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Modeling and transportation planning for US noncombatant evacuation operations in South Korea


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Purpose The purpose of this paper is to investigate US noncombatant evacuation operations (NEO) in South Korea and devise planning and management procedures that improve the efficiency of those missions. Design/methodology/approach It formulates a time-staged network model of the South Korean noncombatant evacuation system as a mixed integer linear program to determine an optimal flow configuration that minimizes the time required to complete an evacuation. This solution considers the capacity and resource constraints of multiple transportation modes and effectively allocates the limited assets across a time-staged network to create a feasible evacuation plan. That solution is post-processed and a vehicle routing procedure then produces a high resolution schedule for each individual asset throughout the entire duration of the NEO. Findings This work makes a clear improvement in the decision-making and resource allocation methodology currently used in a NEO on the Korea peninsula. It immediately provides previously unidentifiable information regarding the scope and requirements of a particular evacuation scenario and then produces an executable schedule for assets to facilitate mission accomplishment. Originality/value The significance of this work is not relegated only to evacuation operations on the Korean peninsula; there are numerous other NEO and natural disaster related scenarios that can benefit from this approach.
Content may be subject to copyright.
Modeling and transportation
planning for US noncombatant
evacuation operations in
South Korea
John A. Kearby,Ryan D. Winz,Thom J. Hodgson,Michael G. Kay,
Russell E. King and Brandon M. McConnell
Operations Research Graduate Program and the Center for Additive Manufacturing
and Logistics, North Carolina State University, Raleigh, North Carolina, USA
Purpose The purpose of this paper is to investigate US noncombatant evacuation operations (NEO) in
South Korea and devise planning and management procedures that improve the efciency of those missions.
Design/methodology/approach It formulates a time-staged network model of the South Korean
noncombatant evacuation system as a mixed integer linear program to determine an optimal ow conguration
that minimizes the time required to complete an evacuation. This solution considers the capacity and resource
constraints of multiple transportation modes and effectively allocates the limited assets across a time-staged
network to create a feasible evacuation plan. That solution is post-processed and a vehicle routing procedure then
produces a high resolution schedule for each individual asset throughout the entire duration of the NEO.
Findings This work makes a clear improvement in the decision-making and resource allocation
methodology currently used in a NEO on the Korea peninsula. It immediately provides previously
unidentiable information regarding the scope and requirements of a particular evacuation scenario and then
produces an executable schedule for assets to facilitate mission accomplishment.
Originality/value The signicance of this work is not relegated only to evacuation operations on the Korean
peninsula; there are numerous other NEO and natural disaster related scenarios that can benet from this approach.
Keywords Korea, Noncombatant evacuation, Time-staged network, US Military,
Vehicle routing procedure
Paper type Research paper
© John A. Kearby, Ryan D. Winz, Thom J. Hodgson, Michael G. Kay, Russell E. King and
Brandon M. McConnell. Published in Journal of Defense Analytics and Logistics. Published by Emerald
Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence.
Anyone may reproduce, distribute, translate and create derivative works of this article (for both
commercial and non-commercial purposes), subject to full attribution to the original publication and
authors. The full terms of this licence may be seen at
Disclaimer: The views expressed in this paper are those of the authors and do not reect the
ocial policy or position of United States Forces Korea, the United States Army, the Department of
State, the Department of Defense or the United States Government.
Disclosure: This work was supported, in part, by a grant from the US Army Research Oce (grant
# W911NF1910055).
The authors gratefully acknowledge the support and assistance of the 2nd Infantry Division C5
and ORSA Planning Stain the development of this paper. Their consideration and insight was
instrumental in framing and focusing the model to ensure its relevance. A NC State colleague Osman
Ozaltin provided useful suggestions that greatly enhanced the presentation of technical details. This
paper also beneted from constructive comments from the editor and two reviewers that improved
both the content and presentation.
Modeling and
Received 28 May 2019
Revised 27 August2019
13 October 2019
15 November 2019
Accepted 20 November2019
Journal of Defense Analytics and
Vol. 4 No. 1, 2020
pp. 41-69
Emerald Publishing Limited
DOI 10.1108/JDAL-05-2019-0010
The current issue and full text archive of this journal is available on Emerald Insight at:
Kearby, J.A., Winz, R.D., Hodgson, T.J. Kay, M.G., King, R.E., and McConnell, B.M. 2020. Modeling and transportation planning for US noncombatant
evacuation operations in South Korea, Journal of Defense Analytics and Logistics, Vol 4, No 1, pp. 41–69.DOI 10.1108/JDAL-05-2019-0010.
1. Introduction
1.1 Noncombatant evacuation operations denition and historical context
Noncombatant Evacuation Operations (NEOs) are operations in which US citizens,
Department of Defense (DoD) civilians and pre-designated host nation (HN) or third-country
nationals (TCN) are transported from within a foreign nation to a separate safe haven (Joint
Doctrine Group, 2010,JP368). These operations generally occur as a result of military
conict, political unrest or natural disaster, but they can be directed for any number of other
reasons by the Department of State (DOS). The manner in which NEOs are conducted can
have far-reaching positive or negative effects across diplomatic, humanitarian, military and
economic realms, and they require deliberate and thoughtful planning to execute well
(Junkins, 2012).
These missions are ultimately the responsibility of the DOS to order and coordinate, but
it is the responsibility of military forces specically Geographic Combatant Commands
(GCC) –“to prepare and maintain plans for the protection and evacuation of US
noncombatants abroad for whom the DoD is responsible(Joint Doctrine Group, 2010,JP3
68). There are six GCCs chartered with this broad mission and generally the GCCs assign
country specic NEO missions to an individual military component commander (Army,
Navy, Marines or Air Force) or they choose to establish a Joint Task Force to conduct the
Historically, the US has conducted over 30 NEO missions dating back to Operation
Frequent Wind in Vietnam in 1975. Frequent Wind evacuated approximately 7,000 people
from Saigon and southern Vietnam to US Navy vessels located in the South China Sea
(Washington, 2015). This mission was successful in that it evacuated a large number of
people, but the uncoordinated efforts of US military aircraft, Vietnamese Air Force and US
Government (USG) supported xed-wing assets resulted in a substantial loss of resources.
Due to a lack of fuel and deck space aboard the US Navy ships, many aircraft were landed at
sea or pushed overboard to make room for additional arriving aircraft. It was this disorder
that provided the impetus for much of the doctrine we see at work in recent missions, such
as Operation Silver Wake in Albania in 1997 depicted in Figure 1. In this mission, the DOS
called for the evacuation of US Embassy personnel following the economic collapse and
subsequent rioting in the capital cityof Tirana. The US Navys 6th Fleet inserted a company
of Marines into the US Embassy and adjacent housing compound to provide establish
security and subsequently evacuate approximately 900 personnel out to ships located in the
Adriatic Sea (Germain, 1997).
This mission is representative of much of the NEO scenarios that dominate the doctrine
in which the populations to be evacuated are less than 1,000 people, the operation itself is a
point-to-point transportation by military aircraft, and there is a non-peer military threat
opposing the mission. This is simply not the case in a South Korean noncombatant
evacuation scenario.
1.2 South Korea characteristics
South Korea presents a number of challenges for an evacuation beyond the base scenarios
covered in the doctrine. First, the scale is drastically different. Typically, less than 1,000
people are evacuated in the course of a NEO, and South Korea has over 150,000 American
citizens and DoD personnel that would require transportation out of the country (United
States Department of State, 2018, Seoul Annual F77 Report). Additionally, the base
scenarios present a centralized evacuation population, where in South Korea that population
is widely distributed across the country. Second, that number of personnel exceeds the
reasonable capacity of military aircraft available for evacuation and therefore the
evacuation plans rely on the public transportation system of South Korea. That aspect of the
plan makes good use of a powerful asset, but it results in a plan that is difcult to rehearse
and rene outside of an actual evacuation. It also inserts a network component into the
evacuation, where generally NEOs have been point to point from an embassy to safe haven.
