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Article

The Casualty Stabilization–Transportation Problem in a Large-Scale Disaster

1
Engineering Sciences Department, Universidad Andres Bello, Santiago 7500971, Chile
2
Transportation and Logistics Center, Universidad Andres Bello, Santiago 7500971, Chile
3
School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaiso 2362807, Chile
*
Author to whom correspondence should be addressed.
Sustainability 2022, 14(2), 621; https://doi.org/10.3390/su14020621
Received: 24 November 2021 / Revised: 30 December 2021 / Accepted: 31 December 2021 / Published: 6 January 2022
(This article belongs to the Special Issue Risk Assessment and Sustainable Disaster Management)

Abstract

:
We address the problem of picking up, stabilizing, and transporting casualties in response to mass-injury disasters. Our proposed methodology establishes the itinerary for collecting, on-site stabilization, and transporting victims considering capacitated vehicles and medical care centers. Unlike previous works, we minimize the time required to achieve on-site stabilization of each victim according to his age and level of severity of the injuries for their subsequent transfer to specialized medical centers. Thus, more critical patients will be the first to be stabilized, maximizing their chances of survival. In our methodology, the victims’ age, the injuries’ severity level, and their deterioration over time are considered critical factors in prioritizing care for each victim. We tested our approach using simulated earthquake scenarios in the city of Iquique, Chile, with multiple injuries. The results show that explicitly considering the on-site stabilization of the vital functions of the prioritized victims as an objective, before their transfer to a specialized medical center, allows treating and stabilizing patients earlier than with traditional objectives.

1. Introduction

Between 1998 and 2017, geophysical and climate-related disasters caused direct economic losses valued at USD 2908 billion, with 4.4 billion injured, displaced, or in need of emergency assistance, and 1.3 million people killed [1]. Some of the events that caused the significant casualties were earthquakes and tsunamis, which have sudden and large-scale onsets, and can cause severe damage in large geographical areas with mass deaths and injuries. Faced with these events, one of the main concerns of those responsible for disaster response management is to reduce deaths and suffering caused by a lack of timely medical attention and treatment [2]. Moreover, it is a well-known fact that the survival probability of casualties is related to the response time of rescue teams, the medical services they provide to the injured [3,4], and their rapid transfer to medical centers. However, the available time and resources for these tasks are limited.
The literature contains several approaches to address this problem. Often, the focus is on methodologies to reduce response times in collecting and transferring the injured to specialized medical care centers, establishing a sequence of care through some rule of prioritizing the injured. Most approaches address this response time as an objective or restriction by minimizing the total sum of response times or setting maximum thresholds or time windows to care for casualties. Nevertheless, for a group of patients that need medical attention and whose injuries present different severity levels, minimizing total pickup and transport times to specialized centers may not be particularly suitable.
This traditional approach allows the wounded with less severe injuries to be cared for before more serious ones. The main goal is that the injured collected are admitted to a medical center as soon as possible, regardless of how they were collected and stabilized. Furthermore, when two or more victims are in the same place and are picked up by one or more vehicles, medical personnel first stabilize the most critical patients and then transport them to a medical facility. Traditional methodologies do not consider this situation. By stabilization, we mean providing casualties with medical and first-aid care to keep them alive by using adequate medical equipment and staff, stabilizing their vital functions for subsequent transport to a specialized medical center. We include in our methodology the on-site stabilization time according to the range of age (as an indicator of vulnerability) and patients’ level of severity of the injuries (LSI) during collection to correct these issues, thus maximizing the probability of survival. On the other hand, the LSI sustained is often used to prioritize the order in which medical care is provided, which may or may not include survival probabilities concerning time. However, as stated in [5], traditional methodologies do not consider quantitative metrics linking response time and human survival in large-scale disasters.
So, we address the problem of collecting and transporting casualties after a large-scale disaster, specifying the order they should be collected, stabilized, and the medical center that they should be transported to minimize the time needed for stabilization and transport for each casualty. To prioritize medical assistance, we consider the age range and the casualties’ severity level and their deterioration over time through non-decreasing functions that depend on each patient’s waiting time. Moreover, we incorporate the required time for on-site stabilization according to the characteristics of each victim. Our methodology proposes establishing a Casualty Pickup, on-site Stabilization, and Transport Schedule (CPST Schedule) with a heterogeneous fleet of emergency vehicles, considering capacitated vehicles and medical centers, minimizing the time required to achieve on-site stabilization and transport casualties. We solve the problem through a heuristic procedure based on an optimization model that allows updating the CPST program and the priority assigned to each victim according to changes in demand and/or availability of emergency vehicles over time.
Considering explicitly the time needed for on-site stabilization of casualties, plus the care prioritization based on the injury’s severity sustained, age range, and the casualty’s deterioration over time is new in the specialized literature of operations research that focuses on the pickup and transport of casualties after a large-scale disaster. The rest of the article is organized as follows: Section 2 reviews the literature. Section 3 describes the problem to be addressed, while Section 4 details the proposed methodology, which is tested in Section 5 on a simulated earthquake scenario in the city of Iquique, Chile. Finally, Section 6 presents the study conclusions.

2. Literature Review

Disaster management has been a widely discussed issue in the operational research literature. Vast reviews of these contributions can be found in [6,7,8,9,10,11,12] and more recently in [5,13,14]. These studies show that, in the phase of response to disasters, the main problems investigated are the transportation and distribution of supplies [15,16,17,18], inventory management [19,20,21,22], route recovery [15,23], evacuation of the population [24], and casualty transport. The casualty transportation problem has been addressed by several authors, who may or may not have included the transport of supplies together with casualties, and may or may not have considered the deterioration of patients’ health over time.
By considering the transportation of casualties and the distribution of aid supplies, [25] present a model for assigning and distributing injured people in helicopters, minimizing the costs of assigning pilots, the number of used helicopters, and the duration of routes. The authors in [26] break down the problem into two stages: creating vehicle routes and transporting multiple products and casualties, minimizing the weighted sum of unsatisfied demand, both in terms of supplies and unattended casualties. The authors in [24] present a two-stage model that minimizes unsatisfied demand, adding the option of having temporary medical centers and split delivery operations. The authors in [27] present a model that minimizes unsatisfied demand for supplies delivering, pickup, and transport casualties, regardless of their severity. The author in [17] proposes a hierarchical model that coordinates the helicopters transporting supplies and medical assistance. Subsequently, [28] uses a network model with a hierarchical cluster and routing approach to coordinate vehicle routes distributing supplies and evacuation activities. The authors in [29] minimize the number of unattended casualties, unsatisfied demand, and the number of dispatched vehicles through stochastic modeling. The authors in [30] develop a dynamic dispatch and routing model in disaster situations, minimizing the total waiting time of casualties and the transport time of supplies.
Transporting casualties separately from aid distribution in the face of extreme events was first considered by [31]. The authors propose a dynamic allocation model, which minimizes the total number of casualties. The authors in [32] design a model for casualty dispatch and routing in disasters, maximizing the number of attended casualties with minimum service times. The authors in [33] present an assignment model for disaster rescue situations, maximizing the number of survivors. The authors in [34] propose two models. The first minimizes the total travel and waiting time of casualties heading to existing medical centers. In contrast, the second activates the implementation of field hospitals depending on the number of unattended casualties. The authors in [35] propose an ambulance routing model that minimizes the time needed for casualties to reach the hospital. The authors in [36] present a mixed-integer programming model for ambulance distribution, casualty assignment to hospitals, and their care sequence, minimizing the overall time when casualties receive treatment. The authors in [37] address the transport of casualties to hospitals after a disaster in highly populated areas, thus maximizing their survival rate.
The deterioration of casualties’ health status over time and care prioritization is addressed in Medical Emergency Literature through the mass-casualty triage issue (a review can be found in [38,39]). In Operations Research literature, this topic has been treated rarely. The authors in [40,41] consider that each patient has a random life whose probability distribution depends on the type of patient. If patients fail to receive medical care before their lifetime, they die; otherwise, they survive. The authors in [42] propose a multi-objective route selection method that considers equity and casualty prioritization by using time limits representing the in-transit tolerable suffering duration according to the degree of severity of the casualty’s injuries. The authors in [43] develop policies for casualty transportation by assigning ambulances to patients and medical centers, considering survival rates and care times for different types of injuries. The authors in [44] propose a model for evacuating casualties to hospitals that maximizes the expected number of survivors in response to a mass casualty incident, considering available resources, the severity of casualties, and their deterioration over time, using survival probabilities. The authors in [45] address the issue of on-site casualty prioritization for transport to a hospital. They formulate a model that considers the availability of resources and the deterioration of patients over time according to a decreasing probability function of survival. The authors in [46] maximize the expected number of survivors and minimize the operating cost of ambulances and helicopters. The equitable distribution of medical resources is considered in conjunction with the severity of the injuries and the casualty’s health deterioration using survival probabilities.
Like [44,45,46], we also consider the severity of the victims and their deterioration over time, in collecting and transferring casualties to medical centers. However, we incorporate the on-site casualties’ stabilization time where they are collected, with the transport time, as the objective to be minimized to maximize the survival of the patients.

3. The Casualty Pickup and Transport Problem: Description

After a large-scale disaster with mass casualties, the authorities’ response begins by gathering information on the availability of the health network, including emergency vehicles and the capacity of health care centers. A single operation center coordinates them, called the medical aid coordination center (MACC). All logistics associated with casualty transport and care are coordinated and controlled by the MACC. The MACC, with the information available, requires allocating the resources available for the timely care of victims through a Casualty Pickup, Stabilization, and Transport Schedule (CPST Schedule). Our objective is to help with this target.
We consider a fleet of airborne (helicopter) and land-based (ambulance) emergency vehicles for casualty pickup and transport procedures. The CPST schedule must be determined for each vehicle by identifying the trip itinerary they must follow until all victims have been assisted. Each trip begins and ends at an MCC. For each trip, the start and end MCC, the patients to collect, the waiting assignment time, stabilization time, and the arrival time to the MCC for each patient are identified. The demand for casualty transport from any node of the network, expressed as the number of casualties according to the LSI requiring transport to a specialized MCC, can be satisfied with different emergency vehicles on multiple visits. At nodes with several casualties, total or partial pickup is also possible. The following explains how to prioritize victims and count attention, waiting, and stabilization times.

