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 ef ﬁciency of those missions. Design/methodology/approach –It formulates a time-staged ne twork model of the South Korean noncombatant evacuation system as a mixed in teger linear program to determine an optimal ﬂow con ﬁguration that minimizes the time required to complete an evacuat ion. 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 solut ion is post-processed and a vehicle routing procedure then produces a high resolution schedule for each indivi dual asset throughou t 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 previouslyunidenti ﬁable 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 signi ﬁcance 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 bene ﬁt 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 Anal ytics and Logistics . Published by Emerald Publishing Limited. This article is published under the Creative Commons Attrib ution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for bothcommercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http:/ /creativecommons.org/lic ences/by/4.0/legalcode Disclaimer: The views expressed in this paper are those of the authors and do not re ﬂect the oﬃcial 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 O ﬃce (grant # W911NF1910055). The authors gratefully acknowledge the support and assistance of the 2nd Infantry Division C5 and ORSA Planning Sta ﬀin 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 OsmanOzaltin provided useful suggestions that greatly enhanced the presentation of technical details. This paper also bene ﬁted from constructive comments from the editor and two reviewers that improved both the content and presentation.Modeling and transportation planning 41 Received 28 May 2019 Revised 27 August 2019 13 October 2019 15 November 2019 Accepted 20 November 2019 Journal of Defense Analytics and Logistics Vol. 4 No. 1, 2020 pp. 41-69 Emerald Publishing Limited 2399-6439 DOI 10.1108/JDAL-05-2019-0010The current issue and full text archive of this journal is available on Emerald Insight at: https://www.emerald.com/insight/2399-6439.htmKearby, J.A., Winz, R.D., Hodgson, T.J., Kay, M.G., King, R.E., & 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, 41–69. 1. Introduction 1.1 Noncombatant evacuation operations de ﬁnition 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 ,J P3 –68). These operations generally occur as a result of military conﬂict, 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 canhave 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 –speciﬁcally 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 ,J P3 – 68). There are six GCCs chartered with this broad mission and generally the GCCs assign country speci ﬁc 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 theoperations. 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 ﬁxed-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, suchas 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 city of Tirana. The US Navy ’s 6th Fleet inserted a company of Marines into the US Embassy and adjacent housing compound to provide establishsecurity 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 noncombatantevacuation scenario. 1.2 South Korea characteristics South Korea presents a number of challenges for an evacuation beyond the base scenarioscovered 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 F –77 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 thereasonable capacity of military aircraft available for evacuation and therefore theJDAL 4,1 42 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 dif ﬁcult to rehearse and re ﬁne 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 thepeninsula 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 con ﬂicts 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 evacuationrequires 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 comprisesnumerous routes and modes of transportation, and there is a nearby credible threat in NorthKorea prepared to disrupt evacuation operations. 1.3 Framing the noncombatant evacuation operations problem for 2nd infantry division While the signi ﬁcance 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 ﬂexible plansFigure 1. Operation Silver Wake, Albania 1997 – Point-to-point evacuation from US Embassy in Tirana to US Navy ships in Adriatic Sea Modeling and transportation planning 43 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 and executing 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 noti ﬁed 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 anad 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 thiscomplexity has made it dif ﬁcult for them to devise a comprehensive and logical approach. Additionally, the presence of a signi ﬁcant North Korean threat occupies much of the 2ID planners ’attention, leaving portions of the evacuation operation unexplored. Speci ﬁcally, 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 toFigure 2. The South Korea NEO mission starklycontrasts with the typical NEO scenario described in Figure 1 JDAL 4,1 44 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 ﬁeld, Section 4 outlines the speci ﬁc 