Third, given the nature of the political landscape and the provocation and escalation
policies employed by North Korea, the threat of large scale military action by units on the
peninsula is real, and that creates a scarcity in terms of the available DoD forces to facilitate
the NEO. In the majority of the evacuation missions conducted over the past 40 years that
has not truly been the case. The evacuation location conicts did not possess peer or near-
peer level militaries that would occupy the attention of the forces conducting the NEO.
Given the nature of the operational environment in Korea, a noncombatant evacuation
requires a dramatically different approach than those pursued in the past. Figure 2
illustrates the complexities of the South Korean NEO mission. There are many assembly
points (APs) that service a distributed population, the evacuation network comprises
numerous routes and modes of transportation, and there is a nearby credible threat in North
Korea prepared to disrupt evacuation operations.
1.3 Framing the noncombatant evacuation operations problem for 2nd infantry division
While the signicance of the NEO mission is considerable, it is important to note that it is
almost never the primary mission of the various military component commands rather it is
an additional responsibility contingent on political or environmental circumstances. And
therefore, the military component commands develop broadly scoped and exible plans
Figure 1.
Operation Silver
Wake, Albania 1997
evacuation from US
Embassy in Tirana to
US Navy ships in
Adriatic Sea
Modeling and
with the understanding that they will have to adjust based on what actually occurs on the
ground. In the case of South Korea, the 2nd Infantry Division (2ID) is the military unit
responsible for planning andexecuting a NEO on the peninsula.
In the event the DOS directs an evacuation, 2ID and subordinate units would elevate
their readiness posture and move to occupy APs and key nodes of interest across the
country. The population to be evacuated would then be notied and directed to report to the
APs for in-processing and transportation. The military elements managing APs would
report the number of evacuees present at their location to the 2ID operations center and then
an ad hoc dispatching of assets would take place to move personnel on designated routes out
of the country. This general process would continue until the total population to be
evacuated has passed through the system.
Further investigation into the planning methodology at work in this concept of the
operation re- emphasizes the challenges at play in South Korea. It is apparent that the
network component and scale of this scenario is problematic for the NEO planners and this
complexity has made it difcult for them to devise a comprehensive and logical approach.
Additionally, the presence of a signicant North Korean threat occupies much of the 2ID
plannersattention, leaving portions of the evacuation operation unexplored. Specically, no
rigorous analysis or modeling of the network has been done to identify critical arcs, the
modeling of evacuees arriving into the system is incomplete, and the allocation of assets to
Figure 2.
The South Korea
NEO mission starkly
contrasts with the
typical NEO scenario
described in Figure 1
deal with the evacuees is reactive and not precisely motivated. This troubling lack of
analysis leaves.
2ID not only without a clear understanding of the time or resources required to complete
an evacuation, but without any real idea of how to shape and manage the operation given
what actually is available.
The rest of the paper is organized as follows: Section 2 presents the overall objectives of
the work and leading assumptions that frame the problem, Section 3 highlights existing
work in the eld, Section 4 outlines the specic approach and methodology applied to solve
the problem, Section 5 demonstrates the usefulness of the work in the form of a case study,
and Section 6 makes nal recommendations for application of this procedure in Korea and
discusses of the novelty of this approach for similar problems.
2. Objectives and assumptions
The overall objective of this work is to better prepare the 2ID Commander and Staff in their
planning, preparation and execution of noncombatant operations. That requires addressing
the current planning deciencies and making the full problem more accessible and
manageable for those involved. That begins with modeling and analyzing the specic
physical transportation network in play during an evacuation and then establishing a
reasonable estimate of how evacuees will enter that system. Then the best and most feasible
manner in which people can be evacuated, given limited resources, can be determined and
those limited resources can be allocated in such a way as to deliberately achieve that best
possible evacuation.
With the general approach determined, there are some leading assumptions that need to
be introduced to make it practical and reasonable to pursue. Foundationally, NEO is a single
task within a large mission set for 2ID, and it must be conducted in conjunction with other
responsibilities. Therefore, any methodology needs to be exible or be able to be easily
adjusted to account for other requirements or changing circumstances. Next, the number of
evacuees will always exceed the capacity of the transportation eet and so each asset will be
used multiple times through the course of a NEO. Additionally, noncombatants are expected
to arrive at multiple pre-determined locations across the country, and they are expected to
do so at variable rates. Finally, there exists a centrally controlled transportation eet that
can be employed to execute a NEO which we limit to buses, helicopters, and trains. We do
not consider xed-wing assets based on communications with 2ID but this is not a limiting
assumption based on the model structure. This collection of initial assumptions provides
context for the approach and better denes the problem itself.
3. Literature review
With the objectives of this problem established, it is instructive to review the procedures and
solutions to similar or related scenarios that could potentially be applied in this case.
3.1 Noncombatant evacuations
The majority of the historic noncombatant operations do not inherently lend themselves to
mathematical modeling as the missions generally involved evacuating from a single location
to a separate safe haven. It is also apparent that the allocation of assets and any network
analysis was done on a purely practical basis during the mission planning processes. As a
result of those factors, past NEO missions do not provide signicant insight into the South
Korea scenario.
While these historical examples have not proven to be particularly relevant in this
instance, meaningful work has been done using multi-agent models to facilitate future
Modeling and
noncombatant evacuation operations. Multi-agent models have been applied to potential
evacuation operations to quickly organize available data concerning population locations,
transportation assets, condition of infrastructure, fuel supplies and other factors, and then
apply a series of hierarchically sorted tasks to determine how to best conduct an evacuation
(Dix et al.,2002). These models make signicant improvements over their control
simulations but would have to be heavily modied to account for the complexity of the
South Korea evacuation network. More generally, multi-agent models have also been
applied to smaller scale evacuations of buildings and urban areas using behavior-related
models of individual evacuees and properties of the physical environment (Karbovskii et al.,
2015). The scope of this multi-agent application is a bit too narrow, as the interest of this
paper is primarily on the performance of a large transportation network and the allocation of
assets rather than attempting to smooth the behavior of individual actors within a system.
In total, the multi-agent work has shown promise, but in the South Korea scenario, there are
operational requirements that allow for a more directed approach.
The most relevant literature focuses on assisting military NEO Planners and consistently
employs discrete event simulation (DES) (Kuchell, 2013;Scheer, 2011;Olsen, 2011;Gregg,
2010;Sumner and Zahn, 1996). These studies comment on the difculty of getting accurate
arrival and process data, making validation difcult; none of them are designed for use
during the operation using situation reports as an operation unfolds. Kuchell (2013) presents
a DES framework with modules representing various NEO network components and
processes with support from an unnamed mixed-integer program to make asset routing
decisions. Other NEO studies are Europe-specic and also rely on discrete event simulation
(Scheer, 2011). The authors study a small NEO with two different xed wing platforms and
two different rotary wing assets. They report the total person-days for the evacuation to
assist determining resource requirement in the network (food, water, etc.).
3.2 Civilian and military medical evacuation models
Emergency medical evacuations conducted by military and civilian organizations represent
a closely related eld of research to noncombatant evacuations. Signicant investigation
into emergency medical services concerning military aeromedical evacuation (MEDEVAC)
and ambulance coverage and their associated response times has been done, and there are
some practical similarities that address some of the issues present in a South Korean NEO.