3.1. Casualty Prioritization

Medical assistance to casualties is generally provided first by the nearby population, the area’s police, and firefighters [47], who request the victims to be transported to an MCC and provide the necessary information to establish the patient’s LSI. Numerous works analyze and determine ways to classify casualties according to their LSI (see [44,48]). There are several important reasons to consider each patient’s LSI and the MCC’s ability to treat such injuries. First, a lack of information can cause many patients to be sent to the nearest MCC, which is not necessarily specialized to deal with the casualty’s injuries, generating congestion in the facility, long waiting times, and the redistribution of patients across the health network. Second, the probability of survival decreases over time and depends on each casualty’s type of injury and physical condition (see [3,49,50,51]). Thus, casualties with a higher LSI should be the first to be stabilized and transported to an MCC to maximize their survival chances. Third, the time required for casualty stabilization on-site depends on each injury’s casualty type and age [52]. Fourth, the emergency vehicle arrival with appropriate medical equipment and personnel at the incident scene allows the LSI to be confirmed. The casualty is stabilized for their subsequent transport to a specialized MCC. Thus, although the arrival time at the medical center is the same for all patients transported in the same emergency vehicle, the waiting time and the moment at which each patient is stabilized will be different according to their LSI.
Let λ k a g be a transport priority index of casualty k of age a and severity g when requesting assistance. λ k a g can be formulated, for each casualty k the age a, as follows:
λ k a g = { l L / g l } [ P G a l + f a l ( α k π l a g ) ] θ k a g l ( 1 θ k a g ( l + 1 ) )
where P G a g is a factor of the severity of the injuries, f k a g ( · ) is a function of deterioration of the injuries of the victim k of age a, which depends on the initial LSI g and the waiting time αk from when he requests medical assistance until he is assigned to the itinerary of an emergency vehicle. π l a g the time when a casualty’s LSI of severity g and age a change to a higher LSI lL, with L as the set of severity levels (for g = l, π l a g = 0 ∀a). We use the binary parameter θ k a g l to relate αk to the time required to increase in severity from g to l for a victim k of age a. Thus θ k a g l = 1 if α k π l a g , and 0 if not, g , l L / g l a A . If   l > | L | ,   then   θ k a g l = 0 .
λ k a g considers the increase in LSI by PGag ( P G a l < P G a s   l < s / l , s L ) and the deterioration function of the victim’s injuries. Therefore, casualties with greater LSI will have higher P G a g than those with a lower LSI. Between two victims with the same LSIs, priority is given to the one with the most significant deterioration of their injuries based on waiting time. Our methodology allows the use of different forms for f k a g ( · ) .

3.2. Total Medical Attention, Waiting, and Stabilization Times for Casualties

Figure 1 represents the total time of medical attention provided to casualty k (TTAk), at the beginning when casualty k appears in the system (TAk), with k representing any person in the zone. Then, the MACC is prompted to transport casualty k to an MCC, and the time the casualty checks into the assigned MCC (TLk). The TTAk is composed of the wait time αk as described above, and the pickup, stabilization, and transport time of casualty k (βk). That is, βk represents the time it takes for the emergency vehicle, from the moment it is allocated to casualty k (TFk), to arrive at the location (TBk), finish the stabilization (TSk), and the time to move them to an MCC (Dk). Since the planning horizon of the vehicle’s CPST Schedule can have several scheduled trips before visiting casualty k, βk will be the sum of the vehicle’s previous trips, plus the time of the trip to pick up casualty k. The time until casualty stabilization k (Ck) is achieved, is defined as the time from when the emergency vehicle is assigned (TFk), until casualty k (TSk) is stabilized. When two or more casualties are in the same node, and are picked up by the same vehicle, medical staff stabilizes one patient at a time according to each casualty’s LSI and age. The time needed to stabilize casualty k of age range a and severity g is determined as follows:
T S k a g = g a G R k g A k a T P a g
where T P a g is the casualty’s stabilization time of age range a and severity g, G R k g is equal to 1 if casualty k has a severity of g and 0, if otherwise, and A k a is equal to 1 if casualty k is in the a age range or 0, if otherwise.

4. Proposed Methodology

4.1. Method Description

We propose a 5-stage methodology that allows solving the problem of casualty collection, on-site stabilization, and transportation in the face of disasters with mass casualties. For an accurate method description, we will establish some preliminary definitions.
Let there be a directed transport network G’(N’,A’), where A’ is the network’s set of arcs and N’ is the set of nodes. Additionally, let H be the set of nodes where the MCCs are located, and Cb be the set of nodes that can be accessed by helicopters. Between each pair of nodes iN’, hH and cCb, we calculate S i j e which represents the minimum expected travel time by vehicle type eE (ambulance and helicopter) through a minimum route problem. Figure 2 shows the procedure through an example. Figure 2a shows a directed transport network G’(N’,A’). We consider the calculation of the arcs of the network G(N,A) to access node 9. In the case of ambulances (Figure 2b), the routes are determined considering the trip by land over the transport network. For the case of helicopters (Figure 2c), the route is determined considering the air travel from node hH to the node cCb closest to node iN’ (from h1 to c1 in Figure 2c), plus the expected travel time on foot between node cCb and node iN’ by the medical team (from c1 to node 9 in Figure 2c). As a result, we obtain an auxiliary graph G(N,A), with N = HCbN’ and A the set of arcs representing the routes of minimum expected travel time. Therefore, for each pair of nodes i, jN and type of vehicle eE, there is an arc (i,j)eA (Figure 2d,e in the example).
Now a short description of the method. The first stage is the initialization of the data set and the construction of the auxiliary graph. In the second stage, the casualties are characterized (location, age, and severity of the injuries), and care priority is established. In the third stage, we work with the auxiliary network. Specifically, we reduce the graph by eliminating all those arcs that begin or end in nodes of N’ that do not contain casualties, considerably reducing the complexity of the problem to be solved in the next stage. In the fourth stage, we solve the Casualty Pickup, on-site Stabilization, and Transport optimization model (CPST Model). Finally, the system is evaluated, and the stopping criterion is established.

4.2. Resolution Procedure

The definition of the method parameters is provided in the next subsection for more clarity.
Stage one: Initialization and construction of the auxiliary network
Plot auxiliary graph G(N,A).
Initially, the set of casualties U p who need to be transported to an MCC is empty and the pickup, on-site stabilization and transport time of casualty β k is a very large (infinite) number, U p = 0 = { } y β k =   k U p = 0 .
TT0 = Current time.
Stage two: New period start, classifying and prioritizing casualties
p = p + 1,
T T p = Start time of period pP.
U A u x = U p
  • Identification of casualties transported to an MCC and in the process of being transported during the previous period:
    • Set of casualties transported to an MCC in period p − 1: U = { k U p 1 / β k T T p }
    • Casualties who are in the process of being transported in period p − 1: U + = { k U p 1 / β k > T T p }
  • Updating the set U p :
    U p = U A u x U +
    For each casualty k U p proceed as follows:
    • Identify PAk and G R k g . PA = {PAk /k U p }.
    • Determine the wait-allocation time of each casualty k at the beginning of period pP as follows: α k = T T p T A k
    • Calculate λ k a g with Equation (1)
    • Sort casualties in ascending order according to their transport priority index λ k a g .
Stage three: Update and reduction in the modeling network
(a)
Identification of the origin node of the vehicle mM, Om.
  • Identify the last trip performed by vehicle mMm) as follows: σ m = M a x v V { v / ( T T p 1 + T m v T T p ) }
    If u m ( σ m + 1 ) = 0 , then, otherwise O m = { h H / z h m ( σ m + 1 ) = 1 } where TTp is the time at which the planning period pP begins and Tmv the time needed by vehicle mM to complete trip vV.
(b)
Update the values of K h g the maximum capacity of patients with g-type LSI ∈L that can be attended by MCC hH. Proceed as follows:
  • K h g p = K h g ( p 1 ) k U p 1 [ m M / u m ( σ m + 1 ) = 0 v = 1 σ m y k h m v G R k g + m M / u m ( σ m + 1 ) > 0 v = 1 σ m + 1 y k h m v G R k g ]
  • K h g = K h g p
    where K h g p is the available capacity in MCC hH to attend casualties of severity gL at the beginning of the period pP, and y k h m v is equal to 1 if vehicle mM transports the casualty k to medical center h on trip v, and 0 otherwise.
(c)
Perform N = HPA, build a new auxiliary network G(N,A) and update values S i j e .
(d)
Update TDme (time required by e-type ∈ E vehicle mM to start operations) for vehicles in use.
  • eE1/ δ m e = 1 proceed as follows:
    If u m ( σ m + 1 ) = 0 , then: T D m e = T m σ m T T p
    If not, T D m e = T m ( σ m + 1 ) T T p
  • eE2/ δ m e = 1 proceed as follows:
    If u m ( σ m + 1 ) = 0 , then: T D m e = T m σ m T T p + T D S e
    If not, T D m e = T m ( σ m + 1 ) T T p + T D S e
    where E1 is the set of land-based vehicles (ambulances), E2 is the set of airborne vehicles (helicopters), and δme is equal to 1 if vehicle mM is of type eE, and 0 otherwise.
(e)
Availability of emergency vehicles m.
Ωmp = 1 if vehicle mM is available at the beginning of period pP, and 0 if otherwise. Thus, M = mmp = 1.
Stage four: CPST Model
Solve Casualty Pickup, on-site Stabilization and Transport Model (4)–(29), CPST Model. In general, the input elements are the MCC and vehicle capabilities, operating times, and preference factors depending on the severity of the victim. In addition, the output elements are associated with decisions in the vehicles, which casualty is served by conveyance, and the time required for on-site rehabilitation.
The detailed mathematical model is presented in the next subsection.
Stage five: System Evaluation
If new casualties are identified, return to stage 2. In the event of any alteration in the system’s response capacity, such as the incorporation or removal of emergency vehicles, or the appearance of new casualties, return to stage 2. Otherwise, keep the CPST Schedule obtained in stage 4.

