Innovative Applications of O.R.The effect of ambulance relocations on the performance of ambulance service providers
Introduction
In emergency situations, the location of ambulances has a huge impact on the response time to an incident, i.e., the total time between an incoming emergency call and the moment that an ambulance arrives at the emergency scene. The evaluation of ambulance services providers, judged by the authorities, heavily relies on their performance regarding these response times. For instance, in The Netherlands, the response time of an ambulance may not exceed 15 minutes in 95 percent of the highest priority emergency cases. To realize short response times, it is crucial to plan ambulance services well. This encompasses a variety of planning problems at the strategic, tactical, and operational level. At the strategic level, the locations of the ambulance base stations are determined. Then, at the tactical level, the number of ambulances and thus crews per base station is specified. At the operational level, real-time dispatching of ambulances to incidents and real-time relocation of ambulances is considered.
In this paper, we focus on the last part of the operational level: the relocation of ambulances. Ambulance vehicles are relocated in real-time, using dynamic and proactive relocation strategies, in order to achieve shorter response times to incidents. These relocation decisions are typically made when an event happens, e.g., when an ambulance is dispatched or when an ambulance is newly free after the service of a patient. However, whether relocations are allowed, and if so, to which locations, depend on regulatory rules. For instance, in Vienna, Austria, moving around ambulances unoccupied by a patient is not allowed, cf. Schmid (2012) as opposed to Edmonton, Canada, cf. Alanis, Ingolfsson, and Kolfal (2013). Moreover, the number of locations at which an ambulance is allowed to park up differs per country. This number can exceed the number of ambulances, as in Montreal, Canada, cf. Gendreau, Laporte, and Semet (2006). Many of these waiting sites are just street corners or different hot spots. In contrast, in The Netherlands, ambulances always must return to a base station, cf. Jagtenberg, Bhulai, and van der Mei (2015). This is a building with several facilities where the ambulance crew can spend its shift when idle. Another difference between countries is the average hospital transfer time. In North America this time can be very large, cf. Carter et al. (2015), as opposed to The Netherlands where the transfer time is usually short.
We consider the Dutch setting in this paper: short transfer times and the dispatcher is allowed to relocate ambulances unoccupied from base station to another one, but the number of locations on which an ambulance can idle, i.e., base stations, is rather small.
Ambulance relocations are not popular among ambulance crews, especially when the crew is idle at a base station and it is relocated to a different one. Instead, they prefer to spend their shift at a base station and not on the road. To keep the personnel motivated, the number of relocations they have to perform is not allowed to increase excessively. If the ambulance crews spend too much time on the road, the ambulance service provider probably will be condemned by an Occupational Safety and Health organization. Furthermore, costs for the ambulance service provider are associated with each relocation. Some ambulance service providers namely have the policy, especially at night, that the salary of the ambulance crew partly depends on their busy time in which their relocation time is included. Therefore, decision makers must make a consideration between the number of ambulance relocations and the effect of these relocations on the performance of the ambulance service provider.
As an alternative, one could also consider the relocation times. Especially if the above-mentioned payment structure is used, it can be cheaper to minimize these relocation times. However, in this paper, we treat the crew’s perspective as our major critical success factor, instead of the financial aspect related to relocations. The number of relocations is a good measure for the crew’s perspective, since crews in general prefer to perform one long relocation rather than several short ones. Of course, there is also a trade-off between number of relocations and relocation times. We will pay attention to this trade-off as well.
The relationship between performance and the number of ambulance relocations is complex. The consequences of moving an ambulance to a different base station are not known a priori, due to uncertainty that plays an important role in the process. It is usually not the case that ‘more’ is ‘better’, i.e., the more relocations are made, the better the performance of the ambulance service provider. But even if this was the case, there is still a trade-off: would one carry out extra ambulance relocations for only a small gain in performance? Opinions of different ambulance providers differ on this question and it is hard to set a standard concerning the execution of relocations. Therefore, useful insights about the relationship between performance and the number of ambulance relocations are desirable.
As stated before, the planning of ambulance services falls apart in three levels. Comprehensive studies of ambulance location and relocation models are done by Brotcorne, Laporte, and Semet (2003) and Li, Zhao, Zhu, and Wyatt (2011). In these papers several deterministic, probabilistic, and dynamic models and their solution procedures are reviewed. Another study on ambulance facility location problems is performed by Owen and Daskin (1998). The operational level falls apart in dispatching and relocation of ambulances. A dispatching algorithm based on the preparedness concept explained by Andersson and Värbrand (2007), is proposed by Lee (2011). Another dispatch method, based on the maximal covering location problem developed by Church and ReVelle (1974), is presented by Lim, Mamat, and Bräunl (2011) and it is shown by simulation that response times to urgent calls can be reduced.
A common way to solve the dynamic ambulance relocation problem is the offline approach: redeployment decisions are precomputed for different states of the system. For instance, compliance tables are computed, which prescribe desired locations for idle ambulances by Gendreau et al. (2006). With this purpose, the Maximal Expected Coverage Relocation Problem (MECRP) is proposed and solved, by formulating this problem as an integer linear program. It is stated by Maleki, Majlesinasab, and Sepehri (2014), that computing compliance tables is just the first part of the computation of relocation decisions. The second part involves the actual assignment of ambulances to base stations. Therefore, the Generalized Ambulance Assignment Problem (GAAP) and Generalized Ambulance Bottleneck Assignment Problem (GABAP) are proposed. Compliance tables are the subject of Alanis et al. (2013) as well: a two-dimensional Markov chain is proposed and analyzed to obtain optimal compliance tables. A two-stage stochastic optimization model for the ambulance redeployment problem that minimizes the number of relocations while maintaining an acceptable service level is presented by Naoum-Sawaya and Elhedhli (2013).