Numerous military emergency medical evacuation models have been developed to resource
and dispatch aerial and ground MEDEVAC assets in such a way as to provide the best possible
service times for units in active combat zones. Investigation in the number and location of
military treatment facilities and the density of military aircraft across a theater of operations
responds to the set covering aspects of this problem (Fulton et al., 2010), while Robbins et al.
(2018) apply a Markov decision process model and approximate dynamic programming to
optimize the dispatching of assets. Similarly, civilian emergency medical evacuation models
generally classify into those that address the staging locations of emergency vehicles, those
that reallocate vehicles by either multi-period mixed integer linear or dynamically
programming when demand is exceeded, or those that are principally concerned with
dispatching and routing vehicles as medical emergencies are reported (Aringhieri et al.,2017).
Most relevant to this scenario are models that are concerned with the reallocation of emergency
vehicles in real-time in response to demand. Bertsimas and Ng (2019) use a two-staged
stochastic and robust planning model to tactically deploy ambulances in a manner that is
resistant to short term uncertainties in demand. This approach yields high-quality solutions for
the emergency medical service, but the model is motivated to limit the number of slow response
times while working to limit the repositioning of assets. To summarize, both military and
civilian emergency, evacuation models provide insight into how to assess the South Korea
scenario while being motivated by a different end. The aim of the NEO is to empty the system
as quickly as possible, while the medical evacuations look to provide the most prompt service
to individual demand points.
3.3 General evacuation models
A number of studies use network ow approaches to plan evacuations of buildings (Kawsar
et al., 2019; Park, 2015; Kisko and Francis, 1985) or cities (Yamada, 1996) without a time-
staged expansion. Other studies use network ows with time-expanded networks for
buildings (Shin et al.,2019;Choi et al.,1988;Chalmet et al., 1982) or cities (Lim et al.,2012)to
accommodate more realistic features (Dhamala, 2014;Lim et al., 2012). Jarvis and Ratliff
(1982) demonstrate the equivalency between three objectives for a time-expanded network
ow as will be discussed below. While effectively minimize the total evacuation time, Lim
et al. (2012) maximize the number of total evacuees for a short notice evacuation windowand
Shin et al. (2019) introduce multiple options for the objective function. For a recent survey of
time-expanded network ow models, refer Dhamala (2014).
For sufciently large problems with computational runtime issues, recent studies have
also explored heuristics and inexact algorithms that use Dijkstras algorithm to identify
evacuation paths feeding a constructive approach that maximizes and schedules the ow on
each path (Shin et al., 2019;Lim et al.,2012). Lu et al. (2005,2003) implement a generalized
shortest path search algorithm for transportation networks and compare performance with
time-expanded network approaches that use linear programming. Saadatseresht et al. (2009)
use a multiobjective evolutionary algorithm for evacuation planning and demonstrates a
geographical information system (GIS) integrated approach for an evacuation scenario of
22,000 people from a 371acre area to 7 safe zones. Others, such as Gan et al. (2016), integrate
optimization with trafc simulation for a hybrid approach.
While specic work on noncombatant evacuations appears limited, the broader category
of evacuations related to natural disasters shows signicantly more breadth and depth of
investigation. Most existing studies recommend implementing contraows or lane reversals
in various critical areas of the networks to smooth outow and reduce congestion and wait
times (Praveen et al.,2010). Other models seek to optimize the total performance of the
system by building objective functions based on the average vehicle speeds across the
network. These produce solutions that recommend metering the trafcow onto key
thoroughfares to keep network accumulation below a critical level to achieve the best
system performance (Zhang et al., 2015). These methods themselves are not cleanly
applicable to South Korea, largely due to the fact that the models rely on the assumption that
the population to be evacuated is itself mobile. That is not the case in South Korea, where
less than 43 per cent of the population has access to a personal vehicle (Sung-jin, 2016) and
that number drops signicantly in urban areas, where the population to be evacuated is
based. These issues point to another aspect of evacuation models specically those that
use the public transportation system. The interested reader may consult the most recent
surveys on general evacuation and disaster operations management (Galindo and Batta,
2013;Altay and Green, 2006;Hamacher and Tjandra, 2002). See also the homeland security-
themed survey by Wright et al. (2006).
3.4 Disaster evacuation models using public transportation systems
Related studies optimizing evacuation roadway trafc address the approximate scale of the
problem such as the evacuation Knoxville and Knox County, TN, requiring 157,733 vehicle
trips (Yuan et al.,2006;Yuan, 2005)yet the most pertinent and promising studies to this
Modeling and
paper concern the construction of models that use the public transportation system to assist
in an evacuation. While the motivation for the evacuation differs from that of NEOs, the
approximate scale and network considerations closely relate to a scenario based in South
A number of signicant storms damaging urban areas in the early 2000s revealed the
need for investigation into the use of public transportation assets to evacuate the car-less
population. Early studies applied mixed-integer linear programming (Sayyady and
Eksioglu, 2010) to use the local bus eet to minimize the total evacuation time, assuming
single trips and known pickup locations. Bish (2011) introduces a model explicitly for bus-
based regional evacuations. Other models capture the demand uncertainty based on arrivals
into the system (Lakshay and Bolia, 2019; Song and Yan, 2016;Goerigk and Grün, 2014;
Abdelgawad et al.,2010) and some use a vehicle routing procedures to recommend bus
routes to minimize total evacuation times. Many are based on known pickup and drop off
locations of the buses and were later extended by Kulshrestha et al. (2014) to select optimal
pickup locations for evacuees to assemble prior to transportation. Goerigk et al. (2015) and
Goerigk and Grün(2014) apply a robustness approach to a bus evacuation but do not
consider alternate transportation modes as the study focuses on the evacuation in the city of
Kaiserslautern (Germany).
While there are some specic nuances that would need to be considered in the case of a
South Korea evacuation, the framework established in these previous studies describes a
practical approach to the problem. Aspects of an evacuation model, constructed for use by
the 2ID, that differ from previous works would need to capture the three distinct modes of
transportation: bus, rail and helicopter. Because it is intended to be a practical tool, it would
need to adopt a multi-period approach so it could rene its recommendations based on
actual arrivals into the system as well as uctuating bus, train and helicopter eet sizes. It
would need to account for capacitated nodes at certain reception or intermittent staging
nodes, and it would need to consider the costs of operating evacuee intake points on the
system. A mixed integer linear program that integrates those facets, along with the existing
works use of demand uncertainty, dened intake locations and the general minimization of
total evacuation time would yield a tool that recommends optimal employment of limited
assets to achieve an evacuation in South Korea.
4. Methodology
Aspects of the South Korea evacuation scenario coupled with the specied objectives of 2ID
naturally point toward the application of a minimum cost network model to optimize the
ow of evacuees through the transportation network. That requires the network structure
itself as well as a model for how evacuees will arrive into the system. Those two pieces can
then be used within a mixed integer linear program to determine the optimal conguration
of evacuee ow that minimizes the total time of the NEO while considering the limited assets
available. After post-processing, that solution can be used within a vehicle routing
procedure to produce a route schedule for each individual asset to facilitate the complete
evacuation. This methodology effectively addresses problems with the existing plans and
gives 2ID mission performance statistics and an actual executable schedule for their assets
to make the complete NEO possible. Figure 3 illustrates the approach.
4.1 Network modeling
Beginning with the evacuation network it is useful to develop a basic understanding of the
sequence of events and the ow of personnel within an evacuation so that the model and its
features can be clearly communicated. First, the most typical scenario for an evacuee
following their arrival to an AP would occur as follows: bus movement to a US military
controlled train station, train movement south to a station located near the relocation center,
bus movement to the relocation center, and then another bus movement to the Air/Sea Port
of Debarkation (A/SPOD) as assets become available to move them off peninsula. Numerous
other alternatives exist: an evacuee could be bused from the AP directly to the port or they
could be own by helicopter from the AP to a more advantageous position south for rail
4.1.1 Structure. The components of that sequence critical to the actual modeling process
are the APs, relocation center, and A/SPOD locations. These form the nodes of the network
and the movement alternatives between them build out the actual structure of the network.