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 ﬁnal 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 addressingthe current planning de ﬁciencies and making the full problem more accessible and manageable for those involved. That begins with modeling and analyzing the speci ﬁc physical transportation network in play during an evacuation and then establishing areasonable estimate of how evacuees will enter that system. Then the best and most feasiblemanner in which people can be evacuated, given limited resources, can be determined andthose limited resources can be allocated in such a way as to deliberately achieve that bestpossible 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 singletask within a large mission set for 2ID, and it must be conducted in conjunction with otherresponsibilities. Therefore, any methodology needs to be ﬂexible 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 ﬂeet and so each asset will be used multiple times through the course of a NEO. Additionally, noncombatants are expectedto arrive at multiple pre-determined locations across the country, and they are expected todo so at variable rates. Finally, there exists a centrally controlled transportation ﬂeet that can be employed to execute a NEO which we limit to buses, helicopters, and trains. We donot consider ﬁxed-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 de ﬁnes 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 locationto a separate safe haven. It is also apparent that the allocation of assets and any networkanalysis was done on a purely practical basis during the mission planning processes. As aresult of those factors, past NEO missions do not provide signi ﬁcant 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 futureModeling and transportation planning 45 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. ,2 0 0 2 ). These models make signi ﬁcant improvements over their control simulations but would have to be heavily modi ﬁed to account for the complexity of the South Korea evacuation network. More generally, multi-agent models have also beenapplied 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 dif ﬁculty of getting accurate arrival and process data, making validation dif ﬁcult; 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-speci ﬁc and also rely on discrete event simulation (Scheer, 2011 ). The authors study a small NEO with two different ﬁxed 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 modelsEmergency medical evacuations conducted by military and civilian organizations represent a closely related ﬁeld of research to noncombatant evacuations. Signi ﬁcant 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 asset s in such a way as to provide the best possible service times for units in active combat zone s. 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 a nd approximate dynamic programming to optimize the dispatching of assets. Similarly, civilian emergency medical evacuation models generally classify into those that address the st aging locations of emergency vehicles, those that reallocate vehicles by either multi- period mixed integer linear or dynamically programming when demand is exceeded, or th ose that are principally concerned with dispatching and routing vehicles as m edical emergencies are reported ( Aringhieri et al.,2 0 1 7 ). Most relevant to this scenario are models that ar e 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 tacti cally 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 repositioni ng of assets. To summarize, both military andJDAL 4,1 46 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 evacua tions look to provide the most prompt service to individual demand points. 3.3 General evacuation models A number of studies use network ﬂow 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 ﬂows with time-expanded networks for buildings ( Shin et al.,2 0 1 9 ;Choi et al.,1 9 8 8 ;Chalmet et al., 1982 ) or cities ( Limet al.,2 0 1 2 )t o 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 ﬂow 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 window and Shin et al. (2019) introduce multiple options for the objective function. For a recent survey of time-expanded network ﬂow models, refer Dhamala (2014) . For suf ﬁciently large problems with computational runtime issues, recent studies have also explored heuristics and inexact algorithms that use Dijkstra ’s algorithm to identify evacuation paths feeding a constructive approach that maximizes and schedules the ﬂow on each path ( Shin et al., 2019 ;Limet al.,2 0 1 2 ).Luet 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 371 acre area to 7 safe zones. Others, such as Ganet al. (2016) , integrate optimization with traf ﬁc simulation for a hybrid approach. While speci ﬁc work on noncombatant evacuations appears limited, the broader category of evacuations related to natural disasters shows signi ﬁcantly more breadth and depth of investigation. Most existing studies recommend implementing contra ﬂows or lane reversals in various critical areas of the networks to smooth out ﬂow and reduce congestion and wait times ( Praveen et al. ,2 0 1 0 ). 