The post-disaster transportation of injured people when hospitals have districts
Authors: Babaqi Tareq , Vizvári Béla 
Published: January 2023

Purpose
The total capacity of ambulances in metropolitan cities is often less than the post-disaster demand, especially in the case of disasters such as earthquakes. However, because earthquakes are a rare occurrence in these cities, it is unreasonable to maintain the ambulance capacity at a higher level than usual. Therefore, the effective use of ambulances is critical in saving human lives during such disasters. Thus, this paper aims to provide a method for determining how to transport the maximum number of disaster victims to hospitals on time.

Design/methodology/approach
The transportation-related disaster management problem is complex and dynamic. The practical solution needs decomposition and a fast algorithm for determining the next mission of a vehicle. The suggested method is a synthesis of mathematical modeling, scheduling theory, heuristic methods and the Voronoi diagram of geometry. This study presents new elements for the treatment, including new mathematical theorems and algorithms. In the proposed method, each hospital is responsible for a region determined by the Voronoi diagram. The region may change if a hospital becomes full. The ambulance vehicles work for hospitals. For every patient, there is an estimated deadline by which the person must reach the hospital to survive. The second part of the concept is the way of scheduling the vehicles. The objective is to transport the maximum number of patients on time. In terms of scheduling theory, this is a problem whose objective function is to minimize the sum of the unit penalties.

Findings
The Voronoi diagram can be effectively used for decomposing the complex problem. The mathematical model of transportation to one hospital is the P‖ΣUj problem of scheduling theory. This study provides a new mathematical theorem to describe the structure of an algorithm that provides the optimal solution. This study introduces the notion of the partial oracle. This algorithmic tool helps to elaborate heuristic methods, which provide approximations to the precise method. The realization of the partial oracle with constructive elements and elements proves the nonexistence of any solution. This paper contains case studies of three hospitals in Tehran. The results are close to the best possible results that can be achieved. However, obtaining the optimal solution requires a long CPU time, even in the nondynamic case, because the problem P‖ΣUj is NP-complete.

Research limitations/implications
This research suggests good approximation because of the complexity of the problem. Researchers are encouraged to test the proposed propositions further. In addition, the problem in the dynamic environment needs more attention.

Practical implications
If a large-scale earthquake can be expected in a city, the city authorities should have a central control system of ambulances. This study presents a simple and efficient method for the post-disaster transport problem and decision-making. The security of the city can be improved by purchasing ambulances and using the proposed method to boost the effectiveness of post-disaster relief.

Social implications
The population will be safer and more secure if the recommended measures are realized. The measures are important for any city situated in a region where the outbreak of a major earthquake is possible at any moment.

Originality/value
This paper fulfills an identified need to study the operations related to the transport of seriously injured people using emergency vehicles in the post-disaster period in an efficient way.