APs are located on established military installations, the relocation center is located in the
vicinity of Busan, and the port of Busan serves as the primary SPOD. Figure 4 depicts
approximate geographic node locations and those points are each generally connected via
bus, train and helicopter arcs. There are a few exceptions related to where the trains can
physically travel, or where helicopters are permitted to land, but in most cases, all nodes
connect to all other nodes. This collection of nodes and their associated connections form the
basis for the network structure.
4.1.2 Time-staged expansion. Recall the leading assumptions that the number of
evacuees exceeds the eet capacity and the notion that people will arrive into the system at
different locations at irregular intervals. These two assumptions lead to performing a time-
staged expansion of the network structure to adequately capture the behavior of the system.
To facilitate that expansion, it is necessary to rst determine the travel times for all of the
bus, train, and helicopter arcs. This is achieved through the use of web-based navigation
Figure 3.
General solution
procedure and
Modeling and
and mapping sites (Waze, 2018), published train schedules (KTX, 2018) and direct
calculation in the case of helicopter arcs considering aircraft cruising speeds. In addition to
the arcs that physically transport evacuees, as a result of the time-staged construction there
are also arcs that carry ow across time periods while remaining at the same node. The
collection of these node-arc travel times is used to construct an incidence matrix for use in
the optimization model. In this conguration it is convenient to include a source and sink
node to easily capture and motivate all ow into and out of the system. The complete results
of the expansion yield a concise network for use by the model.
4.2 Arrivals process
Currently, evacuees are expected to arrive into the system at several different locations
spread across the country at an unknown rate. Due to the scale and political implications of
an evacuation on the peninsula, there is a lack of empirical data from 2ID to describe this
process and so modeling it becomes a necessity. 2ID provided the 2018F-77 Report of
Potential Evacuees (United States Department of State, 2018) which is essentially a census of
the size and distribution of the population to be evacuated. Further, Kuchell (2013) reports
that DOS claims most arrivals are bell-shaped but positively skewed. The interested reader
should also consult Murray-Tuite and Wolshon (2013) for a thorough review of evacuation
demand modeling considerations, though we lacked sufcient data to incorporate them here.
Using the F-77 data and the assumption that people will be evacuated through the nearest
AP, this paper directly calculates the number of people who are expected to be evacuated
Figure 4.
(color online)
Network structure of
South Korea
through each node. That forms the basis of the model, and then through the use of the
Poisson distribution and a mean arrival rate parameter, the number of evacuees who arrive
at each location in each specic time period can be determined. It is reasonable to assume
that arrivals follow a Poisson distribution because the behavior and arrival time of widely
distributed individual evacuees to APs are unrelated to one another and independent. The
following summarizes the modeling of the arrival process:
qit ¼PitfW¼wgpopulationi(1)
= Number of evacuees arriving at node iat time period t
= Total evacuees assigned to assemble at node i;
w!= Probability of complete evacuation of node iat time period t;
= Average time for completion of all arrivals into node i,
z= Segment of interest, equal to 1; and
w= Time for completion of all arrivals into node i.
This permits the unit getting location-specic arrival proles, such as populations closer to
the demilitarized zone evacuating faster than those to the south, while only requiring a
single parameter to estimate. This is important given the lack of data. However, the arrivals
process is modular in that a more sophisticated arrival model need only output q
in the end
to be compatible with the remainder of this paper.
4.3 Model
This section presents a mixed-integer linear program with the objective of minimizing the
total number of people-minutes of an evacuation. The following outlines introduces the
notation, formulates the model and discusses the model.
N= Set of Unique Node Locations;
N= Set of Assembly Points; and
K= {0, 1, 2, 3} for {source, bus, train, helicopter} = Set of Transportation Modes.
Index Use
i, j [N= Indices for Node Locations;
s[N= Super Source Node;
d[N= Sink Node
t= {1, 2, 3,...,T} = Number of 30 minute allocation cycles (or time periods), over the full evac-
uation time horizon; and
k[K= Index for Transportation Mode.
Given Data
= Total number of personnel to be evacuated by assembly node i[N
= Planned personnel arriving at node iin time period t;
ijt = Cost penalizing outow directly related to the time period in which ow occurs;
= Network incidence matrix describing network structure for mode k; and
ij = Transit time (in time periods) from node ito node jusing mode k.
= Minimum number of evacuees to use a single asset for mode k; and
= Total eet capacity for mode kin number of evacuees.
Modeling and
Decision Variables
ij = Evacuee ow from node ito node jusing mode kin time period t; and
ij = Indicator for Evacuee ow from node ito node jusing mode kin time period t
Model formulation
ijt xk
ij t
ðÞ (2)
ðÞ¼qjt 8j;t(3)
qjt (4)
ij t
ji tþpk
ij t
ij t
ðÞ 8k;i;j
ij t
ij t
ðÞ 8k;i;j
ðÞ 8k;i;j
ij t
ðÞ0 and Integer (9)
ij t
ðÞBinary (10)
The objective (2) seeks to minimize the total time of an evacuation through the allocation to
transportation assets across decision cycles. It accomplishes this by establishing a cost for
exiting the network in each period, with the cost increasing according to the period in which
the exit occurs. In the results presented below, ck
ijt ¼t, which is simultaneously equivalent
to minimizing the average time for an evacuee or maximizing the evacuation output in the
rst ntime periods for n#T, where Tis the minimized time to evacuate the network
achieved by (2) (Jarvis and Ratliff, 1982). In general, ck
ijt ¼tshould be a non-decreasing
function in t. Node and arc-level network details are available in Kearby (2019, p. 11, 63).
Constraint (3) ensures evacuees arrive to the assembly points in the right time periods.
This is designed to be modular to permit testing different assumptions which result in
different q
. Constraint (4) requires all evacuees to be evacuated to the super-sink node. The
evacuee ow balance constraint is (5) where the notation i|i,jA
means for igiven that
there exists a feasible (non-zero) arc (i, j)A
for transportation mode k. This is equivalent to
ij xk
ij t
ji xk
ji tþpk
Constraints (6) and (7) work together to provide an upper and lower bound on ows across a
singular arc within an individual period. Constraint (6) denes the eetwide capacities for
each transportationmode. We assume capacities are 45 (people) for buses, 750 for trains, and
35 for helicopters. For example, if there are ve helicopters available, U
=535 = 175.
To incorporate senior leader planning guidance and prevent unnecessarily planning to use
an asset for one person, minimum asset utilization thresholds, the L
, are 30 (people) for
buses, 100 for trains, and 10 for helicopters. Note that (7) is only active until the arrival
process reaches
; where
is the mean arrival completion time parameter applied to each
node. This prevents committing assets early on for one or two evacuees and is unnecessary
once sufcient numbers of evacuees arrive. For later time periods, such trips may be
required to evacuate remaining people (maintains feasibility). If
is non-integer, we
suggest letting using [
] in (7).