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 traf ﬁcﬂow 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 thatthe 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 signi ﬁcantly in urban areas, where the population to be evacuated is based. These issues point to another aspect of evacuation models –speciﬁcally 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 traf ﬁc address the approximate scale of the problem –such as the evacuation Knoxville and Knox County, TN, requiring 157,733 vehicle trips ( Yuan et al.,2 0 0 6 ;Yuan, 2005 )–yet the most pertinent and promising studies to thisModeling and transportation planning 47 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 SouthKorea. A number of signi ﬁcant 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 ﬂeet 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 arrivalsinto the system (Lakshay and Bolia, 2019; Song and Yan, 2016 ;Goerigk and Grün, 2014 ; Abdelgawad et al. ,2 0 1 0 ) and some use a vehicle routing procedures to recommend bus routes to minimize total evacuation times. Many are based on known pickup and drop offlocations 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 Grü n(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 speci ﬁc 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 bythe 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 re ﬁne its recommendations based on actual arrivals into the system as well as ﬂuctuating bus, train and helicopter ﬂeet 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 thesystem. A mixed integer linear program that integrates those facets, along with the existing works use of demand uncertainty, de ﬁned intake locations and the general minimization of total evacuation time would yield a tool that recommends optimal employment of limitedassets to achieve an evacuation in South Korea. 4. Methodology Aspects of the South Korea evacuation scenario coupled with the speci ﬁed objectives of 2ID naturally point toward the application of a minimum cost network model to optimize the ﬂow 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 con ﬁguration of evacuee ﬂow 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 andgives 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 thesequence of events and the ﬂow of personnel within an evacuation so that the model and its features can be clearly communicated. First, the most typical scenario for an evacueeJDAL 4,1 48 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 Portof 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 ﬂown by helicopter from the AP to a more advantageous position south for rail transit. 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 viabus, 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 thebasis for the network structure. 4.1.2 Time-staged expansion. Recall the leading assumptions that the number of evacuees exceeds the ﬂeet 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 ﬁrst determine the travel times for all of the bus, train, and helicopter arcs. This is achieved through the use of web-based navigationFigure 3. General solution procedure and outputs Modeling and transportation planning 49 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 tothe arcs that physically transport evacuees, as a result of the time-staged construction there are also arcs that carry ﬂow 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 inthe optimization model. In this con ﬁguration it is convenient to include a source and sink node to easily capture and motivate all ﬂow 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 locationsspread across the country at an unknown rate. Due to the scale and political implications ofan 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 2018 F-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 suf ﬁcient data to incorporate them here. Using the F-77 data and the assumption that people will be evacuated through the nearestAP, this paper directly calculates the number of people who are expected to be evacuatedFigure 4. (color online)Network structure of South Korea evacuation JDAL 4,1 50 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 arriveat each location in each speci ﬁc time period can be determined. It is reasonable to assume that arrivals follow a Poisson distribution because the behavior and arrival time of widelydistributed individual evacuees to APs are unrelated to one another and independent. The following summarizes the modeling of the arrival process: qit¼PitfW¼wg/C1population i (1) where qit = Number of evacuees arriving at node iat time period t population i = Total evacuees assigned to assemble at node i; PitfW¼wg¼lizðÞ we/C0liz w!