4.3. Casualty Pickup, On-Site Stabilization, and Transport (CPST) Mathematical Model

This subsection describes the sets, parameters, and decision variables used in the 5-step resolution procedure and the mathematical formulation for the Casualty Pickup, on-site Stabilization, and Transport Model (CPST Model).
Sets:
N’: Set of nodes of the direct transport network G’(N’,A’).
H: Set of medical centers.
Cb: Set of nodes where helicopters may land.
N: Set of nodes in the auxiliary network G(N,A). Where N = HCbN’
L: Set of severity categories for casualties.
P: Set por periods.
U p : Set of casualties who need to be transported to an MCC at the beginning of the execution period pP.
M: Set of available emergency vehicles (airborne and land-based). The set M represents the number of available vehicles, regardless of the type of vehicle. This set is updated in each iteration of the method (see stage 3, Section 4.2).
V: Set of trips itineraries.
E: Set of vehicle types ( E = E 1 E 2 ).
E1: Set of land-based vehicles (ambulances)
E2: Set of airborne vehicles (helicopters)
D: Set of age range.
Parameters:
K h g p : The available capacity in MCC hH to attend casualties of severity gL at the beginning of the period pP.
PAk: Node ∈ N’ where casualty k U p is located.
G R k g : 1 if casualty k U p has an LSI gL, and 0 otherwise.
λ k a g : Transport priority index of casualty k U p with gL severity.
Dk: Transport time of victim k from the moment he is stabilized until he enters the MCC.
Om: Origin node (location) of the vehicle m. mM. (See Section 4.2, stage 3).
K h g : Maximum capacity of patients with g-type LSI ∈L that can be attended by MCC hH.
TTp: Time at which the planning period pP begins. Every casualty appears after TT0 = 0.
TDme: Time required by e-type ∈ E vehicle mM to start operations.
TDSe: Time required for the take-off of e-type vehicle eE.
δme: 1 if vehicle mM is of type eE, and 0 otherwise.
S i j e : Expected travel time between node iN and node jN in e-type vehicle eE.
q e: Capacity of e-type vehicle eE.
TATe: Time required for the landing of e-type vehicle eE.
ε: Parameter that represents the level of preference given in relation to stabilization time.
B2: Maximum capacity among all vehicles. B 2 = max e E { q e }
lk: Node lCb closest to the location of casualty k when picked up by helicopter.
t l k : Expected travel time on foot of the paramedics from the pickup node lk to the location PAk of casualty k.
η i j e : General expression to represent the operation and travel time of an e-type vehicle, incorporating elements such as take-off and landing time in the case of aerial vehicles. Thus, it is total operation time between node i and node j in an e-type vehicle, and it can be expressed as:
η i j e = T D S e + S i j e + T A T e
Decision Variables:
y k h m v = { 1 If   vehicle   m M   transports   casualty   k U p   to   medical   center   h H   on   trip   v V 0 e . o . c z h m v = { 1 If   the   vehicle   m M   completes   the   trip   v V   at   the   medical   center   h H 0 e . o . c u m v = { 1 If   vehicle   m M   does   the   trip   v V 0 e . o . c
Tmv:: Time needed by vehicle mM to complete trip vV.
βk: Pickup, on-site stabilization and transport time of casualty k U p .
x i j m v = { 1 If   vehicle   m   on   trip   v   travels   from   node   i   to   node   j 0 e . o . c w k m v = { 1 If   casualty   k U p   is   attended   by   vehicle   m M   on   trip   v V 0 e . o . c
Ck: Time needed for the on-site stabilization of casualty k U p .
Next, the mathematical formulation for the CPST model is exposed:
Objective Function:
a D g L k N λ k a g C k
This function minimizes the time required to stabilize victims on site considering their LSI and wait time. The transport priority index λ k a g is given by the expression (1). Note that β k = C k + D k , where Dk is the transport time of victim k from the moment he is stabilized until he enters the MCC (see Figure 1).
Constraints:
The following group of constraints establishes that every casualty must be attended by only one vehicle on a single trip (5), and in (6), it is prevented that emergency vehicles exceed their capacity.
v V m M w k m v = 1 k U p
k U p w k m v e E q e δ m e m M , v V
Restrictions (7)–(10) establish the sequence of casualty pickups, starting and ending each trip itinerary in an MCC hH, except for the first trip, which begins at the start node OmmM (constraint (8)). The equations in (9) represent flow conservation constraints. The restrictions in (11) prevent a trip from returning to an already visited node, while (12) avoid trips between MCCs. In constraint (7), the parameter VMAX limits the trips to be evaluated and considerer the vehicle autonomy in terms of operation time.
z h m v = i N x h i m ( v + 1 ) m M , h H , v V : v < V M A X
j N x O m j m 1 = 1 m M
i N / i r v V x i r m v j N / j r v V x r j m v = 0 r N , m M , v V
h H z h m v = 1 m M , v V
x i i m v = 0 i N , m M , v V
x i j m v = 0 i , j H , m M , v V / i j
Restrictions (13) and (14) define the sequence of the trip’s itineraries and the assignment of casualties to vehicles on each trip, while (15) ensures that if there are no victims, the vehicle does not make the trip.
u m v u m ( v + 1 ) m M , v V \ v < V M A X
u m v w k m v j U p , m M , v V
u m v k U p w k m v m M , v V
Restrictions (16) and (17) can be used to determine the time required for a vehicle to complete each trip. Constraints (16) are used for the first trip (v = 1). The first term registers the time to start the operations by each vehicle type since the trip’s origin. The second term includes the time used to travel between nodes. The third term of the equation considers the on-site stabilization time required for a casualty of a determined age and severity and the time needed for each vehicle type to get where the casualty is. Finally, the fourth term counts the time to arrive at the MCC. While the constraints (17) are for the next trips, so the first term on the right side includes the previous time needed for each vehicle type to complete each trip. The rest of the terms are like the constraints (16), not including the time to start the operations by each vehicle type.
T m 1 = j N e E ( T D m e + T A T e ) δ m e x O m j m 1 + i N j N e E S i j e δ m e x i j m 1 + k U p ( g L a A T S k a g + e E 2 δ m e t l k ) w k m 1 + + e E ( T D S e + T A T e ) δ m e [ i N j N \ l i l j , l C b x i j m 1 + j N h H x j h m 1 ] m M
T m v = T m ( v 1 ) + i N j N e E S i j e δ m e x i j m v + k U p ( g L a A T S k a g + e E 2 δ m e t l k ) w k m v + + e E ( T D S e + T A T e ) δ m e [ i N j N \ l i l j , l C b x i j m v + j N h H ( x h j m v + x j h m v ) ] m M , v V / v 1
The restrictions in (18) determine each casualty’s pickup, stabilization, and transport times until their admittance into the assigned MCC.
β k T m v B ( 1 w k m v ) k U p , m M , v V
The restrictions in (19) establish the capacity limits of the MCCs. The restrictions in (20) force a vehicle that has picked up a casualty to take it to a medical center, while (21) states that a vehicle can transport the casualties to a medical center only if it ends its journey in the aid center.
k U p m M v V y k h m v G R k g K h g g L , h H
i N x i P A k m v = h H y k h m v k U p , m M , v V
k U p y k h m v B 2 z h m v h H , m M , v V
Constraints (22) and (23) establish the relationship between the decision variables.
w k m v = i N x i P A k m v k U p , m M , v V
i N x i h m v = z h m v h H , m M , v V
The restrictions in (24)–(27) allow determining the stabilization time of the casualties considering the different situations that can appear (several casualties in the same node, casualties in different nodes, vehicles with capacities to attend several victims, and the number of the trip). Constraint (24) is used to calculate the time needed for a vehicle to attend the first casualty in the first trip (v = 1). The first term in (24) considers the time to start operations; the second terms register the stabilization time needed, including the time needed by the paramedics to get the casualties when they arrived by helicopter. The last two terms are used to bound or not the time according to the use of the vehicles attending the casualties and traveling between nodes. Constraint (25) considers cases where two or more casualties are simultaneously in the same node and are attended by the same vehicle. Similarly, is consider the on-site stabilization time of each victim, the time used by the paramedics to arrive where the casualties are, and a term (the last one) to bound the time if the vehicle is used. The restrictions in (26) consider the case of a vehicle aiding two casualties located in different nodes on the same trip using a helicopter due to its capacity (ambulances only can take one casualty). In contrast, (27) calculates the stabilization time of the first casualty of a trip when the trip is not the first in the casualty pickup plan.
C k e E ( T D m e + η O m P A k e ) δ m e + ( g L a A T S k a g + e E 2 δ m e t l k ) B ( 1 w k m 1 ) B ( 1 x O m j m 1 ) k U p , h H , m M
C k C d + e E 2 δ m e ( t l d + t l k ) + g L a A T S k a g + B ( v V x P A d P A k m v 1 ) d , k U p , m M / P A d = P A k
C k C d + e E 2 δ m e ( t l d + t l k ) + e E δ m e ( η P A d P A k e ) + e E 2 / l d l k , l C b δ m e ( T D S e + T A T e ) + g L a A T S k a g + B ( v V x P A d P A k m v 1 ) d , k U p / P A d P A k , m M
C k T m ( v 1 ) + e E δ m e ( T D S e + T A T e + η i j e ) + g L a A T S k a g + e E 2 δ m e t l k B ( 1 w k m v ) B ( 1 z h m ( v 1 ) ) k U p , h H , m M , v V \ v 1
Restrictions (28) and (29) show the nature of the decision variables.
x i j m v , y k h m v , z h m v , w k m v , u m v { 0 , 1 } i , j N , k U p , h H , v V , m M
C k , T m v , β k 0 m M , v V , k U p