In addition to the offline approach, a large part of the ambulance literature focuses on the online computation of relocation decisions. Whenever an event occurs, e.g., an ambulance becomes available again, the dispatcher has the opportunity to control the system. Based on the information of the state of the system, one computes a relocation decision. Such a relocation decision needs to be obtained in a very short time, and thus is the main focus of this literature on heuristics. For instance, a heuristic called the Dynamic Maximum Expected Coverage Location Problem (DMEXCLP) is proposed by Jagtenberg et al. (2015). This problem, based on the MEXCLP presented by Daskin (1983), computes a new location for an ambulance that just finished service of a patient. Moreover, a parallel tabu search heuristic is used for the real-time redeployment of ambulances by Gendreau, Laporte, and Semet (2001). Andersson and Värbrand (2007) use the notion of preparedness. This preparedness is a measure for the ability to serve potential patients now and in the future. Moreover, a dynamic relocation model named DYNAROC and a heuristic to solve this model is presented. In addition, some papers use approximate dynamic programming for determining relocation strategies, for instance, Maxwell, Restrepo, Henderson, and Topaloglu (2010); Maxwell, Henderson, and Topaloglu (2013) and Schmid (2012). Relocation decisions are made at the time of call arrivals and when an ambulance becomes available again by Maxwell (2011). In this work, it is shown that making relocation decisions at such times is equivalent to the usage of a nested compliance table policy. At last, a comprehensive study on both online and offline redeployment is executed by Zhang (2012).
In this paper, we study the relationship between number of ambulance relocations and the performance of the ambulance service provider. Theretofore, we present an ambulance redeployment model, in which we are able to incorporate different performance criteria. We use a heuristic method that computes an action concerning the relocation of ambulances in such a way that the expected performance is maximized. This computation is done at decision moments: the time of occurrence of a new incident or the time of the idle report of an ambulance. We use a heuristic policy instead of the optimal one because computation of the optimal policy is very complex, if not impossible. Besides, even if it was possible to compute, the optimal policy is probably a complex one: it is not easy to understand and to execute by the dispatcher. Instead, we use a heuristic method that is not too far-fetched, while it is highly likely that this heuristic policy contains the same characteristics as the optimal one.
This paper differs from the mainstream literature in two respects
- 1.
Most of the papers in the literature, e.g., Jagtenberg et al. (2015), assume that the computed action is always carried out. However, it may be the case that the expected gain in performance by taking this action is very small and that this benefit does not outweigh the disadvantages regarding the number of additional ambulance relocations to achieve this gain. Therefore, we use the heuristic method to determine whether the redeployment action is really necessary, and we show results on several quantifications of ‘really necessary’.
- 2.
Another important difference between the mainstream literature and this paper is the way in which a redeployment action is carried out. We compute, using the heuristic method, a location that serves as origin, from which an ambulance needs to depart, and a base station serving as destination. However, it is not necessarily one particular ambulance that has to move from origin to destination, as assumed in most papers. Instead, we can use other idle ambulances, either driving or at a base station, in this relocation process in order to decrease the time required to attain the new ambulance configuration. However, this comes at the expense of extra relocations. We put restrictions on the number of other ambulances that may be relocated, and we show consequences on the resulting performance to obtain useful insights in the relationship between number of relocations and performance.
Section snippets
Model description
To investigate the above-mentioned relationship, we introduce the ambulance redeployment model described in this section. We consider the Dutch setting as explained in Section 1 and we model the region of interest as a directed graph. Geographical regions, e.g., neighborhoods, postal codes or streets, are represented by nodes. Moreover, arcs in this graph are weighted and the length of an arc represents the driving time (in seconds) between the nodes. These driving times are derived from a
Heuristic method
For the evaluation of the usefulness of ambulance motions and relocations, we present a heuristic that can easily handle several types of restrictions on the decisions of the dispatcher. First, we describe the heuristic method. Then, we will provide a more detailed explanation regarding the incorporation of these constraints.
The key idea of this method is as follows: at a decision moment, the dispatcher observes the current state of the system. Given this information, the dispatcher executes
Experimental setup
In this section, we show results for Flevoland, displayed in Fig. 3. Flevoland is a region in the Netherlands and covers approximately 2,500 km2. The number of inhabitants is nearly 400,000 of which 49 percent lives in the largest city: Almere. The remaining percentage of the population is mainly concentrated in one of the other five major towns, while only approximately 15,000 people live outside these six towns. All of these cities have exactly one base location at the dots in Fig. 3.
Summary and conclusion
In this paper, we analyzed the effect of ambulance relocations on the performance of the ambulance service provider. Theretofore, we described an ambulance redeployment model, in which a performance measure related to the response time can be chosen by the ambulance service provider by defining a corresponding penalty function. Moreover, we presented a heuristic for computing ambulance motions and relocations at decision moments. In this heuristic, we restricted the number of ambulance
Acknowledgements
This research was financed in part by Technology Foundation STW under contract 11986, which we gratefully acknowledge. We also would like to thank the ambulance service providers of the regions of Flevoland and Amsterdam for providing data, and the RIVM for providing the driving time tables.
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