= Probability of complete evacuation of node iat time period t; li = 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-speci ﬁc arrival pro ﬁles, 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 qitin 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 thenotation, formulates the model and discusses the model. Sets N = Set of Unique Node Locations; NA/C26N= 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 population i= Total number of personnel to be evacuated by assembly node i[NA; qit = Planned personnel arriving at node iin time period t; ckðÞ ijt= Cost penalizing out ﬂow directly related to the time period in which ﬂow occurs; A(k)= Network incidence matrix describing network structure for mode k; and pkðÞ ij= Transit time (in time periods) from node ito node jusing mode k. Parameters L(k)= Minimum number of evacuees to use a single asset for mode k;and U(k)= Total ﬂeet capacity for mode kin number of evacuees.Modeling and transportation planning 51 Decision Variables xkðÞ ij= Evacuee ﬂow from node ito node jusing mode kin time period t; and ykðÞ ij= Indicator for Evacuee ﬂow from node ito node jusing mode kin time period t Model formulation min xX ijktckðÞ ijtxkðÞ ijtðÞ (2) x0ðÞ s;j2NAtðÞ¼qjt 8j;t (3) X iktxkðÞ i;dtðÞ¼X jtqjt (4) X iji;j2AkðÞxkðÞ ijtðÞ/C0X iji;j2AkðÞxkðÞ jitþpkðÞ ji/C16/C17 ¼08j;k;t (5) xkðÞ ijtðÞ#UkðÞykðÞ ijtðÞ 8k;i;jðÞ2AkðÞ;t (6) xkðÞ ijtðÞ/C21LkðÞykðÞ ijtðÞ 8k;i;jðÞ2AkðÞ;t¼1;... ;li (7) Xt t¼t/C0pkðÞ ij/C0/C1þxkðÞ ijtðÞ#UkðÞ8k;i;jðÞ2AkðÞ;t(8) xkðÞ ijtðÞ/C210 and Integer (9) ykðÞ ijtðÞBinary (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 forexiting the network in each period, with the cost increasing according to the period in which the exit occurs. In the results presented below, ckðÞ ijt¼t, which is simultaneously equivalent to minimizing the average time for an evacuee or maximizing the evacuation output in the ﬁrstntime periods for n#T, where Tis the minimized time to evacuate the network achieved by (2) ( Jarvis and Ratliff, 1982 ). In general, ckðÞ ijt¼tshould 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 indifferent q it. Constraint (4) requires all evacuees to be evacuated to the super-sink node. TheJDAL 4,1 52 evacuee ﬂow balance constraint is (5) where the notation i|i ,jA(k)means for igiven that there exists a feasible (non-zero) arc ( i, j)A(k)for transportation mode k. This is equivalent to X iakðÞ ijxkðÞ ijtðÞ/C0X iakðÞ jixkðÞ jitþpkðÞ ji/C16/C17 ¼0 8j;k;t (11) Constraints (6) and (7) work together to provide an upper and lower bound on ﬂows across a singular arc within an individual period. Constraint (6) de ﬁnes the ﬂeetwide capacities for each transportation mode. We assume capacities are 45 (people) for buses, 750 for trains, and 35 for helicopters. For example, if there are ﬁve helicopters available, U(helo)=5/C235 = 175. To incorporate senior leader planning guidance and prevent unnecessarily planning to usean asset for one person, minimum asset utilization thresholds, the L (k), are 30 (people) for buses, 100 for trains, and 10 for helicopters. Note that (7) is only active until the arrival process reaches li; where liis 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 suf ﬁcient numbers of evacuees arrive. For later time periods, such trips may be required to evacuate remaining people (maintains feasibility). If liis non-integer, we suggest letting using [ li] in (7). Constraint (8) is a multi-period ﬂeet capacity constraint that effects ﬂows across time periods and accounts for evacuation ﬂows already underway. It ensures that for all allocations of the ﬂeet, the assets in use never exceeds the total ﬂeet capacity in any one time period. To illustrate how this constraint functions, reference Figure 5 . In that example, if scheduling ﬂow when t= 2, the ﬂow 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 groupingsand working to provide a tighter bound on the capacity. The notation (z) þ:max( z,0 ) . Figure 5. Time-staged expansion example Modeling and transportation planning 53 Finally, constraints ( 9–10) 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 xkðÞ ijtðÞin (9) is unnecessary. For any feasible, ykðÞ ijtðÞ2f0;1gthe remaining constraint matrix in xkðÞ ijtðÞremains total unimodular ( Wolsey, 1998 ;Chen et al., 2010 ). Thus keeping the binary requirement in (10) but relaxing the integer requirement (9) on xkðÞ ijtðÞfor the full 156k evacuation population reduces the solution time from 6 min to 20 s (with 0.1 per cent optimality gap) and converts the model into a mixed integer linearprogram (MILP). The solution to this formulation determines the optimal ﬂow con ﬁguration 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 detailsthe time instance speci ﬁcﬂow of every arc across the full time horizon. The position of an individual ﬂow 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 thecapacity of each asset type, the number of assets required is directly calculated. Rede ﬁning the optimal ﬂows as the number of full asset shipments necessary, each with de ﬁned 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 theircapacities 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 Clarke –Wright 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 ﬂow travel times to motivate the heuristic. Once the routes are constructed, two-opt improvement performs an exhaustiveseries of edge exchanges to ensure the optimum collection of route sequences. The complete solution to the vehicle routing procedure is a time speci ﬁc 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 ﬂeet 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 Clarke –Wright savings procedure will construct. 