5. Methodology Implementation

5.1. Numerical Example

To test the performance of our methodology, we generated a small numerical example with three MCCs and five casualties (identified by V1 to V5). V1 and V5 are in the same node, as are V3 and V4. The performance of both an ambulance (with a capacity for one patient) and a helicopter with three patients is evaluated. Additionally, the impact of considering different LSI and age ranges is tested by minimizing both the time required to stabilize the victims (Ck) and the total time of each trip βk. MCC 1 is the only one that can treat victims with LSI 3. Helicopters start their operations from a heliport. Table 1 shows the ambulance and helicopter travel times between medical care centers (MCCs) and casualties, and Table 2 shows the time required to stabilize casualties of different age ranges and severity, T S k a g .
Table 3 shows the results after the implementation of the methodology considering four scenarios: (a) casualties with equal LSI, (b) casualties with equal LSI and different age ranges, (c) casualties with different LSI and the same age range, and (d) casualties with different LSI and different age ranges. For better exposure, Figure 3 shows the results for the scenarios (a) and (c).
Scenario (a) Casualties with equal LSI (Table 3a and Figure 3): By using only an ambulance, the same solution is obtained by minimizing each objective function (Ck and βk). The closest casualties are treated first (V3 and V4), then V2, and finally V1 and V5, requiring an itinerary of five trips (one trip for each patient). When only the helicopter is used, by minimizing Ck, three patients are collected and stabilized in the first trip (V3, V4, and V1), and in a second trip, the other victims are stabilized and transported (V2 and V5). However, when the objective is to minimize patients’ arrival time at the MCC, βk, each casualty is transported independently (five different trips). This situation is since the transfer times are significantly shorter than the stabilization times (ca. 7 min vs. 62.14 min), so it is more convenient for the model to perform more trips so as not to increase the time of arrival at the MCC of the casualties to the detriment of postponing their stabilization.
Scenario (b) Casualties with the same LSI and different age ranges (Table 3b): We modified the age range for casualties V2, V3, and V5, which modifies the time needed to stabilize the victims and the priority index for transporting. The same results are obtained for ambulance use by minimizing Ck and βk. The order of visits prioritizes the care of victims with lower age ranges who require longer stabilization times. In the case of helicopters, by minimizing Ck, the first trip’s collection and stabilization sequence consider victims of higher priority λ k a g   (V2 and V3) and V4, which is in the same node as V3. By minimizing βk, again, we opt for five trips (one for each patient), favoring the rapid arrival at the MCC and not the casualty’s stabilization (TSk).
Scenario (c) Casualties with different LSI and the same age range: We now consider that victims V2 and V3 have LSI2 and V5 LSI1 (Table 3c and Figure 3). Note that this again alters the priority index λ k a g . As in previous cases, the same results are obtained when using an ambulance by minimizing Ck or βk. In both cases, the most severe victims are prioritized. Considering the use of a helicopter, by minimizing the casualties’ stabilization time, Ck, in the first round, the two casualties with the highest LSI (V1 and V3) are treated together with the V4 victim in the same node as V3. By minimizing βk, again, it is chosen to make five trips, minimizing the time at which the casualties arrive at the MCC, but not the moment of stabilization. This reduces the probability of survival of the casualties.
Scenario (d) Casualties with different LSI and different age ranges: Casualties of low age (age range 1) and greater severity should be prioritized. From Table 3d, it is observed that, when using an ambulance, the three most severe and vulnerable victims are always prioritized according to their age, attending first to V4 with LSI2 and age range 1, then V1 with LSI3, and then V2 with LSI2 and age range 1. This effect is also observed when using a helicopter. In this case, minimizing Ck effectively the V4, V1, and V2 casualties who are treated in the first trip, thus prioritizing their stabilization. As before, minimizing βk prioritizes the rapid arrival of patients to the MCCs and not their stabilization, postponing the stabilization of all victims.

5.2. Case Study: Iquique, Chile

The proposed methodology was implemented in AMPL and tested in Iquique, Chile, with CPLEX 12.9.0.0, using a PC with an Intel Core i-7, 3.4 GHz processor with 6 Gb of RAM. This city is located at the center of the seismic gap that causes large-scale seismic events in northern Chile. The subduction zone along the coast of northern Chile has been broken twice; mega-earthquakes with a magnitude of the seismic moment (Mw) of ~8.8 in 1877 [53], Mw 8.2 in 2014. However, experts agree that this last earthquake is not the last to be expected and that an even bigger one can still take place in northern Chile and southern Peru [54]. Given these antecedents, the Research Center for Integrated Disaster Risk Management (CIGIDEN) in Chile has established a set of seismic scenarios for the north of the country, with magnitudes ranging from Mw 8.42 to Mw 8.95 [55]. To implement our methodology, we used the scenario for an earthquake with Mw 8.95, an epicenter 102 km southwest of Iquique, in the morning rush hour (7:30–8:30 a.m.), on a working day. This scenario produces the highest casualties from all simulated scenarios [55].

5.3. Iquique Population, Health Network, and Other Modeling Parameters

Figure 4a shows the geographical distribution of the Iquique population. The city has 163,281 inhabitants, distributed across 1652 population units (PU) used to group the population. Each PU is represented as a point on the map where the population is aggregated. Table 4 shows the population of Iquique by age range. We considered the strategic road network, medical care centers, and feasible helicopter landing areas that can be seen in Figure 4b. The transport network is made up of 464 nodes and 1141 arcs. Each arc of the network features information about its length and operating speed under normal conditions at different times of day [56]. Seventy-two feasible landing areas were identified for helicopters inside the city, mainly sports facilities in educational and municipal establishments.
We considered three LSI sustained by casualties, corresponding to those used in [57]. The health network has six available MCCs, eight ambulances, and three helicopters with a capacity of one patient each [57]. Table 5 shows the capacity of each MCC by LSI, represented by the number of available beds. LSI1 corresponds to minor injuries that do not require hospitalization but do require transportation to an MCC; LSI2 shows injuries that require a greater degree of medical care than LSI1; LSI3 includes injuries that may be life-threatening unless appropriately treated. A casualty may only have one LSI at a time, which may worsen in time unless medical attention is provided. Without loss of generality, casualties who died immediately after the event are not considered in the CPSTS. However, they could easily be incorporated as a type 4 LSI. Table 6 determines the average stabilization time of the casualties according to their age range and LSI, which was based on a thorough review of the specialized literature, which summarizes the times needed to stabilize patients with different types of injuries according to their age range (see [52,58,59,60,61,62,63,64,65,66,67,68,69]).
The travel times of ambulances after an earthquake were determined considering that the operating speed of each arc in the network is only 30% of its speed under normal conditions at the time of the event [70,71]. Operating speeds gradually return to normal soon after.
We considered an average travel speed of 4 km/h [71] to estimate the expected time of travel by land (tli) of paramedics from the collection node li closest to i until the location node of the casualty i. Finally, TD m1 = 1 min, TD m2 = 5 min, and TDS1 = TAT1 = 0.75 min is assumed. For the estimation of λ j g , we considered the expression (1) as an exponential deterioration function of the type f k a g ( α k ) = κ a g e ϖ a g + φ a g α k , with κag, ϖag and φag parameters to be calibrated according to LSI, with gL and aD. π1–2 = 2880, π2–3 = 360 min, TDS1 = TAT1 = 0.75 min.

5.4. Requirements for Pickup, Stabilization, and Transport of Casualties in a Mw 8.95 Scenario

Table 6 and Figure 1c show the estimated number and location of casualties according to their LSI for the simulated earthquake scenario of Mw 8.95, whose epicenter is 102 km southwest of Iquique, at 07:30 a.m. on a business day [55]. A total of 606 casualties were estimated, of which 492 have LSI1, 103 LSI2, and 11 LSI3. Without loss of generality, and to better present the results, we assumed that 80% of casualties with LSI1 go to MCCs either by their own means, or with the help of relatives and neighbors, and are treated in emergency rooms without making use of the bed capacity shown in Table 5. The remaining 20% require specialized transportation (98 people), either due to difficulty moving or lack of means. All casualties with LSI2 (103 people) and LSI3 (11 people) require specialized transportation by ambulance or helicopter. Thus, a total of 212 people will require pickup, stabilization, and transport services to an MCC during an emergency.

5.5. Methodology Implementation

Not all casualties appeared immediately after the earthquake. Although the methodology can be applied every time a new casualty appears, or there is a change in the supply of the health network, to present the results, we have simulated the appearance of casualties and the calculation of the CPST program by executing our algorithm in seven different moments after the earthquake, updating the number and status of the casualties and the CPST program with the itineraries of each vehicle. Table 7 shows the evaluated scenarios. The first two columns of the table show the identification number and the start time of the methodology according to the simulation. Columns three to six show the total number of casualties and casualties by the LSI that requires medical attention at the beginning of each period. The number of medical care centers, ambulances, and helicopters that we assume are available at the beginning of each period is shown in columns seven to nine (identified with the initials MCC, A, and H followed by a consecutive number, respectively). The decreased percentage in the road network’s operating speed for each period is shown in column ten.

5.6. Casualty Pickup, Stabilization, and Transport Schedule (CPST Schedule)

We consider that the earthquake starts at exactly 7:30 a.m. After a few minutes, the MACC begins receiving requests for medical assistance. At 7:41 a.m. our methodology is executed, obtaining the results of Table A1 in Appendix A and Figure 5. Note that, according to Table 7, when executing our methodology, there are 64 injured and the availability of 3 MCC, 4 ambulances, and 2 helicopters. We have arranged Table A1 according to the resulting itinerary for each vehicle and sequence of care for the injured. The first column shows the vehicle identification code (four ambulances and two helicopters). Columns two to five show the identification code, the location node (li), the age range, and the LSI of each of the 64 reported casualties. Column six shows the time necessary to stabilize each victim according to their age and LSI (see Table 5), while column seven shows the transport priority index according to equation (1). Column eight shows which trip (v) of the vehicle’s itinerary cares for the casualty. Columns nine to twelve show the time the patient is assigned to a collection schedule (TFk), the time of arrival of the vehicle at the patient’s location (TBk), the time at which the patient was stabilized (TSk), and time at which the patient is checked into the medical care center (TLk). The MCC allocated to the casualty can be seen in the last column.
On the other hand, Figure 5 graphically shows the CPST program for each vehicle. Towards the right, each rectangle represents a casualty, and the length is the time from when the vehicle begins its journey towards the victim until the latter is entered into the MCC. The red color represents the most severe casualties (LSI3), and the blue represents the least severe casualties (LSI1). Thus, we can see that our methodology prioritizes casualties with higher LSI in their injuries, first serving LSI3 victims, then LSI2, ending with LSI1 casualties.
To illustrate the results, consider the itinerary of the A1 ambulance from Table A1 and Figure 5. The first trip began at 7:41 a.m., arriving at casualty V1 (less than 14 years old, LSI 3) at 09:15:18. The casualty needed 93.3 min to stabilize (see Table 2), achieving stabilization of her vital signs at 09:42:46. The patient V1 was admitted into MCC1 at 10:10:14, thereby completing the first trip in 89 min. The second trip of the A1 itinerary begins from MCC1, arriving at patient V17 at 10:40:08, achieving stabilization at 11:02:45. Finally, patient V14 is admitted to MCC2 at 11:20:58. A1′s itinerary includes seven more trips, attending casualties V21, V26, V45, V50, V54, V64, and V62. If there are no modifications to the system, this ambulance is expected to complete its operations at 17:43:12, that is, 10 h and 2 min after initiating its activities. The other available rescue vehicles (ambulances A2, A3, and A4; helicopters H1 and H2) follow the itinerary as laid out in Table 6 until all the casualties entered the system have been taken care of. Thus, the pickup, stabilization, and transport operations for the 64 patients reported at the beginning of period 1 (07:41 a.m.) will conclude when the last patient (V63) transported by the helicopter H1 is admitted into MCC1.
If two or more casualties with different LSI are in the same place, our methodology favors stabilizing those with more severe injuries. In turn, between two casualties of the same LSI but of different ages, our methodology favors the stabilization of those most vulnerable according to their age. This is the case of casualties located in node ID 36020 of Table 8. Casualties V2 and V4, both with LSI3, are prioritized over the other casualties in the itinerary of ambulance A3 and helicopter H1, respectively. The aid sequence for the rest of the casualties follows this same logic, continuing with LSI2 casualties and ending with LSI1. Moreover, when two casualties have the same LSI, priority is given to the person that has been waiting for the longest.
After obtaining the first CPST program (7:41 a.m.) and while rescue operations are scheduled, new casualties appear in the system, and new rescue vehicles and MCCs are incorporated. All these changes modify the conditions in which the initial CPST schedule was established for each vehicle (period 1), so it is necessary to redefine them in consideration of the LSI of the new victims and the deterioration of those casualties who have not yet been taken care of. Table A2 and Figure 6 show the results after the methodology execution according to Table 7.
At the start of period 2 (09:26), all vehicles in operation were carrying out casualty stabilization and transport activities. Our methodology takes this into account and, for each vehicle, reschedules activities from the first trip that ends after 9:26 a.m. This is represented from the start time of each period in Figure 6. From then on, the new schedule begins. To better illustrate this, consider the operations of helicopter H1, shown in Figure 5 and Figure 6. Under the itinerary developed in period 1 (Table A1 and Figure 5), H1 began operations by aiding casualties V3 with LSI3, and then sequentially a set of casualties with LSI2 and LSI1, where the first casualties LSI2 were V10, V15, V13, and V16. The reprogramming of H1′s routes occurs as it transports casualties V10 with LSI2 (see period 2 from Figure 6). Once this route has finished, their activities are prioritized to aid the new casualty V66, who has an LSI3, delaying the care of V15 with LSI2, who is assigned to ambulance A1. The prioritization of critical patients to the detriment of those less serious is clearly observed in our methodology. Consider casualty V33, who, according to the schedule for period 1 (Table A1), should be stabilized at 14:07:16 by ambulance A3 personnel on their fifth trip. However, given the appearance of more serious casualties, the care and transport of casualty V33 is postponed until period 6, at 18:52:38 (Table A2), by ambulance A5, accumulating a wait of almost 5 h.
In many real situations, such long waiting times for low-severity casualties encourage transport via alternative forms of transportation, such as transport by neighbors or relatives at their own expense. However, we chose not to include these phenomena, which are easy to consider showing the effects on waiting times and possible changes in the casualty LSI using the proposed methodology. Thus, prioritizing casualties of greater severity to the detriment of those with lower LSI, or with longer wait-allocation time when they have an equal LSI, may cause a deterioration in the injuries of waiting casualties, which is also considered in our methodology.

