models normally take a considerable amount of computer time to execute so that the number of solution evaluations needed by most optimization algorithms is not feasible within a reasonable time frame. This research develops a highly efficient evolutionary simulation-based decision making procedure which can be applied in real-time management situations. It basically divides the entire process time horizon into a series of small time intervals and operates simulation optimization algorithms for those small intervals separately and iteratively. This method improves computational tractability by decomposing long simulation runs; it also enhances system dynamics by incorporating changing information/data as the event unfolds. With respect to simulation optimization, this procedure solves efficient analytical models which can approximate the simulation and guide the search procedure to approach near optimality quickly.The methods of agent-based discrete event simulation modeling and evolutionary simulation-based decision making developed in this dissertation are implemented to solve a set of disaster response planning problems. This research also investigates a unique approach to validating low-probability, high-impact simulation systems based on a concrete example problem. The experimental results demonstrate the feasibility and effectiveness of our model compared to other existing systems

OPTIMIZATION MODEL AND SIMULATION FOR IMPROVING AMBULANCE SERVICE SYSTEM

Abstract This paper presents a brief survey of operations research works for ambulance service design, focusing on two mainstreams, i.e., facility location and simulation methods. Then we show some application examples of those methods using actual ambulance dispatch data