4.5 Output summary Following this solution methodology ultimately produces signi ﬁcant 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 optimalsolution. This is a tremendous improvement over the state of the existing plan where thetime and resource requirements of this mission were essentially unknown. Now 2ID can actually manage and allocate resources at the outset of a NEO to shape the operation to meet its other mission requirements. Second, this method addresses another weaknesses in thecurrent planning, speci ﬁcally the assignments of the transportation assets under 2ID control. Whereas before the strategy of purely reactive; now the routing procedure yields aJDAL 4,1 54 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 inthe Appendix. 5. Case study 5.1 Base scenario and performance metrics The standard model outputs are useful, but the tru e 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 eva cuation, we present a series of experiments based on a plausible evacuation scenario. This study consists of two parts: one focused onplanning the evacuation under additional mi ssion requirements and the second revolving around responding to changes in the envi ronment as the operation is conducted. For the purposes of this exercise, the base scenario to be investigated will evacuate 156,545 noncombatants with a ﬂeet 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 completeassembly. The logic for starting at this con ﬁguration 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 con ﬁguration 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 58.3 h, andon average the AP sites close at 5.9 days. Figure 6 describes the in ﬂow of arrivals into the system and captures their out ﬂow and the completion of the evacuation. For clarity, these plots use a 1 h time step. 5.2 Planning requirements and adjustmentsTo demonstrate the value of this model as a tool for 2ID requires employing it under morerealistic conditions. In the course of a real evacuation it is understood that 2ID will be Figure 6. (color online) In ﬂow and out ﬂow v time period of the base scenario Modeling and transportation planning 55 conducting numerous missions simultaneously and that NEO requirements will be in competition for organizational energy and resources. This study attempts to replicate anevacuation scenario that is representative of the true requirements for 2ID by building inthree additional requirements. Consider the following scenario: the deterrence efforts of the USA, South Korea and the broader international community have faltered and direct military con ﬂict with North Korea appears imminent. The US Department of State has indicated that a NEO of all DoDFamilies, USG Employees and US Citizens will begin in two days. 2ID has elevated itsreadiness posture and is planning for forward mobilization and occupation of designateddefensive battle positions in 9.5 days. 2ID scouts, who for the purposes of this case studyoperate AP3, are expected to establish a screen and conduct reconnaissance and surveillancemissions beginning in six days. Additionally, stores of bulk rations and water are limitedand can only reasonably support the population that needs to be evacuated for 24 h. 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 ﬁrst requirement focuses strictly on ending the mission before the base experimentation conditions say it can be completed. As previouslymentioned, 2ID can shift focus and reposition its own resources and this iteration will meetthe new mission requirements by determining just how much additional ﬂeet capacity of each mode is required to satisfy the need. The second stipulation implies that the earlyclosure of an AP is necessary, and this directed model adjusts the arc capacity according tothe required closure time to ensure that occurs. The third requirement is aimed at limiting thewaiting time of evacuees as they move through the system. Evacuees are told to assemblewith food and water, but 2ID would have supporting rations available and therefore the waittime through the system needs to be less than 24 h. This iteration of planning investigates theimpact of metering arrivals into the system by making directed announcements to speci ﬁc slices of the evacuation population. This case study attempts to demonstrate how earlyplanning with the model can be re ﬁned to meet real-world operational requirements ( Table 1 ). 5.2.1 Requirement 1. Early AP closure. Theﬁrst additional requirement is the mandated closure of an AP on a particular day. It is necessary to start with this requirement as it canbe achieved only by modifying the structure of the time-staged network. Once thisadjustment is made, subsequent required changes will all operate within the new frameworkand the results will build in a cumulative manner; otherwise, they would be independent andthus less useful. Table 1. Case study requirements beyond the base scenarioIssue addressedArrival profile (mean arrivals complete at day) Helo Bus TrainEvac time (hours)Evac time (days)Average evacuee waiting time (hours)AP site 3 closure Base scenario 2.5 12 100 24 207.50 8.65 58.32 8.96 Planningrequirements –– – – 180 7.5 24 4JDAL 4,1 56 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 ﬁrst necessary to ensure that whatever