A Combined Optimization and Simulation Based ...

A Combined Optimization and Simulation Based Methodology for Locating Search and Rescue Helicopters Nasuh Razi Turkish Naval Academy Institute of Naval Science and Engineering Tuzla, Istanbul, Turkey [email protected]

Mumtaz Karatas Turkish Naval Academy Industrial Engineering Dept. Tuzla, Istanbul, Turkey [email protected]

Murat M.Gunal Turkish Naval Academy Industrial Engineering Dept. Tuzla, Istanbul, Turkey [email protected]

SAR operations is the most crucial operation to establish the safety of the vessel or person in distress. SAR at sea is an emergency response operation for rendering aid to persons in distress to prevent loss of life, injury and catastrophic damages. Quick response to an incident has considerable impact on the survival rate of the victim and success of the operation. Furthermore, the difference between life and death in a maritime accident is sometimes measured in minutes. Moreover, a SAR operation conducted at sea requires considerable amounts of time, money and effort [18]. Thus, determining an effective allocation plan for SAR units is essential.

ABSTRACT

Maritime Search and Rescue (SAR) operation is a critical process which aims to minimize the loss of life, injury, material damage by rendering aid to persons in distress or imminent danger at sea. Response time to incidents is the most crucial performance metric in SAR operations. Fatalities, injuries and damage can be reduced if incidents are responded as quickly as possible. However, uncertainty of location, time and severity of an incident make these operations difficult to conduct and complicated to plan. Furthermore, quick response relates to rational planning and allocation as well as the use of modern and fast SAR resources. In this paper, we combine optimization and simulation methodologies and study the problem of allocating SAR helicopters. Our methodology works in two stages; we first determine an optimal allocation scheme of helicopters with the objective of minimizing the average response time to incidents in the responsibility region. Next, we use a discrete event simulation model to test the performance of our analytical solution under stochastic demand. Using 2014 incident data of the Aegean Sea, we demonstrate a case study in the western sea region of Turkey.

Deployment of SAR resources is a strategic process in which a number of parameters such as cost, resource capability and quantity, geographic features of the area and accident density must be taken into account. Therefore, SAR resource allocation models that incorporate only national or political decisions are no longer appropriate. Similar problems in literature are studied as sub-cases of resource allocation problems. In general, a resource allocation problem deals with the assignment of available (and mostly scarce) resources to various uses for specific purposes. Locating emergency response systems is a prevalent resource allocation problem which is applicable to conduct operations research methods. Furthermore, the study [9] displays that OR/MS applications bring out a remarkable benefit on objectives.

Author Keywords

Search and Rescue (SAR); optimization; discrete event simulation.

In the literature, resource allocation studies are categorized under three main problem types: p-median problems (pMP) [6,10], p-center problems (p-CP) [11,23], covering problems with two classifications, the maximal covering location problems (MCLP) [13,22] and set-covering problems (SCP) [5,21]. The p-MP seeks to determine the locations of p facilities which minimizes the total distance between each demand point and its closest facility. In p-CP, the objective is to minimize the maximum distance from any facility to any of the demand points. The MCLP aims to determine an allocation plan that maximizes the demand which can be satisfied within a stated service distance or time given a limited number of facilities. SCP

ACM Classification Keywords

I.6.3 SIMULATION AND MODELING Applications. 1. INTRODUCTION

As humanity grows up, the sea becomes a weighty area of trade, leisure, power generation and industrialization. However, the rapid expansion of marine traffic increases the risk of maritime safety. The safety of vessels and their crew against marine hazards is ensured by Search and Rescue (SAR) units, post-accident operations and accident investigations after hazardous situations which rely on International Maritime Organization (IMO) legislation and classification society rules [12]. Among these measures SpringSim-ANSS, 2016 April 3-6, Pasadena, CA, USA © 2016 Society for Modeling & Simulation International (SCS)

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seeks to minimize location costs satisfying a specified level of coverage.

at sea. Next, we develop a DES model to measure the performance of an analytic solution.

Narrowing the scope of our review to SAR resource allocation problems, we confront with a number of studies which utilize the abovementioned techniques. However, the method which will be applied relates to decision makers’ objectives. Researchers, concentrating on coverage level, apply MCLP and SCP; on the other hand, researchers, interested in distance and response time, utilize p-MP or pCP. For example, in [3] the author formulates the problem of allocating SAR helicopters with MCLP method. In his work [1], Acar implements both SCP and MCLP techniques to allocate Turkish Air Force (TUAF) SAR resources. In [25] Wagner and Radovilsky individually practice locating United States Coast Guard (USCG) boats among stations using a Mixed Integer Problem (MIP). In [19], Pelot et al. utilize three location models, maximal covering location problem, maximal expected covering location problem, and maximal covering location problem with workload capacity to allocate SAR resources in North Atlantic, Canada.

As a case study, we consider the western sea region of Turkey and use 2014 incident data of the Aegean Sea. In this case study, we first utilize historical incident data to generate demand points and determine an analytic solution with our p-MP formulation with respect to the locations of helicopters. Secondly, we use our DES model to test the performance of the analytic solution. Finally, we create different scenarios for the DES model by altering the number of helicopters at each activated helipad and analyze experimental results. These scenarios particularly focus on generating incidents randomly by using a probability distribution associated with historical incidents. This paper is organized as follows. We discuss our motivation to study this problem in Section 2. Details of our optimization and simulation models are presented in Section 3. In Section 4, we experiment and measure the performance of our approach with respect to the Aegean Sea. Finally, we present the results and conclusion of our work in Section 5.