6. Conclusions

We propose a new approach to the problem of collecting and transporting casualties in response to mass-casualty incidents. Our methodology allows the creation of a schedule that minimizes pickup time, on-site stabilization, and casualty transport while considering the availability of emergency vehicles and the capacity of the medical care centers. We consider the LSI and how it deteriorates as time is spent waiting and include on-site stabilization time by age range and severity of the casualties as one of the significant variables to determine priority.
Our methodology allows creating a Casualty Pickup, Stabilization, and Transport Schedule (CPST Schedule) for each vehicle. All casualties are included in one of the routes in the collection schedule. The start and end MCC, the casualties to be collected, the sequence of visits, the waiting time, the stabilization and transport of the casualties, and their arrival at an MCC are all defined for each trip. Our procedure has five stages based on a mixed-integer programming model, which may be executed whenever a change in the health system’s offer or demand for casualty transport. We tested the methodology in a numerical example and in a real simulated earthquake scenario in the city of Iquique, Chile, to verify its effectiveness.
The findings show that our methodology prioritizes casualties with higher LSI in their sustained injuries. If two or more casualties with different LSI are in the same place, our methodology guarantees that those with greater severity are stabilized first. Moreover, when two casualties have the same LSI, the one waiting for the longest is given priority.
When new victims appear in the system, or new MCCs or vehicles are incorporated into rescue activities, the conditions in which the initial CPST schedule of each vehicle was established, making it necessary to reset them by considering the LSI of the new casualties, the waiting time to be assigned to the itinerary of a vehicle and deterioration times of the casualties that have not yet been aided. Our methodology also considered this by determining the corresponding priority for each casualty. The results show that the new CPST schedule prioritized casualties with greater severity and waiting times. The injuries of some casualties also worsened while waiting for treatment.
Our methodology can significantly contribute to decision makers, allowing them to allocate resources when collecting and transporting casualties better, maximizing survival by prioritizing and stabilizing the most severe cases. For example, when faced with an event with several injuries, our methodology will make it possible to generate itineraries for all available emergency vehicles in such a way as to minimize the time for stabilization of vital functions and subsequent transfer of each victim. The decision maker may recalculate as many times as he wishes such itineraries according to the appearance of new victims or changes in the capacity of the MCCs or the number of available vehicles.
This study can be extended in several ways. Our methodology could benefit from updating the capacity of medical care centers by incorporating discharged casualties. Moreover, letting field hospitals assist casualties when there is no more capacity in the health network could be an interesting improvement to consider. Our methodology can easily include this type of situation where there is an increase in the medical care capacity for casualties. Another interesting aspect to consider is the existence of many national and international actors who must coordinate and cooperate to achieve an adequate response to disasters. Our methodology can be modified to include different modes of operation in emergencies where different actors must collaborate to coordinate through a single command center.

Author Contributions

Conceptualization, A.B.; methodology, A.B. and S.R.; software, D.B.G.; resources, A.B. and G.P.-B.; writing—original draft preparation, A.B., D.B.G. and S.R.; writing—review and editing, P.P.A. and G.P.-B.; visualization, D.B.G.; supervision, A.B.; funding acquisition, A.B. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by FONDECYT grant no. 11170549 and the Research Center for Integrated Disaster Risk Management (CIGIDEN), ANID/FONDAP/15110017. The APC was funded by Universidad Andres Bello.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Acknowledgments

We gratefully acknowledge the support by FONDECYT grant no. 11170549 and the Research Center for Integrated Disaster Risk Management (CIGIDEN), ANID/FONDAP/15110017. Paredes-Belmar gratefully thanks the support of FONDECYT grant no. 1210183.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A. Methodology implementation. Casualty Pickup, Stabilization, and Transport Schedule