the desired AP closure time occurs after evacuee assembly is complete. The assemblytimeline acts as a lower bound for site closures, as the operating assumption is that a sitecannot be closed down while evacuees are still arriving. If that condition is met, then it ispossible 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 modi ﬁcation essentially ensures that all evacuees that arrive into AP3 have departed before the upper bound is applied. Oncethis constraint is factored into the model, the objective function will allocate assets in such away 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 aboutthe sensitivities to changes in certain ﬂeet sizes. Twelve additional experimental runs were made, while varying the levels of each speci ﬁc 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 (orother ground transportation assets) are the most abundant transportation asset available to 2ID, and while other asset con ﬁgurations 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 ﬂeet sizes provides understanding of the trade-offs involved and the relative value of assets. Applying theresponse surface model showed that adding 31 buses will ensure that the plan meets themission requirement of completing the evacuation in under 7.5 days, but it is necessary tocheck 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 evacuationtime of 162 h, and so it is unnecessary to add all 31 buses to meet the requirement. Thevalues 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 planningby 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 waitingtime through the system. With a limited supply of rations available the wait time in thesystem needs to be less than 24 h. Due to the fact that for much of the evacuation process themodel is operating at maximum capacity, it is necessary to try and in ﬂuence the arrival proﬁle 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 in ﬂuence or direct the behavior of the evacuees, when they will actually arrive is dif ﬁcult to predict with a high degree of con ﬁdence. That uncertainty is built into the arrival process during the initial formulation, but the adjustments made in thisModeling and transportation planning 57 Issue AddressedArrival profile (mean arrivals complete at day) Helo Bus TrainEvac time (hours)Evac time (days)Average evacuee waiting time (hours)AP site 3 closure 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 4.00NEO complete by Day 7.5 2.5 12 121 24 180.00 7.50 49.79 4.00Less 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 ﬁnal row, all factors have been addressed and enough assets have been added to keep performance within the acceptable rangeTable 2. Progression of the planning requirements casestudyJDAL 4,1 58 consideration further those early arrival assumptions. The ﬁrst formulation makes the assumption that the arrival process will be complete in a speci ﬁed number of days based on when evacuees are noti ﬁed. This new consideration advances that assumption by supposing that individual portions of the total evacuee population will behave independently according to their noti ﬁcation. 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 noti ﬁcation and report when they are directed. But as the evacuee population expands to US Citizens or TCNs, this assumption may erode and the arrival pro ﬁle 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 pro ﬁle that could aid in reducing the evacuee wait time through the system. With that assumption in place, the arrival pro ﬁle can be modi ﬁed by the number of notiﬁcations and evacuee population slices they address. Inherently, there are risks present in this option as those evacuees who are not noti ﬁed 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 noti ﬁcations further experimentation with the model is necessary and so the number of noti ﬁcations is incrementally increased until the waiting time is reduced to below the working threshold. For example, if there are to be three notiﬁcations, one third of the evacuees will be noti ﬁed 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 pro ﬁle is modi ﬁed 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 andFigure 7 . 5.3 Disruptions and adjustments The next phase of this case study is focused on the execution of an evacuation and how touse 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 ﬂeet sizesTotal evacuation time (Hours) Helicopters 3 6 9 12 15 18 Buses 50 391.5 379.5 369.5 354.5 342 33775 284.5 271.5 263 260 259.5 248.5100 218 214.5 211 207.5 204.5 203.5 125 183 182 178 176 175 172.5 150 161 160 157 155 154 151175 147 144 141 140 139 138200 129.5 129 128.5 128 127.5 126.5 Note: Here the train ﬂeet is held constant at 24. All values are the results from the optimization model in section 4.3Modeling and transportation planning 59 for while scheduling assets. Consider the following likely events: loss of transportation assets as a result of military con ﬂict, 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 ofeight helicopters from the ﬂeet 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 thenetwork. 