Constraint (8) is a multi-period eet capacity constraint that effects ows across time
periods and accounts for evacuation ows already underway. It ensures that for all
allocations of the eet, the assets in use never exceeds the total eet capacity in any one time
period. To illustrate how this constraint functions, reference Figure 5. In that example, if
scheduling ow when t= 2, the ow originating from Node 2 when t= 1 must be considered
since that arc, and its capacity, is still underway during the scheduling time period. In the
actual formulation, this constraint is active across bus, train, and helicopter arc groupings
and working to provide a tighter bound on the capacity. The notation (z)
Figure 5.
expansion example
Modeling and
Finally, constraints (910) enforce non-negativity and the appropriate discrete values. Note
that as written, the model is a integer (linear) program. However, given integer population
and transportation capacity data, the integer requirement on xk
ij t
in (9) is unnecessary. For
any feasible, yk
ij t
ðÞ2f0;1gthe remaining constraint matrix in xk
ij t
ðÞ remains total
unimodular (Wolsey, 1998;Chen et al., 2010).
Thus keeping the binary requirement in (10) but relaxing the integer requirement (9) on
ij t
for the full 156k evacuation population reduces the solution time from 6min to 20s
(with 0.1 per cent optimality gap) and converts the model into a mixed integer linear
program (MILP). The solution to this formulation determines the optimal ow conguration
of personnel to minimize the required time of an evacuation.
4.4 Vehicle routing procedure
The solution to the time-staged network model linear program is a single vector that details
the time instance specicow of every arc across the full time horizon. The position of an
individual ow within this vector indicates the quantity of people moving as well as the
period it is scheduled to occur. The location within the vector also describes
the transportation mode responsible for executing a particular movement and knowing the
capacity of each asset type, the number of assets required is directly calculated. Redening
the optimal ows as the number of full asset shipments necessary, each with dened start
times, readies the model solution for the application of a vehicle routing procedure. To
complete the formulation, constraints are applied to each transportation type to limit their
capacities to a single shipment, and assign a depot to initiate and end route sequences.
A vehicle routing strategy is used using a savings route construction procedure followed
by two-opt improvement. The savings procedure follows the ClarkeWright heuristic that
calculates the savings associated with merging shipment pairs as opposed to conducting
them independently (Vigo and Toth, 2014). Routes are then constructed based on
minimizing the total cost of completing all shipments. In this instance, cost is equivalent to
time, and as such the procedure uses the time-staged network ow travel times to motivate
the heuristic. Once the routes are constructed, two-opt improvement performs an exhaustive
series of edge exchanges to ensure the optimum collection of route sequences. The complete
solution to the vehicle routing procedure is a time specic location sequence for each asset
available to 2ID.
The vehicle routing procedure solution preserves the constraints built into the model.
Since the shipments and associated time constraints are they themselves governed by eet
size and total capacity, the routing procedure effectively carries those boundaries forward
into the route construction. This represents a novel approach, in that it indirectly constrains
the number of routes the ClarkeWright savings procedure will construct.
4.5 Output summary
Following this solution methodology ultimately produces signicant results for two major
aspects of this problem. First, model results provide 2ID with performance statistics that
describe the actual evacuation operation. Total evacuation time, rate of evacuation, wait
times through the system, and closure times for APs are all easily lifted from the optimal
solution. This is a tremendous improvement over the state of the existing plan where the
time and resource requirements of this mission were essentially unknown. Now 2ID can
actually manage and allocateresources at the outset of a NEO to shape the operation to meet
its other mission requirements. Second, this method addresses another weaknesses in the
current planning, specically the assignments of the transportation assets under 2ID
control. Whereas before the strategy of purely reactive; now the routing procedure yields a
detailed schedule for each asset that is driven by the solution to minimize evacuation time.
Example reports to help manage a NEO at the tactical and operational level are provided in
the Appendix.
5. Case study
5.1 Base scenario and performance metrics
The standard model outputs are useful, but the true utility of this methodology is demonstrated
in the form of a case study. To illustrate this and prove its ability to aid decision makers in both
planning and orchestrating a noncombatant evacuation, we present a series of experiments
based on a plausible evacuation scenario. This study consists of two parts: one focused on
planning the evacuation under additional mission requirements and the second revolving
around responding to changes in the environment as the operation is conducted.
For the purposes of this exercise, the base scenario to be investigated will evacuate
156,545 noncombatants with a eet of 12 CH-47 Helicopters, 100 passenger buses, 24 trains
and will consider an arrival rate that corresponds to an average of 2.5 days to complete
assembly. The logic for starting at this conguration is that it represents a middle position
between likelihood of occurrence and stress placed on the system and will therefore be of the
greatest value for 2ID (LTC Erickson, 2018).
This conguration results in the evacuation taking 8.6 days or 207.5 h to complete, the
evacuation rate is 754.4 people/h, the average evacuee wait time in the system is 58.3h, and
on average the AP sites close at 5.9days. Figure 6 describes the inow of arrivals into the
system and captures their outow and the completion of the evacuation. For clarity, these
plots use a 1 h time step.
5.2 Planning requirements and adjustments
To demonstrate the value of this model as a tool for 2ID requires employing it under more
realistic conditions. In the course of a real evacuation it is understood that 2ID will be
Figure 6.
(color online) Inow
and outow v time
period of the base
Modeling and
conducting numerous missions simultaneously and that NEO requirements will be in
competition for organizational energy and resources. This study attempts to replicate an
evacuation scenario that is representative of the true requirements for 2ID by building in
three additional requirements.
Consider the following scenario: the deterrence efforts of the USA, South Korea and the
broader international community have faltered and direct military conict with North Korea
appears imminent. The US Department of State has indicated that a NEO of all DoD
Families, USG Employees and US Citizens will begin in two days. 2ID has elevated its
readiness posture and is planning for forward mobilization and occupation of designated
defensive battle positions in 9.5 days. 2ID scouts, who for the purposes of this case study
operate AP3, are expected to establish a screen and conduct reconnaissance and surveillance
missions beginning in six days. Additionally, stores of bulk rations and water are limited
and can only reasonably support the population that needs to be evacuated for 24h.
There are three requirements in the case study:
(1) early closure of AP3;
(2) time limit for the evacuation;
(3) evacuee wait times of less than 24 h.
Each facet of this scenario explores a different constraint, or a different way to adapt the
model to meet the needs of 2ID. The rst requirement focuses strictly on ending the mission
before the base experimentation conditions say it can be completed. As previously
mentioned, 2ID can shift focus and reposition its own resources and this iteration will meet
the new mission requirements by determining just how much additional eet capacity of
each mode is required to satisfy the need. The second stipulation implies that the early
closure of an AP is necessary, and this directed model adjusts the arc capacity according to
the required closure time to ensure that occurs. The third requirement is aimed at limiting the
waiting time of evacuees as they move through the system. Evacuees are told to assemble
with food and water, but 2ID would have supporting rations available and therefore the wait
time through the system needs to be less than 24 h.This iteration of planning investigates the
impact of metering arrivals into the system by making directed announcements to specic
slices of the evacuation population. This case study attempts to demonstrate how early
planning with the model can be rened to meet real-world operational requirements (Table 1).
5.2.1 Requirement 1. Early AP closure. The rst additional requirement is the mandated
closure of an AP on a particular day. It is necessary to start with this requirement as it can
be achieved only by modifying the structure of the time-staged network. Once this
adjustment is made, subsequent required changes will all operate within the new framework
and the results will build in a cumulative manner; otherwise, they would be independent and
thus less useful.
Table 1.
Case study
requirements beyond
the base scenario
Issue addressed
Arrival profile
(mean arrivals
complete at day) Helo Bus Train
Evac time
Evac time
Average evacuee
waiting time
AP site 3
Base scenario 2.5 12 100 24 207.50 8.65 58.32 8.96
requirements ––180 7.5 24 4
Constructing an evacuation plan that ensures AP3 is closed before Day 4 is slightly more
complicated than a direct parameter adjustment, but is still easily handled by the model.
