Abstract
With emergencies being, unfortunately, part of our lives, it is crucial to efficiently plan and allocate emergency response facilities that deliver effective and timely relief to people most in need. Emergency Medical Services (EMS) allocation problems deal with locating EMS facilities among potential sites to provide efficient and effective services over a wide area with spatially distributed demands. It is often problematic due to the intrinsic complexity of these problems. This paper reviews covering models and optimization techniques for emergency response facility location and planning in the literature from the past few decades, while emphasizing recent developments. We introduce several typical covering models and their extensions ordered from simple to complex, including Location Set Covering Problem (LSCP), Maximal Covering Location Problem (MCLP), Double Standard Model (DSM), Maximum Expected Covering Location Problem (MEXCLP), and Maximum Availability Location Problem (MALP) models. In addition, recent developments on hypercube queuing models, dynamic allocation models, gradual covering models, and cooperative covering models are also presented in this paper. The corresponding optimization techniques to solve these models, including heuristic algorithms, simulation, and exact methods, are summarized.
4 Conclusion and discussion
With emergencies unfortunately being part of our lives, it is crucial to efficiently plan and allocate emergency response facilities to deliver effective and timely relief to people most in need. This paper reviewed covering models and optimization techniques for emergency response facility location and planning, from the perspective of mathematical models and operations research. The earlier studies of the covering models are represented by the Location Set Covering Problem (LSCP) and the Maximal Coverage Location Problem (MCLP). The LSCP is a mandatory covering model in which all the demand points are covered at least once, while the MCLP attempts to maximize coverage, given limited resources. Both the LSCP and MCLP have a common drawback in that once an EMS facility is dispatched to serve an emergency call, other demands in its coverage area are not covered by it any more. In this context, multiple coverage concept was introduced to handle excess demands in some locations, such as the recent Double standard Model (DSM) that was proposed to remedy this situation by allocating facilities among potential sites to provide full coverage within a longer distance standard, and to maximize coverage within a shorter distance standard. Another strand of research designed to overcome this drawback is to explicitly model the busy probabilities and reliabilities of facilities. The most frequently used probabilistic models are the Maximum Expected Covering Location Problem (MEXCLP) and the Maximum Availability Location Problem (MALP). Further research developed hypercube queuing models to relax the strong assumptions in previous probabilistic models and obtain a more accurate analysis of the system. Dynamic models were proposed to allocate facilities in real time and provide better coverage for demands. Recently, the commonly used “all or nothing” assumption about the coverage of demands is relaxed by gradual covering models that model the gradual decline of coverage along with the increase of distance by mathematical functions. In addition, the individual assumption that only the nearest facility determines whether a demand point is covered or not is relaxed by cooperative covering models.