Table A1. Casualty Pickup, Stabilization and Transport Schedule (CPST Schedule). Period 1, start 07:41 a.m.
Table A1. Casualty Pickup, Stabilization and Transport Schedule (CPST Schedule). Period 1, start 07:41 a.m.
Vehicle ID CodeCasualty ID CodeNode ID (li)Age RangeLSI T S k a g   ( min ) λ k a g Trip (v)TFkTBkTSkTLkMCC Assigned
A1V1440300–14393.35.10517:41:008:09:289:42:4610:10:14MCC1
V173602015–59229.90.89527:41:0010:32:5111:02:4511:20:58MCC2
V21380800–142420.89537:41:0011:38:3712:20:3712:38:16MCC2
V26410500–142420.89547:41:0012:56:1813:38:1814:09:47MCC3
V454302015–59115.040.37257:41:0014:38:5514:53:5715:08:53MCC2
V503704015–59115.040.37267:41:0015:16:2615:31:2815:39:00MCC2
V54101900–14114.980.37277:41:0015:53:5616:08:5516:23:50MCC2
V641120015–59115.040.37287:41:0016:27:3016:42:3216:46:11MCC2
V62290800–14114.980.37297:41:0017:02:2817:17:2717:43:12MCC1
A2V54203015–59362.145.10517:41:008:06:059:08:139:32:17MCC1
V113806015–59229.90.89527:41:009:57:1210:27:0610:52:00MCC1
V253602015–59229.90.89537:41:0011:15:1811:45:1212:08:30MCC1
V304403015–59229.90.89547:41:0012:32:3113:02:2513:26:26MCC1
V343906015–59115.040.37257:41:0013:51:1414:06:1614:23:11MCC2
V42420500–14114.980.37267:41:0014:25:5314:40:5214:43:34MCC2
V464205015–59115.040.37277:41:0014:58:3015:13:3215:42:41MCC3
V603704015–59115.040.37287:41:0016:16:3616:31:3817:05:33MCC3
A3V236020≥603655.10517:41:008:04:189:09:189:31:36MCC1
V1443030≥60227.60.89527:41:009:53:1710:20:5310:42:34MCC1
V183602015–59229.90.89537:41:0011:07:2811:37:2212:02:17MCC1
V294403015–59229.90.89547:41:0012:11:0212:40:5612:53:28MCC3
V3339060≥6019.30.37257:41:0013:25:4313:35:0114:07:16MCC3
V444402015–59115.040.37267:41:0014:39:3914:54:4115:15:10MCC2
V514203015–59115.040.37277:41:0015:34:3115:49:3316:08:54MCC2
V594205015–59115.040.37287:41:0016:27:1916:42:2117:00:45MCC2
A4V94206015–59229.90.89517:41:008:12:058:41:599:00:12MCC2
V8420100–142420.89527:41:009:18:2410:00:2410:23:02MCC1
V205908815–59229.90.89537:41:0010:44:4311:14:3711:36:18MCC1
V244103015–59229.90.89547:41:0012:02:4612:32:4012:54:42MCC2
V3241010≥60227.60.89557:41:0013:12:2113:39:5713:57:36MCC2
V373704015–59115.040.37267:41:0014:23:4214:38:4415:09:15MCC1
V494205015–59115.040.37277:41:0015:18:5115:33:5315:43:29MCC1
V564205015–59115.040.37287:41:0016:14:0016:29:0216:59:33MCC1
H1V33906015–59362.145.10517:41:007:50:028:52:108:57:51MCC1
V104205015–59229.90.89527:41:009:04:349:34:289:40:33MCC2
V153603015–59229.90.89537:41:009:45:1010:15:0411:10:36MCC2
V1340300–142420.89537:41:0010:21:2411:03:2411:10:36MCC2
V164103015–59229.90.89547:41:0011:15:1311:45:0711:50:51MCC3
V234102015–59229.90.89557:41:0011:56:5112:26:4512:31:38MCC2
V283602015–59229.90.89567:41:0012:36:4013:06:3413:11:35MCC2
V313603015–59229.90.89577:41:0013:16:2813:46:2213:51:15MCC2
V383602015–59115.040.37287:41:0013:58:2714:13:2914:43:07MCC2
V393602015–59115.040.37287:41:0014:20:5414:35:5614:43:07MCC2
V43590610–14114.980.37297:41:0014:50:1915:05:1815:12:29MCC2
V47430300–14114.980.372107:41:0015:17:2415:32:2315:37:18MCC2
V5542050≥6019.30.372117:41:0015:42:1215:51:3016:22:23MCC2
V524003015–59115.040.372117:41:0016:00:1016:15:1216:22:23MCC2
V574205015–59115.040.372127:41:0016:29:3516:44:3716:52:27MCC1
V613704015–59115.040.372137:41:0016:58:3217:13:3417:20:09MCC3
H2V43602015–59362.145.10517:41:007:50:028:52:108:57:51MCC1
V64206015–59229.90.89527:41:009:02:189:32:1210:20:48MCC3
V7410400–142420.89527:41:009:33:5610:15:5610:20:48MCC3
V124201015–59229.90.89537:41:0010:26:2010:56:1411:01:46MCC3
V193603015–59229.90.89547:41:0011:08:0311:37:5711:44:15MCC3
V22410400–142420.89557:41:0011:53:0012:35:0012:43:21MCC1
V274105015–59229.90.89567:41:0012:51:1113:21:0513:28:55MCC1
V353708015–59115.040.37277:41:0013:35:0013:50:0213:56:07MCC1
V36370700–14114.980.37287:41:0014:00:3414:15:3314:44:29MCC2
V404106015–59115.040.37287:41:0014:22:1514:37:1714:44:29MCC2
V414203015–59115.040.37297:41:0014:51:5115:06:5315:15:17MCC3
V484205015–59115.040.372107:41:0015:24:0315:39:0515:47:52MCC3
V531007015–59115.040.372117:41:0015:53:5416:08:5616:14:32MCC1
V584205015–59115.040.372127:41:0016:19:4816:34:5016:40:06MCC1
V632806015–59115.040.372137:41:0016:45:3517:00:3717:06:06MCC1
Table A2. Casualty Pickup, Stabilization, and Transport Schedule (CPST Schedule), after execution of 7 periods.
Table A2. Casualty Pickup, Stabilization, and Transport Schedule (CPST Schedule), after execution of 7 periods.
PeriodVehicle ID CodeCasualty ID CodeNode ID (li)Age RangeLSI T S k a g   ( min ) λ k a g Trip (v)αkTFkTBkTSkTLkMCC ASSIGNED
1A1V1440300–14393.305.10107:418:099:4210:10MCC1
A2V23602060+365.005.10107:418:049:099:31MCC1
A3V54203015–59362.145.10107:418:069:089:32MCC1
H1V33906015–59362.145.10107:417:508:528:57MCC1
H2V43602015–59362.145.10107:417:508:528:57MCC1
A4V94206015–59229.900.90107:418:128:419:00MCC2
A4V8420100–14242.000.90207:419:1810:0010:18MCC2
H1V104205015–59229.900.90207:419:049:349:40MCC2
H2V64206015–59229.900.90207:419:029:3210:19MCC2
H2V7410400–14242.000.90207:419:3310:1510:19MCC2
2H1V664005015–59362.145.10309:269:4410:4610:51MCC1
A5V654005015–59362.145.10109:269:4110:4411:05MCC1
A2V113806015–59229.901.3521057:419:5610:2610:30MCC5
A3V1443030≥ 60227.601,3521057:419:5310:2110:31MCC4
H2V124201015–59229.901.3531057:4110:2310:5310:56MCC5
A2V173602015–59229.901.3531057:4110:3111:0111:03MCC5
A3V205908815–59229.901.3531057:4110:4111:1111:17MCC5
A1V153603015–59229.901.3521057:4110:4011:1011:20MCC5
H1V164103015–59229.901.3541057:4110:5711:2611:30MCC5
H2V193603015–59229.901.3541057:4111:0011:3011:34MCC5
A4V1340300–14242.001.3531057:4110:4411:2611:37MCC5
A2V244103015–59229.901.3541057:4111:0811:3811:43MCC5
A3V253602015–59229.901.3541057:4111:1911:4911:51MCC5
A5V183602015–59229.901.3521057:4111:3012:0012:04MCC5
A1V21380800–14242.001.3531057:4111:2212:0412:06MCC5
A4V304403015–59229.901.3541057:4111:3912:0912:12MCC5
H2V274105015–59229.901.3551057:4111:4012:1012:16MCC5
H1V22410400–14242.001.3551057:4111:3612:1812:25MCC5
A2V26410500–14242.001.3551057:4111:4612:2812:30MCC5
3A6V1094501015–59362.145.101011:4611:5212:5413:11MCC1
H3V283602015–59229.902.6812457:4111:5512:2412:28MCC5
A3V313603015–59229.902.6852457:4111:5512:2512:29MCC5
A7V294403015–59229.902.6812457:4111:5712:2712:31MCC6
A1V3241010≥60227.602.6842457:4112:0712:3412:35MCC5
A5V234102015–59229.902.6832457:4112:0812:3812:42MCC5
A4V673602015–59229.901.5951409:2612:1812:4812:54MCC5
H1V69405015–59229.901.5961409:2612:2812:5813:02MCC4
H2V68360200–14242.001.5961409:2612:2113:0313:10MCC4
A2V722806015–59229.901.5961409:2612:3413:0413:16MCC4
H3V70405015–59229.901.5921409:2612:3713:0713:17MCC4
A3V71420500–14242.001.5961409:2612:3213:1413:22MCC4
A1V735904915–59229.901.5951409:2612:4213:1213:25MCC4
A7V754206015–59229.901.5921409:2612:5113:2113:34MCC4
A5V745904815–59229.901.5941409:2612:5413:2313:40MCC4
H1V764104015–59229.901.5971409:2613:0913:3913:46MCC4
H2V774104015–59229.901.5971409:2613:1413:4413:48MCC4
A4V79360100–14242.001.5961409:2612:5713:3913:49MCC4
A6V814105015–59229.901.5921409:2613:1613:4613:51MCC6
H3V803601015–59229.901.5931409:2613:2313:5313:58MCC4
A1V832410015–59229.901.5961409:2613:3314:0314:10MCC4
A3V821803015–59229.901.5971409:2613:3214:0214:11MCC4
A2V78410400–14242.001.5971409:2613:2414:0614:13MCC4
4H1V151420500–14393.305.108013:2613:4915:2215:28MCC1
A7V150360200–14393.305.103013:2613:4115:1415:31MCC1
A5V852308015–59229.902.6152409:2613:4714:1714:25MCC4
A6V864004015–59229.902.6132409:2613:5414:2414:28MCC6
H2V842404015–59229.902.6182409:2613:5314:2314:28MCC4
A4V875904715–59229.902.6172409:2613:5614:2614:37MCC2
H3V883602015–59229.902.6142409:2614:0314:3314:39MCC2
A2V1114206015–59229.901.32810011:4614:2414:5415:04MCC4
A1V1104203015–59229.901.32710011:4614:2014:5015:05MCC2
H2V1174205015–59229.901.32910011:4614:3215:0215:07MCC2
A5V11341030≥60227.601.32610011:4614:3315:0015:11MCC2
A3V112420600–14242.001.32810011:4614:2015:0215:15MCC2
A4V1154205015–59229.901.32810011:4614:4815:1815:28MCC2
H3V116420500–14242.001.32510011:4614:4415:2615:30MCC2
A6V1144103015–59229.901.32410011:4614:4715:1715:33MCC2