However, before changes to the model are made it is rst necessary to ensure that whatever
the desired AP closure time occurs after evacuee assembly is complete. The assembly
timeline acts as a lower bound for site closures, as the operating assumption is that a site
cannot be closed down while evacuees are still arriving. If that condition is met, then it is
possible to achieve an early AP closure by placing an upper bound of zero on the trans-
period arcs beginning on the required closure day. That modication essentially ensures
that all evacuees that arrive into AP3 have departed before the upper bound is applied. Once
this constraint is factored into the model, the objective function will allocate assets in such a
way to ensure all evacuees are clear before Day 4.
This can be seen in the allocation of assets on Day 4 as well as the summarized results of
the descriptive statistics for the full schedule. Table 2 highlights the changes in the key
metrics and details how the new schedule meets the additional requirements. It should be
noted that this constraint slows the evacuation slightly and that further adjustment and
experimentation is necessary to ensure the schedule meets the new planning requirements.
5.2.2 Requirement 2. Time limit. The second requirement to plan against is the
evacuation completion suspense at NEO þ7.5 days as a result of another operation. Further
experimentation with the model at the population level of interest yields information about
the sensitivities to changes in certain eet sizes. Twelve additional experimental runs were
made, while varying the levels of each specic transportation mode, as opposed to the
simple capacity adjustments made during earlier experimentation.
Using the results from those additional runs, a simple linear response surface model
(Law, 2007) was constructed to allow for the quick and reasonably accurate calculation of
evacuation times based on varying quantities of bus, helicopter and train assets. Buses (or
other ground transportation assets) are the most abundant transportation asset available to
2ID, and while other asset congurations do exist, for simplicity and feasibility only buses
and helicopters have been adjusted to illustrate the impact of changing capacities. Table 3
illustrates how running the model for a variety of bus and helicopter eet sizes provides
understanding of the trade-offs involved and the relative value of assets. Applying the
response surface model showed that adding 31 buses will ensure that the plan meets the
mission requirement of completing the evacuation in under 7.5days, but it is necessary to
check this estimated performance using the model as the relationship is not strictly linear.
For example, running the model with 31 additional buses actually produces an evacuation
time of 162 h, and so it is unnecessary to add all 31 buses to meet the requirement. The
values in Table 3 are results from repeated runs of the optimization model. Application of
the predictive expression and simple adjustment of the parameters represent the most direct
way to improve model performance, and it lends invaluable insight for advanced planning
by 2ID. For more details see Kearby (2019).
5.2.3 Requirement 3. Evacuee wait times. The third new mission requirement to plan
against concerns the available supply of rations for the evacuees and therefore the waiting
time through the system. With a limited supply of rations available the wait time in the
system needs to be less than 24 h. Due to the fact that for much of the evacuation process the
model is operating at maximum capacity, it is necessary to try and inuence the arrival
prole to affect wait times through the system.
The arrival process represents one of the areas of greatest uncertainty within the model,
and so while it is possible to inuence or direct the behavior of the evacuees, when they will
actually arrive is difcult to predict with a high degree of condence. That uncertainty is
built into the arrival process during the initial formulation, but the adjustments made in this
Modeling and
Issue Addressed
Arrival profile (mean arrivals
complete at day) Helo Bus Train
Evac time
Evac time
Average evacuee waiting
time (hours)
AP site 3
Base schedule 2.5 12 100 24 207.50 8.65 58.32 8.96
AP3 closure on Day 4 2.5 12 100 24 207.50 8.65 62.90 4.00
NEO complete by Day 7.5 2.5 12 121 24 180.00 7.50 49.79 4.00
Less than 24 hr wait time Meter at 2.5, 3.5, 4.5, 5.5 12 121 24 185.00 7.71 20.39 4.00
All planning requirements Meter at 2.5, 3.5, 4.5, 5.5 12 126 24 179.50 7.48 18.24 4.00
Notes: Each row depicts the impact of each additional planning factor on the performance of the evacuation operation. In the nal row, all factors have been
addressed and enough assets have been added to keep performance within the acceptable range
Table 2.
Progression of the
requirements case
consideration further those early arrival assumptions. The rst formulation makes the
assumption that the arrival process will be complete in a specied number of days based on
when evacuees are notied. This new consideration advances that assumption by
supposing that individual portions of the total evacuee population will behave
independently according to their notication. For the smallest populations this is not
unreasonable as DoD families and USG personnel have likely experienced some NEO
training and can be expected to understand the implications of staggered notication and
report when they are directed. But as the evacuee population expands to US Citizens or
TCNs, this assumption may erode and the arrival prole may become more variable.
Operating as if the assumption is valid, it is possible to notify slice elements of the total
population in to produce an arrival prole that could aid in reducing the evacuee wait time
through the system.
With that assumption in place, the arrival prole can be modied by the number of
notications and evacuee population slices they address. Inherently, there are risks present
in this option as those evacuees who are not notied to assemble may remain in a hostile
area for a longer period, but this represents a working strategy to reduce waiting times.
Again, to determine the required number of notications further experimentation with the
model is necessary and so the number of notications is incrementally increased until the
waiting time is reduced to below the working threshold. For example, if there are to be three
notications, one third of the evacuees will be notied on each subsequent day. This
effectively meters the arrivals into the system and limits evacuee wait time. It is important
to note that as the arrival prole is modied by multiple announcements, other key metrics
change as well, and so any complete solution will require further adjustments.
5.2.4 Planning requirements case study result. The planning portion of this case study
illustrates how the model can be employed to handle a number of different planning
considerations beyond the direct evacuation mandate. Applying the changes discussed for
each of the additional requirements to the model produces the schedule performance
captured in the Table 2 and Figure 7.
5.3 Disruptions and adjustments
The next phase of this case study is focused on the execution of an evacuation and how to
use the model in response to disruptions or other variable circumstances. Building on the
planning scenario, three additional disruptions will be applied that the model must account
Table 3.
Visualization of total
evacuation time
changes against
varying bus and
helicopter eet sizes
Total evacuation time (Hours)
3 6 9 12 15 18
50 391.5 379.5 369.5 354.5 342 337
75 284.5 271.5 263 260 259.5 248.5
100 218 214.5 211 207.5 204.5 203.5
125 183 182 178 176 175 172.5
150 161 160 157 155 154 151
175 147 144 141 140 139 138
200 129.5 129 128.5 128 127.5 126.5
Note: Here the train eet is held constant at 24. All values are the results from the optimization model in
section 4.3
Modeling and
for while scheduling assets. Consider the following likely events: loss of transportation
assets as a result of military conict, closure of a route or arc and the irregular arrival of
evacuees to APs. In terms of the actual implementation, the model will account for the loss of
eight helicopters from the eet from Day 3 forward, the closure of all bus routes from AP1
Camp Casey to Busan beginning on Day 4, and the irregular behavior of arrivals into the
Summarizing disruptions to the evacuation:
(1) irregular arrival of evacuees;
(2) loss of assets; and
(3) closure of evacuation routes.
5.3.1 Disruption 1. Irregular arrivals. Real time utilization of the model and transportation
asset scheduler is driven by the reporting of arrivals by the units managing each AP. To this
point, arrivals to APs have been approximated by the Poisson distribution detailed in
Section 4.2. This adjustment marks a change how arrivals come into the system by
attempting to simulate an irregular arrival distribution for the model to schedule against
since actual NEO arrival patterns can vary greatly(Scheer, 2011;Kuchell, 2013). This is
accomplished rst isolating the periods in which arrivals occur and recording the
corresponding arrival quantities. Those arrival quantities are then randomly assigned to the
range arrival periods to create a new, and irregular distribution for the model to deal with.
