A Chance Constrained Programming Model for Reliable Emergency Vehicles Relocation Problem

AbstractEmergency vehicles relocation is one mechanism of increasing preparedness for potential emergencies. This paper addresses the problem of designing reliable emergency vehicles relocation system. Under this respect, we extend the DYNACO model with chance-constrained programming framework for the optimal redeployment of emergency vehicles. The model deals with the availability of emergency vehicles by approximate hypercube. In addition, other random elements including travel time and emergency demand are taken into account in the model. Solution procedure based on genetic algorithm and Monte-Carlo simulation is developed to solve the stochastic model. Computational experiences are reported to illustrate the performance and the effectiveness of the proposed solution

Facility location problem for emergency and on-demand transportation systems

Although they have different objectives, emergency response systems and on-demand transportation systems are two similar systems in the sense that both deal with stochastic demand and service time which create congestions for moderate level of demand. Emergency response system location problems are one of the early problems immensely dealt in the literature. These problems are modeled by either set covering or transportation models which do not give much attention to the stochastic nature of the problem. On-demand transportation is a newly developing type of transportation system and literature is not broad enough but has similarities with emergency response systems. In this research, our aim is to solve facility location problem with stochastic demand and service time. Specifically we are dealing with temporal and spatial stochasticity which emerge because of the uncertainty in demand and service time. Recently we have developed a mixed aggregate hypercube model which are extensions to Larson (1974) and Boyacı and Geroliminis (2012). Results are promising and applicable to real life instances

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

Hypercube queueing models for emergency response systems

Spatial queueing systems (SQS) can be defined as a type of queue that mobile servers are assigned to travel to the customer and provide on-scene service or the customers travel to service facilities to have service. It has a lot of application areas in literature from emergency response to vehicle repair services, dial-a-ride to paratransit. In this research, our aim is to find a rapid approach to calculate performance measures of SQS. Our ultimate aim is to utilize this rapid approach as an instance solver inside some optimization algorithms such as simulated annealing (SA) and variable neighborhood search (VNS) to find better location for systems such as ambulances, fire brigades. For this purpose, we have developed two methods to calculate performance measures of an instance of SQS. To check accuracy and efficiency, the approach is compared with simulation results on some instances. Then the two methods are used with SA and VNS to improve server locations. Results show that the approach is promising and can be applied as a tool inside some optimization algorithms

Extended Hypercube Models for Large Scale Spatial Queueing Systems

Different than the conventional queueing systems, in spatial queues, servers travel to the customers and provide service on the scene. This property makes them applicable to emergency response (e.g. ambulances, police, fire brigades) and on-demand transportation systems (e.g. shuttle bus services, paratransit, taxis). The difference between the spatial queues and conventional queueing systems is various types of customers and servers and different service rates for different customer-server pairs. For the Markovian arrival and service characteristics, one of the methods to find system performance measures is to model and calculate steady state probability of the Markov chain for the hypercube queueing model. One of the obstacles on the way to apply hypercube queueing models to real life problems is the size of the problem; it grows exponentially with the number of servers and a linear system with exponential number of variables should be solved for each instance. In this research, in order to increase scalability of the problem, we propose two new models. In addition to that, we modeled the problem by using Monte Carlo simulation and tested the convergence and stability properties of the simulation results and compare them with stationary distributions. In the final part, a mixed integer linear programming formulation is given for optimal server configuration with different objectives improving different performance measures. As a future work, we are planning to use the optimal solutions of this formulation to evaluate different dispatching policies

Extended Hypercube Models for Location Problems with Stochastic Demand

In spatial queues, servers travel to the customers and provide service on the scene. This property makes them applicable to emergency response (e.g. ambulances, police) and on-demand transportation systems (e.g. paratransit, taxis) location problems. However, in spatial queues, there exist a different service rate for each customer-server pairs which creates Markovian models with enormous number of states and makes these approaches difficult to apply on even medium sized problems. Because of demand uncertainty, the nearest servers to a customer might not be available to intervene and this can significantly increase the service times. In this paper, we propose two new aggregate models and an approximate solution method with a dynamic programming heuristic. Results are compared with existing location models on hypothetical and real cases

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

Dispatching Fire Trucks under Stochastic Driving Times

In this paper we discuss optimal dispatching of fire trucks, based on a particular dispatching problem that arises at the Amsterdam Fire Department, where two fire trucks are send to the same incident location for a quick response. We formulate the dispatching problem as a Markov Decision Process, and numerically obtain the optimal dispatching decisions using policy iteration. We show that the fraction of late arrivals can be significantly reduced by deviating from current practice of dispatching the closest available trucks, with a relative improvement of on average about $20\%$, and over $50\%$ for certain instances. We also show that driving-time correlation has a non-negligible impact on decision making, and if ignored may lead to performance decrease of over $20\%$ in certain cases. As the optimal policy cannot be computed for problems of realistic size due to the computational complexity of the policy iteration algorithm, we propose a dispatching heuristic based on a queueing approximation for the state of the network. We show that the performance of this heuristic is close to the optimal policy, and requires significantly less computational effort.Comment: Submitted to Computers and Operations Research (December 08, 2018

Using genetic algorithms to optimise current and future health planning - the example of ambulance locations

<p>Abstract</p> <p>Background</p> <p>Ambulance response time is a crucial factor in patient survival. The number of emergency cases (EMS cases) requiring an ambulance is increasing due to changes in population demographics. This is decreasing ambulance response times to the emergency scene. This paper predicts EMS cases for 5-year intervals from 2020, to 2050 by correlating current EMS cases with demographic factors at the level of the census area and predicted population changes. It then applies a modified grouping genetic algorithm to compare current and future optimal locations and numbers of ambulances. Sets of potential locations were evaluated in terms of the (current and predicted) EMS case distances to those locations.</p> <p>Results</p> <p>Future EMS demands were predicted to increase by 2030 using the model (R²= 0.71). The optimal locations of ambulances based on future EMS cases were compared with current locations and with optimal locations modelled on current EMS case data. Optimising the location of ambulance stations locations reduced the average response times by 57 seconds. Current and predicted future EMS demand at modelled locations were calculated and compared.</p> <p>Conclusions</p> <p>The reallocation of ambulances to optimal locations improved response times and could contribute to higher survival rates from life-threatening medical events. Modelling EMS case 'demand' over census areas allows the data to be correlated to population characteristics and optimal 'supply' locations to be identified. Comparing current and future optimal scenarios allows more nuanced planning decisions to be made. This is a generic methodology that could be used to provide evidence in support of public health planning and decision making.</p