H2V1184202015–59229.901.321010011:4615:1215:4215:47MCC2
A2V1214402015–59229.901.32910011:4615:1215:4215:53MCC2
A1V1194202015–59229.901.32810011:4615:1815:4816:01MCC2
A3V1204103015–59229.901.32910011:4615:2615:5616:06MCC2
H1V1243602015–59229.901.32910011:4615:3616:0516:13MCC1
H3V1273601015–59229.901.32610011:4615:3716:0716:15MCC1
A5V122440200–14242.001.32710011:4615:2516:0716:21MCC2
A6V1264201015–59229.901.32510011:4615:4216:1216:21MCC2
A4V1254201015–59229.901.32910011:4615:4116:1116:25MCC2
A7V1233602015–59229.901.32410011:4615:4516:1516:30MCC1
5H2V1814107015–59362.145.1011015:3615:5116:5417:00MCC1
A2V1524205015–59229.901.511013013:2616:0116:3116:41MCC1
A1V1533603015–59229.901.51913013:2616:1116:4116:52MCC1
H1V1553602015–59229.901.511013013:2616:1816:4816:54MCC1
H3V1604205015–59229.901.51713013:2616:2016:5016:56MCC1
A3V154370500–14242.001.511013013:2616:1416:5617:06MCC1
A6V1572804015–59229.901.51613013:2616:2916:5917:09MCC1
A4V15642050≥60227.601.511013013:2616:3217:0017:12MCC1
A5V158420500–14242.001.51813013:2616:2917:1117:21MCC1
A7V1594004015–59229.901.51513013:2616:4317:1317:26MCC1
A2V1654201015–59229.901.511113013:2616:5217:2117:32MCC1
H1V1624205015–59229.901.511113013:2617:0017:3017:36MCC1
H3V1644205015–59229.901.51813013:2617:0217:3217:38MCC1
H2V1614205015–59229.901.511213013:2617:0517:3517:41MCC1
A1V163370500–14242.001.511013013:2617:0217:4417:55MCC1
A3V1664201015–59229.901.511113013:2617:1617:4617:56MCC1
A6V1834205015–59229.900.907015:3617:2217:5218:05MCC1
A4V1844206015–59229.900.9011015:3617:2417:5418:07MCC1
A5V1824203015–59229.900.909015:3617:3318:0218:14MCC1
H3V1893601015–59229.900.909015:3617:4318:1318:18MCC1
H1V1873601015–59229.900.9012015:3617:4318:1318:20MCC1
A2V1884105015–59229.900.9012015:3617:4318:1318:24MCC1
A7V185420300–14242.000.906015:3617:3718:1918:31MCC1
H2V190410700–14242.000.9013015:3617:4718:2918:34MCC1
A1V1863602015–59229.900.9011015:3618:0818:3818:51MCC1
A6V1924205015–59229.900.909015:3618:1618:4618:58MCC1
A3V191420300–14242.000.9013015:3618:0918:5119:03MCC1
A4V353708015–59115.040.50124757:4118:1718:3218:33MCC5
A5V343906015–59115.040.50104757:4118:2518:4018:41MCC5
6H3V1934206015–59229.901.741116015:3618:2318:5318:58MCC6
H1V2004201015–59229.900.9014018:1618:2518:5519:00MCC6
A2V1984206015–59229.900.9015018:1618:3419:0319:13MCC1
A4V1994206015–59229.900.9014018:1618:3419:0319:14MCC6
A7V2023708015–59229.900.909018:1618:4019:1019:20MCC6
H2V201360100–14242.000.9016018:1618:3919:2119:26MCC6
A5V2031602015–59229.900.9014018:1618:5319:2319:33MCC6
H3V2044205015–59229.900.9014018:1619:0619:3619:44MCC6
A5V3339060≥6019.300.55116357:4118:4218:5118:52MCC5
A1V42420500–14114.980.55136357:4118:5619:1119:12MCC2
H1V36370700–14114.980.55166357:4119:0519:2019:23MCC5
A6V393602015–59115.040.55116357:4119:1119:2619:30MCC5
A1V454302015–59115.040.55156357:4119:1819:3319:36MCC5
A3V373704015–59115.040.55156357:4119:1719:3219:36MCC5
A4V444402015–59115.040.55166357:4119:2519:4019:42MCC5
A2V383602015–59115.040.55176357:4119:2619:4119:45MCC5
A7V47430300–14114.980.55116357:4119:3019:4519:47MCC5
A6V414203015–59115.040.55136357:4119:3219:4719:49MCC5
H1V404106015–59115.040.55186357:4119:2919:4419:50MCC5
A5V494205015–59115.040.55166357:4119:3619:5119:53MCC3
H2V43590610–14114.980.55186357:4119:3419:4919:55MCC5
7A3V21141030≥60227.600.901209:3618:2018:4718:58MCC6
A1V2104103015–59229.900.901209:3618:1918:4919:00MCC6
A4V2124103015–59229.900.901309:3618:2618:5619:06MCC6
A8V503704015–59115.040.5817157:4118:1818:3318:35MCC1
H3V5542050≥6019.300.58107157:4118:2918:3918:43MCC5
A2V464205015–59115.040.58137157:4118:2718:4218:44MCC5
A7V514203015–59115.040.5877157:4118:2918:4418:46MCC5
A6V524003015–59115.040.5887157:4118:3218:4718:51MCC5
H1V484205015–59115.040.58137157:4118:3618:5118:57MCC5
H2V531007015–59115.040.58147157:4118:3918:5418:57MCC5
A8V641120015–59115.040.5827157:4118:3818:5318:59MCC6
A5V54101900–14114.980.58127157:4118:4218:5718:59MCC5
H3V584205015–59115.040.58127157:4118:4619:0119:05MCC5
A2V574205015–59115.040.58147157:4118:4819:0319:06MCC5
A7V564205015–59115.040.5887157:4118:4919:0419:08MCC5
A6V613704015–59115.040.58107157:4118:5219:0719:11MCC4
A5V62290800–14114.980.58137157:4119:0019:1519:19MCC4
H1V632806015–59115.040.58157157:4119:0119:1619:20MCC4
H2V603704015–59115.040.58157157:4119:0119:1619:21MCC4
A3V594205015–59115.040.58147157:4119:0719:2219:23MCC5
A4V96240100–14114.980.54156109:2619:0919:2419:26MCC6
A2V89420100–14114.980.54166109:2619:0719:2219:28MCC2
H3V904201015–59115.040.54136109:2619:0819:2319:28MCC4
A8V934202015–59115.040.5436109:2619:0919:2419:30MCC4
A1V914504015–59115.040.54146109:2619:1019:2519:31MCC4
A7V924202015–59115.040.54106109:2619:1119:2619:31MCC4
A5V974205015–59115.040.54156109:2619:2019:3519:37MCC4
A6V94390600–14114.980.54126109:2619:1719:3119:37MCC4
A3V984205015–59115.040.54166109:2619:2319:3819:43MCC4
H2V1014107015–59115.040.54176109:2619:2419:3919:43MCC4
H1V953906015–59115.040.54176109:2619:2519:4019:44MCC4
H3V102904015–59115.040.54156109:2619:3119:4619:50MCC2
A8V103904015–59115.040.5446109:2619:3319:4819:51MCC4
A7V1083601015–59115.040.54126109:2619:3419:4919:52MCC4
A1V1063602015–59115.040.54166109:2619:3419:5019:54MCC2
A4V1003601015–59115.040.54176109:2619:3719:5219:59MCC4
A2V99360200–14114.980.54186109:2619:3619:5120:00MCC2
A6V105423015–59115.040.54146109:2619:4019:5520:00MCC2
A5V104904015–59115.040.54176109:2619:4119:5620:02MCC2
H2V1073602015–59115.040.54196109:2619:4720:0220:06MCC2
A1V1304107015–59115.040.501747011:4619:5620:1120:12MCC2
H1V1324107015–59115.040.501947011:4619:5120:0620:13MCC2
A3V1313806015–59115.040.501747011:4619:5020:0520:14MCC2
H3V128420500–14114.980.501647011:4619:5520:1020:15MCC2
A7V136420100–14114.980.501347011:4619:5720:1220:18MCC2
A8V129420500–14114.980.50547011:4619:5920:1420:23MCC2
A2V134420100–14114.980.501947011:4620:0620:2120:27MCC2
A5V139410300–14114.980.501847011:4620:0820:2320:28MCC2
A4V1373806015–59115.040.501847011:4620:0720:2220:30MCC2
H2V1354201015–59115.040.502047011:4620:1120:2620:31MCC2
A6V133470200–14114.980.501547011:4620:0920:2420:33MCC2
H1V1383603015–59115.040.502047011:4620:1820:3320:38MCC2
A1V140360200–14114.980.501847011:4620:1820:3320:39MCC2
A3V1422401015–59115.040.501847011:4620:2020:3520:42MCC2
H3V141360200–14114.980.501747011:4620:2220:3720:44MCC2
A7V144420500–14114.980.501447011:4620:2720:4220:52MCC1
A8V1454205015–59115.040.50647011:4620:2920:4420:53MCC1
H2V1473603015–59115.040.502147011:4620:3520:5020:56MCC1
A2V1434205015–59115.040.502047011:4620:3320:4820:56MCC1
A4V1492401015–59115.040.501947011:4620:3620:5120:59MCC1
A1V1694004015–59115.040.471937013:2620:4320:5821:00MCC6
A5V146360300–14114.980.501947011:4620:3820:5321:02MCC2
H1V1684205015–59115.040.472137013:2620:4320:5821:04MCC1
A6V148410300–14114.980.501647011:4620:4220:5721:07MCC1
A3V1714201015–59115.040.471937013:2620:4721:0221:11MCC1
H3V1672804015–59115.040.471837013:2620:5021:0621:12MCC1
A1V1794101015–59115.040.472037013:2621:0221:1721:20MCC6
H2V1703602015–59115.040.472237013:2621:0221:1721:24MCC1
A7V173360300–14114.980.471537013:2621:0121:1621:25MCC6
A2V1743603015–59115.040.472137013:2621:0421:1921:27MCC1
A8V1724204015–59115.040.47737013:2621:0421:1921:29MCC1
A5V1764205015–59115.040.472037013:2621:0721:2221:29MCC1
A4V1774205015–59115.040.472037013:2621:0721:2221:30MCC1
H1V1754205015–59115.040.472237013:2621:1021:2521:31MCC1
H3V1963601015–59115.040.431924015:3621:1721:3221:36MCC1
A6V178370800–14114.980.471737013:2621:1521:3021:38MCC1
A3V1803601015–59115.040.472037013:2621:1921:3421:41MCC1
H2V1944203015–59115.040.432324015:3621:2821:4321:48MCC1
A1V1953602015–59115.040.432124015:3621:2921:4421:52MCC1
A7V197410500–14114.980.431624015:3621:3421:4921:57MCC1
H1V2084205015–59115.040.39238018:1621:3621:5121:58MCC6
A2V2074205015–59115.040.39228018:1621:3621:5122:00MCC6
A5V2094205015–59115.040.39218018:1621:3721:5222:00MCC6
A8V2063809015–59115.040.3988018:1621:3821:5322:01MCC1
H3V2143601015–59115.040.3720019:3621:4221:5722:03MCC6
A4V2053809015–59115.040.39218018:1621:4021:5522:06MCC6
A6V2133704015–59115.040.3718019:3621:4622:0122:09MCC6

