The Optimal Dynamic Distribution of Ambulance Stations for a Large Crowd Planned Event: Case Study in Al-Mshaer during Hajj

Abstract

The location of emergency medical services (EMS) is critical and significant for adequate service provision, particularly during large-scale events. For the optimal planning of EMS, the formulation of mathematical models where the relationship between the problem variables is appropriately incorporated helps optimize decisions. However most EMS literature examines the location and allocation of ambulance services in non-planned emergencies whether natural or man-made disasters, and there is little emphasis on handling the EMS needs for planned crowd events, such as religious gatherings, elections, entertainment, and sporting events. The scenario involving a large number of people gathering in a small area is not commonly considered when planning for EMS, as EMS planning is typically established based on regular non-extreme demand spread across the year. Therefore, in this study, EMS planning is examined for a large planned gathering, namely the Hajj. The focus is on the EMS planning needed during this religious event, held annually in Makkah, Saudi Arabia. In large gatherings, such as the Hajj, calamity can strike with little or no warning, leaving large amounts of devastation behind due to the condensed crowding of people in a relatively small area. In addition, during Hajj, people of different ages and ethnicity are present, and these are considerations that need to be accommodated when planning EMS in Makkah. This research aims to study and formulate accurate mathematical models to determine the EMS response for ambulance location and allocation in planning large-scale events. A threestage mathematical model is presented to design emergency response strategies based on the positioning of EMS resources to plan for the threats arising in large-scale gatherings. This new model takes into consideration variability in demand priority and limited resources. The objective of the developed model is to minimize the unmet demand based on different priority levels requiring different response time thresholds. In the first stage, the location and allocation of both ambulance stations and vehicles are determined. The aim is to reduce response times so that all demand from the demand zones is covered within the time threshold assigned to each priority level. In the second stage, a team assigning problem is formulated to assign the most suitable ambulance teams to the various regions across a large-scale event. The team assignment model aims to improve the effectiveness of ambulance teams by assigning the more highly skilled medical employees to the demand zones of critical medical need and also matching translators to the major languages spoken in the various demand zones. In the third stage, a hospital assignment problem is formulated to send patients in these highly crowded events to the closest suitable hospital. In order to solve the proposed model and to apply it to the case study, several approaches will be used. For our purposes, the physical locations to be determined are the actual point of demand and other EMS relevant areas. For this we use Google Maps to pinpoint the exact locations via their latitude and longitude coordinates. To import and process our data collected from a variety of government and non-government sources, we use Python in Google Colab. To cluster our data, we apply the k-means clustering algorithm together with the elbow technique. To compute the shortest distance between the demand, available hospitals and ambulance stations, we utilize the Haversine method. Finally, to find the optimal solutions from our proposed models on the case study data from Hajj 2017 and 2018, we formulate their objective functions together with their constraints in Google Colab.