# Optimizing Ambulance Allocation in Dynamic Urban Environments: A Historic Data-Driven Approach
## 2 Literature Review  
Optimizing ambulance relocation is crucial for effective emergency medical services (EMSs). As urban areas grow, so does the complexity of ensuring timely medical interventions. This literature review explores key methodologies in existing research aimed at improving EMS efficiency and response times. Ambulance deployment studies are broadly divided into the location set covering problem (LSCP) and the maximal covering location problem (MCLP). The LSCP is a model that calculates the minimum number of vehicles required to fully cover the demand area. The MCLP is a study of where to locate the maximum number of vehicles to cover the demand area with a fixed number of vehicles. From a firefighting force optimization perspective, the location set covering problem (LSCP) was first introduced in [2] and has since been extended to include the study of dynamic dispatch. The dynamic available coverage location (DACL), designed to respond efficiently to varying demand over time, was presented in [3]. Based on the double standard model (DSM), a mathematical model using the integer programming method was presented [4]. The presented model ensures that all regions can be supplied with emergency services within a certain time. A methodology incorporating real-time traffic information and social media data to predict traffic congestion and dynamically position ambulances was also introduced [5]. However, it should be noted that, in the LSCP, the number of vehicles is not fixed, which could pose economic feasibility issues. The first model of the MCLP was proposed in [6]. They did not consider the probability of an available ambulance when an emergency call came in. The maximum expected coverage location problem (MEXCLP) was proposed in [7]. They presented a mathematical model based on integer programming to reflect the probability of ambulance availability. Later, an extension of the model to a multi-period model was presented in [8]. They validated the effectiveness of the proposed model with real data from Amsterdam. There are studies that have evaluated the economics of static and dynamic models [9]. They verified that dynamic dispatching is efficient based on real data from Montreal. A study [10] examined minimizing paramedic travel distance while maximizing demand coverage. They derived the solution based on a two-phase integer programming method and evaluated the solution through a discrete-event simulator. Another study [11] discussed the problem with the objective of minimizing the queue time of emergency calls in a rescue center. They presented a methodology for dispatching and relocating ambulances to maximize demand coverage while reducing the queue time at emergency rescue centers. In the paper, they proposed an algorithm that integrates discrete-event simulation and mathematical models. They validated the effectiveness of the proposed algorithm on a real dataset from Montreal. Another study was presented that categorized and weighted the importance of emergency medical calls [12]. They presented a mathematical optimization model based on integer programming that considers the relocation of ambulances. They implemented a decision support system (DSS) and verified its effectiveness through practical applications. Recent studies on time-dependent MEXCLPs are similar to our study in that they reflect ambulance relocation based on patterns of demand. However, our study differs in that we focused our analysis on the zero zone, which is outside of the golden time. Looking at other studies related to optimizing ambulance operations, one study focused on the ambulance location problem, considering the rarity and randomness of road crashes [13]. They presented a methodology for determining the optimal location of ambulances using an edge maximal covering model and the Empirical Bayes method. Another study addressed ambulance deployment by simultaneously considering demand at one point in time and at the next point in time [14].