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Figure 1. Total attention time TTAk (waiting, pickup, stabilization, and transport of casualties).
Figure 1. Total attention time TTAk (waiting, pickup, stabilization, and transport of casualties).
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Figure 2. Example of construction of the auxiliary network. Calculation of access arcs to node 9 of the auxiliary network G(N,A) from network G’(N’,A’). (a) Transport Network G’(N,A), (b) Example of calculation of auxiliary graph G(N,A) for Node 9—ambulance case, (c) Example of calculation of auxiliary graph G(N,A) for Node 9—helicopter case, (d) Resulting auxiliary graph G(N,A) for Node 9, helicopter case, and (e) Resulting auxiliary graph G(N,A) for Node 9, ambulance case.
Figure 2. Example of construction of the auxiliary network. Calculation of access arcs to node 9 of the auxiliary network G(N,A) from network G’(N’,A’). (a) Transport Network G’(N,A), (b) Example of calculation of auxiliary graph G(N,A) for Node 9—ambulance case, (c) Example of calculation of auxiliary graph G(N,A) for Node 9—helicopter case, (d) Resulting auxiliary graph G(N,A) for Node 9, helicopter case, and (e) Resulting auxiliary graph G(N,A) for Node 9, ambulance case.
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Figure 3. Graphical results of itineraries for the scenario (a) casualties with equal LSI, and (c) casualties with different LSI and the same age range. For both scenarios (a, c): (i) Only ambulance, minimizing Ck, (ii) Only helicopter, minimizing Ck, and (iii) Only helicopter, minimizing βk.
Figure 3. Graphical results of itineraries for the scenario (a) casualties with equal LSI, and (c) casualties with different LSI and the same age range. For both scenarios (a, c): (i) Only ambulance, minimizing Ck, (ii) Only helicopter, minimizing Ck, and (iii) Only helicopter, minimizing βk.
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Figure 4. (a) Population density, city of Iquique; (b) Road network, MCC locations, and areas enabled for helicopter landing, city of Iquique, Chile; (c) Location of 212 casualties by LSI in each Population Unit (PU) in the city of Iquique, a simulated scenario with an Mw 8.95 earthquake.
Figure 4. (a) Population density, city of Iquique; (b) Road network, MCC locations, and areas enabled for helicopter landing, city of Iquique, Chile; (c) Location of 212 casualties by LSI in each Population Unit (PU) in the city of Iquique, a simulated scenario with an Mw 8.95 earthquake.
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Figure 5. Casualty Pickup, Stabilization and Transport Schedule (CPST Schedule), Period 1 (start 07:41).
Figure 5. Casualty Pickup, Stabilization and Transport Schedule (CPST Schedule), Period 1 (start 07:41).
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Figure 6. Casualty Pickup, Stabilization, and Transport Schedule, after an execution of 7 periods.
Figure 6. Casualty Pickup, Stabilization, and Transport Schedule, after an execution of 7 periods.
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Table 1. Ambulance and helicopter travel times between medical care centers (MCCs) and casualties. Numerical example.
Table 1. Ambulance and helicopter travel times between medical care centers (MCCs) and casualties. Numerical example.
Ambulance Travel Times (min) Helicopter Travel Times (min)
MCC 1MCC 2MCC 3V1V2V3V4V5 MCC 1MCC 2MCC 3V1V2V3V4V5
V129.1923.9136.6406.678.338.330V17.426.787.8905.465.515.515
V227.4620.9632.646.6706.616.616.67V27.16.477.515.4605.465.465.46
V322.6318.2130.098.336.61008.33V36.936.297.435.515.46005.51
V422.6318.2130.098.336.61008.33V46.936.297.435.515.46005.51
V529.1923.9136.6406.678.338.330V57.426.787.8905.465.515.510
Table 2. Average stabilization time (minutes) according to age range and LSI.
Table 2. Average stabilization time (minutes) according to age range and LSI.
ID Age RangeAge Range (Years)Stabilization Time According to LSI (min)
LSI 1LSI 2LSI 3
10–1414.984293.3
215–5915.0429.962.14
360 or more9.327.665
Table 3. (a) Casualties with equal LSI. (b) Casualties with equal LSI and different age ranges. (c) Casualties with different LSI and the same age range. (d) Casualties with different LSI and different age ranges.
Table 3. (a) Casualties with equal LSI. (b) Casualties with equal LSI and different age ranges. (c) Casualties with different LSI and the same age range. (d) Casualties with different LSI and different age ranges.
Ambulance with 1 patient capacityHelicopter with capacity for 3 patients
Min Ck Min CkMinβk
Casualty ID CodeLSIAge Range λ k a g T S k a g (min)Trip (v)TBk(min)TSk(min)TLk(min)Casualty ID CodeLSIAge Range λ k a g T S k a g (min)Trip (v)TBk(min)TSk(min)TLk(min)Trip (v)TBk(min)TSk(min)TLk(min)
V1325.162.15482.6544.7573.9V1325.162.118.170.3206.318.170.375.1
V2325.162.13243.3305.4332.9V2325.162.12213.8275.9357.94229.4291.6299.0
V3325.162.1123.685.8108.4V3325.162.1172.9135.0206.3280.7142.9148.5
V4325.162.12131.0193.2215.8V4325.162.11138.5200.7206.33154.2216.4222.0
V5325.162.14362.1424.2453.4V5325.162.12285.6347.8357.95309.1371.3381.4
(a)
Ambulance with 1 patient capacityHelicopter with capacity for 3 patients
Min Ck Min CkMinβk
Casualty ID CodeLSIAge Range λ k a g T S k a g (min)Trip (v)TBk(min)TSk(min)TLk(min)Casualty ID CodeLSIAge Range λ k a g T S k a g (min)Trip (v)TBk(min)TSk(min)TLk(min)Trip (v)TBk(min)TSk(min)TLk(min)
V1325.162.14424.4486.5515.7V1325.162.12282.1344.2426.53219.7281.9286.7
V2318.793.32167.0260.3287.8V2318.793.31109.5202.8277.32114.6207.9215.0
V3318.793.3123.6116.9139.6V3318.793.319.0102.3277.319.0102.3107.5
V4325.162.13310.4372.6395.2V4325.162.11210.0272.1277.34291.8354.0359.2
V5335.165.05544.9609.9639.1V5335.165.02351.3416.3426.55369.3434.3444.5
(b)
Ambulance with 1 patient capacityHelicopter with capacity for 3 patients
Min Ck Min CkMinβk
Casualty ID CodeLSIAge Range λ k a g T S k a g (min)Trip (v)TBk(min)TSk(min)TLk(min)Casualty ID CodeLSIAge Range λ k a g T S k a g (min)Trip (v)TBk(min)TSk(min)TLk(min)Trip (v)TBk(min)TSk(min)TLk(min)
V1325.162.12137.6199.7228.9V1325.162.118.270.3175.618.270.375.1
V2220.929.94320.6350.5371.5V2220.929.92182.7212.6250.04193.6223.5230.0
V3220.929.93251.5281.4299.6V3220.929.91140.5170.4175.63152.7182.6187.2
V4325.162.1123.785.8108.4V4325.162.1174.9137.0175.6280.3142.4147.6
V5120.415.05395.4410.4434.3V5120.415.02224.3239.3250.05239.6254.6264.1
(c)
Ambulance with 1 patient capacityHelicopter with capacity for 3 patients
Min Ck Min CkMinβk
Casualty ID CodeLSIAge Range λ k a g T S k a g (min)Trip (v)TBk(min)TSk(min)TLk(min)Casualty ID CodeLSIAge Range λ k a g T S k a g (min)Trip (v)TBk(min)TSk(min)TLk(min)Trip (v)TBk(min)TSk(min)TLk(min)
V1325.162.12168.8230.9260.1V1325.162.11107169.1224.52112.3174.4179.2
V2211.942.03287.5329.5350.5V2211.942.01175.4217.4224.53186.3228.3234.7
V3220.929.94368.7398.6416.8V3220.929.92229.6259.5289.04239.3269.2273.7
V4318.793.3123.6116.9139.6V4318.793.319102.3224.519102.3107.5
V5130.49.35440.7450.0473.9V5130.49.32269.5278.8289.05283.2292.5302.0
(d)
Table 4. Population of the city of Iquique separated by category, according to age range.
Table 4. Population of the city of Iquique separated by category, according to age range.
ID Age RangeAge Range (Years)Population (Persons)
10–1441.163
215–59106.744
360 or more15.374
Table 5. Medical care center (MCC) capacity according to LSI [57].
Table 5. Medical care center (MCC) capacity according to LSI [57].
Medical Care Center IDCapacity (No. of Beds)
LSI1LSI2LSI3
MCC1233020
MCC224210
MCC324210
MCC416190
MCC524210
MCC625220
Table 6. People injured by LSI. Simulated scenario, earthquake Mw 8.9.
Table 6. People injured by LSI. Simulated scenario, earthquake Mw 8.9.
Age Range IDAge Range (Years)People Injured by LSI
LSI 1LSI 2LSI 3
10–1424233
215–5972757
360 or more251
Table 7. Number of casualties who require transport to an MCC, availability of the health network, and decrease in the speed of operation of the road network for each modeling period.
Table 7. Number of casualties who require transport to an MCC, availability of the health network, and decrease in the speed of operation of the road network for each modeling period.
Period IDPeriod Start TimeNumber of Casualties (People)Availability of the Health Network% Decrease in Speed
TotalLSI 1LSI 2LSI 3Available MCCSAmbulances AvailableHelicopters Available
Period 107:4164322753 (MCC1, 2 and 3)4 (A1, A2, A3, A4)2 (H1, H2)70%
Period 209:2644202225 (MCC 1, 2, 3, 4, 5)5 (A1, A2, A3, A4, A5)2 (H1, H2)70%
Period 311:4641221816 (MCC 1, 2, 3, 4, 5, 6)7 (A1, A2, A3, A4, A5, A6, A7)3 (H1, H2, H3)50%
Period 413:2631141526 (MCC 1, 2, 3, 4, 5, 6)7 (A1, A2, A3, A4, A5, A6, A7)3 (H1, H2, H3)50%
Period 515:361741216 (MCC 1, 2, 3, 4, 5, 6)7 (A1, A2, A3, A4, A5, A6, A7)3 (H1, H2, H3)30%
Period 618:16126606 (MCC 1, 2, 3, 4, 5, 6)7 (A1, A2, A3, A4, A5, A6, A7)3 (H1, H2, H3)30%
Period 719:3652306 (MCC 1, 2, 3, 4, 5, 6)8 (A1, A2, A3, A4, A5, A6, A7, A8)3 (H1, H2, H3)10%
Table 8. Excerpt. Casualty pickup, stabilization, and transport activity at node 36020. Period 1.
Table 8. Excerpt. Casualty pickup, stabilization, and transport activity at node 36020. Period 1.
Vehicle ID CodeCasualty ID CodeNode ID (li)Age RangeLSI T S k a g   ( min ) λ k a g Trip (v)TFkTBkTSkTLkMCC Assigned
A3V236020≥603655.10517:41:008:04:189:09:189:31:36MCC1
H2V43602015–59362.145.10517:41:007:50:028:52:108:57:51MCC1
A1V173602015–59229.90.89527:41:0010:32:5111:02:4511:20:58MCC2
A3V183602015–59229.90.89537:41:0011:07:2811:37:2212:02:17MCC1
A2V253602015–59229.90.89537:41:0011:15:1811:45:1212:08:30MCC1
H1V283602015–59229.90.89567:41:0012:36:4013:06:3413:11:35MCC2
H1V383602015–59115.040.37287:41:0013:58:2714:13:2914:43:07MCC2
H1V393602015–59115.040.37287:41:0014:20:5414:35:5614:43:07MCC2
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Bronfman, A.; Beneventti G., D.; Alvarez, P.P.; Reid, S.; Paredes-Belmar, G. The Casualty Stabilization–Transportation Problem in a Large-Scale Disaster. Sustainability 2022, 14, 621. https://doi.org/10.3390/su14020621

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Bronfman A, Beneventti G. D, Alvarez PP, Reid S, Paredes-Belmar G. The Casualty Stabilization–Transportation Problem in a Large-Scale Disaster. Sustainability. 2022; 14(2):621. https://doi.org/10.3390/su14020621

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Bronfman, Andrés, Diego Beneventti G., Pamela P. Alvarez, Samantha Reid, and Germán Paredes-Belmar. 2022. "The Casualty Stabilization–Transportation Problem in a Large-Scale Disaster" Sustainability 14, no. 2: 621. https://doi.org/10.3390/su14020621

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