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 thispoint, arrivals to APs have been approximated by the Poisson distribution detailed inSection 4.2. This adjustment marks a change how arrivals come into the system byattempting to simulate an irregular arrival distribution for the model to schedule againstsince actual NEO “arrival patterns can vary greatly ”( Scheer, 2011 ;Kuchell, 2013 ). This is accomplished ﬁrst isolating the periods in which arrivals occur and recording the corresponding arrival quantities. Those arrival quantities are then randomly assigned to therange 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 PoissonFigure 7. (color online) In ﬂow and out ﬂow v. time of the solution to the planning case study JDAL 4,1 60 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 modelcan 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 irregulararrival pro ﬁle 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 asthe arrival pro ﬁle 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 andscheduling 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 ﬂeet 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 tomaintenance issues. The model can account for t his change in capacity through the adjustment of the train constraints beginning on Day 3. Con ceptually, this is fairly straightforward however due to the time-staged nature of the netwo rk it is a tedious implementation. Currently, the capacity constraints operate in three ways . Single arcs have an upper bound related to the totalﬂeet capacity of a particular transportation mode. Transportation mode arcs are also grouped by type and are collectively assigne d an upper bound according to their total ﬂeet capacity across a number of time periods. Thi se n s u r e st h a tt h ec a p a c i t yi sn o te x c e e d e di n either a single time period or a series of time periods where transportation is occurring. Thethird constraint only applies through the ﬁrst half of the arrival process and ensures that arc ﬂow, if scheduled, will only occur above a speci ﬁed minimum occupancy l evel. Therefore, no trips of single digit passengers will be schedul ed by the model. As a result of this formulation, adjusting the capacity of a particular transpo rtation mode within the schedule essentially requires the construction of a second com plete set of constraints to reduce the ﬂow beginning in Figure 8. (color online) In ﬂow and out ﬂow v time considering irregular arrivals, loss of assets and arc closures Modeling and transportation planning 61 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 per formance. Comparing against Table 4 ,t o t a l 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 miss ion within their requirements. 5.3.3 Disruption 3. Arc closures. As with the mandatory closure of an AP on a speci ﬁed 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 con ﬂict, 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 andTable 4 highlight the complete effect of all disruptions, arc closures, the attrition of train assets, and the irregular arrival pro ﬁle. 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 2ID needs todetermine 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 perform ance to within an acceptable range. That said, this model provides a fast and expedient method t o 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) In ﬂow and out ﬂow v. time of the complete case study solution JDAL 4,1 62 Issue addressedArrival profile (mean arrivals complete at day) Helo Bus TrainEvac time (hours)Evac time (days)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 4.00AP1 bus arc closed on Day 4 Irregular 4 126 24 213.00 8.88 26.345 3.979All 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 speci ﬁc periods Table 4. Progression of the disruptions case studyModeling and transportation planning 63 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 ﬁnal schedule performance factoring the additiona l assets that are required to get the schedule within the acceptable performance levels. T he 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. ConclusionThe primary goal of this work was to model the noncombatant transportation network inSouth 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 ﬂow 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 ﬂeet 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 speci ﬁc routes and nodes in response to disruptions. And it has been shown how affecting the pro ﬁle of arrivals can be used to limit waiting time through the system. The procedures described in 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 ﬂuid 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 model ’s 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 Sout h Korea present a complex problem with many intriguing areas for future research. An exploration of the sensitivity of this model to changingJDAL 4,1 64 arrival rate parameters based on proximity to Nor th Korea, variable travel times to account for trafﬁc 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 speci ﬁc routes within the schedule could be identi ﬁed to reduce risk and formulate a more robust solution, better prepared to avoid and manage disruptions. This a rich andmeaningful problem with many opportunities for further investigation.