Depending on what requirements the model is attempting to account for, the irregular
distribution could present a better or worse alternative to the incumbent Poisson
Figure 7.
(color online) Inow
and outow v. time of
the solution to the
planning case study
distribution. With the new arrival distribution generated to simulate the reporting of APs,
the remaining disruptions can be applied to the model to further demonstrate how the model
can be used during the course of an evacuation. Figure 8 highlights the performance of
model considering this irregular distribution of arrivals. Of interest, this particular irregular
arrival prole erodes the performance of the schedule as it yields a slower total evacuation
and longer wait times than that of the planned scenario. This will not always be the case as
the arrival prole could as easily skew early as opposed to the slightly early distribution
created for this model. This further reinforces the utility of running of the model and
scheduling procedure repeatedly as new information is reported from the APs.
5.3.2 Disruption 2. Loss of assets. It is probable that over the course of an evacuation the
size of the transportation eet could change as a result of maintenance issues or military action.
Suppose that on the third day of the planned evacuation, eight helicopters are lost to
maintenance issues. The model can account for this change in capacity through the adjustment
of the train constraints beginning on Day 3. Conceptually, this is fairly straightforward
however due to the time-staged nature of the network it is a tedious implementation. Currently,
the capacity constraints operate in three ways. Single arcs have an upper bound related to the
total eet capacity of a particular transportation mode. Transportation mode arcs are also
grouped by type and are collectively assigned an upper bound according to their total eet
capacity across a number of time periods. Thisensuresthatthecapacityisnotexceededin
either a single time period or a series of time periods where transportation is occurring. The
third constraint only applies through the rst half of the arrival process and ensures that arc
ow, if scheduled, will only occur above a specied minimum occupancy level. Therefore, no
trips of single digit passengers will be scheduled by the model. As a result of this formulation,
adjusting the capacity of a particular transportation mode within the schedule essentially
requires the construction of a second complete set of constraints to reduce the ow beginning in
Figure 8.
(color online) Inow
and outow v time
considering irregular
arrivals, loss of assets
and arc closures
Modeling and
a particular time period. Building on the results of the initial case study and factoring in the loss
of assets, Figure 9 depicts the revised schedule performance. Comparing against Table 4,total
evacuation time slips from 179.5 to 186.5 hours with the loss, and so 2ID would need to look to
shift assets to complete the mission within their requirements.
5.3.3 Disruption 3. Arc closures. As with the mandatory closure of an AP on a specied
day, the closure of any arc is easily accounted for by the adjustment of its upper bound.
Within this scenario, the bus arcs connecting AP1 at Camp Casey to Busan Station, the
Reception Center and the SPOD have been disrupted as a result of the military conict,
beginning on day 4. At this point, to adjust the model to account for the constraint, an upper
bound of zero can be applied to the bus arcs from AP1 beginning in time period 192, or day 4.
With this constraint, the model will schedule assets around these closed arcs and still seek to
minimize the total time of the evacuation. Figure 9 and Table 4 highlight the complete effect
of all disruptions, arc closures, the attrition of train assets, and the irregular arrival prole.
In total, this disrupted evacuation fails to meet a number of the requirements established
in the planning portion of this case study, and therefore to satisfy those demands 2IDneeds to
determine what additional assets are required to achieve the required schedule performance.
5.4 Complete case study solution
The disruptions applied to an evacuation within this case study illuminate the structural
challenges present in keeping schedule performance to within an acceptable range. That said,
this model provides a fast and expedient method to analyze and adjust the plan to meet mission
requirements in response to disruptions. For the purposes of this evacuation scenario and
considering the disruptions, 2ID would need to source 42 additional buses following the loss of
Figure 9.
(color online) Inow
and outow v. time of
the complete case
study solution
Issue addressed
Arrival profile (mean arrivals
complete at day) Helo Bus Train
Evac time
Evac time
Average evacuee
waiting time (hours)
AP site
3 closure
Planning case study solution Irregular 12 126 24 181.50 7.56 11.27 4.00
Loss of 8 helicopters on Day 3 Irregular 4 126 24 186.50 7.77 11.24 4.00
AP1 bus arc closed on Day 4 Irregular 4 126 24 213.00 8.88 26.345 3.979
All planning requirements and disruptions Irregular 4 168 24 179.5 7.4792 10.156 3.979
Notes: Each row depicts the impact of each disruption on the performance of the operation. The last row describes the full operation performance building on
the planning solution by adding in assets or rerouting based on attrition and closures in specic periods
Table 4.
Progression of the
disruptions case
Modeling and
8 helicopters and the closure of bus routes out of AP1 to keep the schedule on track to meet the
required metrics. Table 4 shows the accumulating effects of the disruptions and shows the nal
schedule performance factoring the additional assets that are required to get the schedule
within the acceptable performance levels. The impact of these disruptions on schedule
performance is considerable and may point to some inherent weakness in the evacuation
network itself that 2ID could look to design around moving forward.
6. Conclusion
The primary goal of this work was to model the noncombatant transportation network in
South Korea and devise an intelligent method for the allocation of transportation assets to
facilitate a timely evacuation. The next objective was to analyze the performance of the
model under various circumstances and identify ways to improve or respond to additional
planning factors or address issues that could arise during the execution of the mission.
Viable asset allocation schedules were created through the development and application
of a time-staged network ow model coupled with a Poisson arrival process which facilitates
an understanding of the required time and resources complete evacuation. Depending on the
scenario, it is possible to calculate, and subsequently verify, how adding to or subtracting
from the eet size of a particular transportation mode impacts the evacuation time. It is
possible to bound the model in such a way as to close APs early and schedule around the
closure of specic routes and nodes in response to disruptions. And it has been shown how
affecting the prole of arrivals can be used to limit waiting time through the system. The
procedures describedin this paper provide 2ID, and similarly situated GCCs, with a working
methodology that can be applied to their circumstances to successfully allocate and schedule
resources to complete noncombatant evacuation missions.
This work contributes to military NEO applications and the literature in a few ways. It
seeks to improve the decision-making and resource allocation methodology used by 2ID in
South Korea, and addresses an obvious need in that instance. But broadly, this work is
productive for noncombatant operations as a mission set. This work has clear application in
the Baltic States and Germany, where similar population levels and infrastructure require
intelligent resource allocation in the event of an evacuation. And looking inward, military
support to natural disaster evacuations within the USA provides another application for this
model, albeit with different motivating circumstances. The formulation of this problem is
based on the optimization of tactical decisions within an evacuation mission. This is unique
in that previous works are planning-oriented and focus on what resources can be pre-
positioned, what routes and locations will be used and how can we optimize an evacuation
on the front end. This work constructs process to use in near-real time to conduct evacuation
optimization in response to arrivals and a uid transportation infrastructure where assets
are re-allocated and adjusted throughout a mission using situation reports. To summarize,
this work contributes to the military understanding and execution of NEO missions by
using optimization tools to make tactical decisions within the execution of an operation.
The recommended course of action for 2ID is to use the model and scheduler during the
annual South Korea NEO simulations: Operations Courageous Channel and Ulchi Freedom
Guardian. The transportation assets can be allocated according the models solution and
updated in real time as reports of arrivals come into system and disruptions occur. Through
iteration, that process would likely reveal other areas to improve and streamline the function
of the complete system so that 2ID could be better prepared to respond and facilitate a
successful operation in the event of a real world NEO.
Noncombatant evacuation operations in South Korea present a complex problem with many
intriguing areas for future research. An exploration of the sensitivity of this model to changing
arrival rate parameters based on proximity to North Korea, variable travel times to account for
trafc and congestion, and accounting for mis-routed transportation assets would all be of
interest in future work. Study of the evacuation network itself would also be invaluable; critical
nodes and specic routes within the schedule could be identied to reduce risk and formulate a
more robust solution, better prepared to avoid and manage disruptions. This a rich and
meaningful problem with many opportunities for further investigation.
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Modeling and
The coupling of the optimization model with the vehicle routing procedure post-processing the
solution provides two different useful operational reporting capabilities. Obviously, by denition the
solution provides immediate visibility into evacuee ow by mode and by location over time. This can
be aggregated, as demonstrated in Figure A1, to product a high-level overview of the schedule
suitable for certain military echelons.
However, this still requires units to assign these trips from the schedule to individual assets (including
pilots, drivers, etc.). Fortunately, the vehicle routing procedure produces this level of detail which is nested
with the aggregate view. This provides detailed instructions for individual assets and a summary utilization
report, depicted by Figure A2, showing when each asset will be in operation. This also permits visualizing
downtime for maintenance planning and assists in being able to quickly redirect assets as things inevitably
change throughout a day. Other examples of visualizations may be found in Kearby (2019, p. 27, 29, 31-32).
Figure A1.
Example report
showing next three
days of evacuee
movements by mode
of transportation
List of acronyms
2ID = 2nd Infantry Division;
AP = Assembly Point;
A/SPOD = Air/Sea Port of Debarkation;
DoD = Department of Defense;
DOS = Department of State;
GCC = Geographic Combatant Command;
HN = Host Nation;
MEDEVAC = Military Aeromedical Evacuation;
MILP = Mixed Integer Linear Program;
NEO = Noncombatant Evacuation Operation;
TCN = Third-Country National; and
USG = US Government.
Corresponding author
John A. Kearby can be contacted at:
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Figure A2.
Example utilization
report for buses on
Day 2
Modeling and
... Ref. [116] extended the work of [117] in addressing both the vehicle routing as well as the flow of arrival of evacuees pattern similar to [118], which, according to the author, would improve the effectiveness of the evacuation planning. A network consisting of two sub-network is proposed where the former addressed the maximum flow as well as the earliest arrival pattern flow of evacuees, while the latter is attributed to the vehicle routing of buses in transporting evacuees to a safe shelters with limited capacity. ...
... A Noncombatant Evacuation Operation (NEO) is considered by [118] to facilitate the decision makers in evacuating civilians as well as other noncombatant in South Korea to a safe location. A time staged network model is proposed as a MILP model with the objective of minimising the required evacuation time. ...
... Furthermore, ref. [53] addressed the cooperation between air and land transport. More depictions of inter-modal networks are seen in [33,52,90,104,118]. Additionally, the routing problem is not unique to just land vehicles. ...
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The growing field of humanitarian operations is driven by frequent events of disasters seen in the world today. Within this field, Operations Research (OR) plays a critical role in alleviating the suffering of victims that are impacted by disasters. This paper focuses on the branch of a well-known OR problem, known as the Vehicle Routing Problem (VRP), within the selected scope of humanitarian operations. A total of 123 papers of the last decade are reviewed and classified under the humanitarian operations of supply and delivery, evacuation as well as rescue operations. Besides specific disaster management phases and disaster types, various modelling challenges are highlighted, hinting towards a richer and more complex VRP seen under selected model characteristic classifications. Furthermore, established solution approaches, including hybrid solutions, are highlighted and classified, discussing how they are applied in the context of these humanitarian operations. The inclusion of a machine learning solution approach under the same classification is proposed. Finally, the trend and future outlook of VRP for the suggested humanitarian operations are discussed and highlighted.
... Their objective also seeks to minimize helicopter fleet utilization as well as minimize the cost of helicopter routes. Unlike the DARP problem, many military applications prioritize other objectives over cost with approaches optimizing mission objectives, readiness, robustness, resilience and other factors (Kirby et al., 2020;Longhorn and Stobbs, 2021). ...
... Their objective also seeks to minimize helicopter fleet utilization as well as minimize the cost of helicopter routes. Unlike the DARP problem, many military applications prioritize other objectives over cost with approaches optimizing mission objectives, readiness, robustness, resilience and other factors (Kirby et al., 2020;Longhorn and Stobbs, 2021). ...
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Purpose The purpose of this study was to create an air movement operations planning model to rapidly generate air mission request (AMR) assignment and routing courses of action (COA) in order to minimize unsupported AMRs, aircraft utilization and routing cost. Design/methodology/approach In this paper, the US Army Aviation air movement operations planning problem is modeled as a mixed integer linear program (MILP) as an extension of the dial-a-ride problem (DARP). The paper also introduces a heuristic as an extension of a single-vehicle DARP demand insertion algorithm to generate feasible solutions in a tactically useful time period. Findings The MILP model generates optimal solutions for small problems (low numbers of AMRs and small helicopter fleets). The heuristic generates near-optimal feasible solutions for problems of various sizes (up to 100 AMRs and 10 helicopter team fleet size) in near real time. Research limitations/implications Due to the inability of the MILP to produce optimal solutions for mid- and large-sized problems, this research is limited in commenting on the heuristic solution quality beyond the numerical experimentation. Additionally, the authors make several simplifying assumptions to generalize the average performance and capabilities of aircraft throughout a flight. Originality/value This research is the first to solve the US Army Aviation air movement operations planning problem via a single formulation that incorporates multiple refuel nodes, minimization of unsupported demand by priority level, demand time windows, aircraft team utilization penalties, aircraft team time windows and maximum duration and passenger ride time limits.
... Application of the predictive expression and simple adjustment of the parameters represent the most direct way to improve model performance, and it lends invaluable insight for advanced planning by 2ID. For more details see Kearby (2019). 5.2.3 Requirement 3. Evacuee wait times. ...
Purpose: The purpose of this paper is to investigate US noncombatant evacuation operations (NEO) in South Korea and devise planning and management procedures that improve the efficiency of those missions. Design/methodology/approach: It formulates a time-staged network model of the South Korean noncombatant evacuation system as a mixed integer linear program to determine an optimal flow configuration that minimizes the time required to complete an evacuation. This solution considers the capacity and resource constraints of multiple transportation modes and effectively allocates the limited assets across a time-staged network to create a feasible evacuation plan. That solution is post-processed and a vehicle routing procedure then produces a high resolution schedule for each individual asset throughout the entire duration of the NEO. Findings: This work makes a clear improvement in the decision-making and resource allocation methodology currently used in a NEO on the Korea peninsula. It immediately provides previously unidentifiable information regarding the scope and requirements of a particular evacuation scenario and then produces an executable schedule for assets to facilitate mission accomplishment. Originality/value: The significance of this work is not relegated only to evacuation operations on the Korean peninsula; there are numerous other NEO and natural disaster related scenarios that can benefit from this approach.
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Introduction Fencing is a combat sport with fierce confrontation and variations in offense and defense. To a certain extent, speed is the decisive factor in winning the game. Objective To explore the influence of different training methods on the reaction time of fencers. Method 20 fencers were selected and divided into three groups with different fencing levels, in addition to one control group. The experimental groups trained in three 10-minute sessions a week. The control group trained for 3 hours in the afternoons, from Monday to Saturday. Results After training, the experimental group fencers showed a highly significant difference in the selective response to foot movement (t=4.004, P=0.001<0.01). The simple reaction test of the fencers in the control group improved slightly after training, but it was not statistically significant (t=2.223, P=0.09>0.05). In the selective reaction time test without foot movement, the reaction time of the control group was significantly lower after training (t=3.450, P=0.026<0.05). Conclusion Regardless of the student›s fencing level, different training methods can significantly improve their reaction time. Level of evidence II; Therapeutic studies - investigation of treatment results. Keywords: Response; Training; Reaction Time
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