Beside analytic approaches, a number of simulation models have developed aiming at expressing uncertainty associated with the environment or elements. For instance, there are a number of studies that consider the uncertainty in the location of an incident at sea which is subject to drifting. [4] studies the behavior of floating objects at sea and present a complex network approach with direct simulation method to show drifting objects’ motion. In [7] the authors construct a discrete event simulation (DES) model considering the voluntary maritime rescue system in the Gulf of Finland. They model the system as multiple customer and server systems and evaluate the performance of the system. In [2] Afshartous et al. developed an optimization and simulation based methodology to study the problem of determining effective locations for the USCG air stations to respond emergency distress calls. They modeled the problem as p-MP and Uncapacitated Facility Location Problem (UFLP), and used simulation to test the robustness of their solution. In their study [17], Nguyen and Kevin implement goal programming considering two main allocation problem, p-MP and MCLP, to Canadian current SAR organization (SAR aircraft and helicopter). Furthermore, they utilize queuing theory based-simulation methodology to evaluate performance of existing plan and suggested solution.

2. MOTIVATION

In case of a maritime incident, the victim overboard combats hypothermia and other obstacles such as sharks, waves, etc. To have a better understanding of the importance of quick response, the critical times of survival for various water temperatures are given in Table 1 from [16]. It is obvious that as the water temperature decreases, early response becomes more critical for survival. Water Temp. (°C) 0.3° 0.3–4.4° 3.3–10° 10–15.6° 15.6–21.1°

Under 2 min. Under 3 min. Under 5 min. 10 to 15 min. 30 to 40 min.

Expected Time Before Unconsciousness < 15 min. 15 – 30 min. 30 – 60 min. 1 – 2 hrs. 2 – 7 hrs.

21.1–26.7°

1 to 2 hrs.

3 – 12 hrs.

> 26.7°

2 to 12 hrs.

Indefinite

Loss of Dexterity

Expected Time of Survival 45 min. 30 – 90 min. 1 – 3 hrs. 1 – 6 hrs. 2 – 40 hrs. 3 hrs.– indefinite Indefinite

Table 1. Expected time of survival and expected time before unconsciousness of a victim for various water temperatures.

Thus, helicopters are the most preferred vehicles to provide immediate on-scene operations with diverse range of significant emergencies, such as respond to fires, hazardous materials, SAR, and other emergencies in the marine environment. Modern SAR helicopters provide an enormous advantage in such missions due to their range, flexibility, state of the art equipment and capacity. However these benefits come at a cost. These vehicles are built to perform demanding operations and as expected their capability needs to evolve to match the constantly changing needs. This brings the high costs associated with the purchasing, maintaining and operating a SAR helicopter and operating helicopter landing pads (helipad). Besides, to be able to operate in a large range of terrain and weather conditions, well-trained pilots and crew bring additional

In this study, we consider the tactical aspect of the emergency incident response problem, i.e., determining locations of SAR helicopters. Concerning the importance of immediate response to hazardous situations and limited air resources associated with SAR operations, we practiced a p-MP, with the objective of minimizing total distance traveled by SAR helicopters. By minimizing traveled distance, hence minimizing total response time to incidents, we seek to increase success of a SAR operation conducted

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costs to organizations. On the other hand, helicopters are notorious for breaking down, because there are so many working parts. They have limited flight times per sortie and however fast it is, one helicopter can only be in one place at one time. Therefore, these tradeoffs in utilizing helicopters in SAR missions motivate us to study the problem of determining optimal helicopter locations.

operation range of a helicopter. We also impose a number of business rules. In particular, we define a maximum yearly operation hour for each helicopter and assume that demand satisfied from a helipad cannot exceed the total available operation hours of that helipad. Total available operation hours is simply computed by the product of the maximum yearly operation hour of a helicopter and the number of helicopters assigned to that helipad. We further assume that to activate a helipad a minimum amount of demand should be assigned to it. The model aims to minimize the total distance traveled to respond the incidents (objective function value). Other outputs are the activation decision for each helipad (binary decision variable) and the helipad-incident assignments (binary decision variable). In the optimization model we do not consider the number of helicopters that should be allocated to each helipad, and instead, assuming an infinite helicopter supply, we determine the helipads to be activated. In the simulations, we test the performance of the analytic model under three different scenario where the number of helicopters are varied.

3. OPTIMIZATION AND SIMULATION MODELS

We develop a combined optimization and simulation methodology, as shown in Figure 1, to allocate SAR helicopters optimally. In step 1, we formulate a Mixed Integer Programming (MIP) p-MP to determine optimal allocation plan of SAR helicopters with the objective of minimizing total distance traveled between helipads and each incident.

3.2. Simulation Model

DES is one of the most practical techniques to evaluate the systems that have state changes at discrete time intervals. Queuing systems, manufacturing and inventory systems are typical examples of such systems [8].

Figure 1. Structure of methodology. Our main goal in step2 is to evaluate the performance of optimization methodology against scheduling/ query factors. Thus, we develop a DES model to test the performance of optimization model’s allocation plan with stochastic demand initially. Then, allocation plan is experimented with different scenarios considering alteration on total number of helicopters.

In our work, we conceptualized the system we defined earlier as a queueing system and built a DES model of the flow diagram in Figure 2. In this queuing system, each intercepted incident is considered as a customer and each helicopter /helipad is regarded as a server. As shown in Figure 2, the model starts with reading the historical incident data. We partitioned the whole SAR responsibility area into smaller rectangular sub-areas according to the incident density. Next, for each sub-area, we draw a histogram of inter-incident times, and use them to generate inter-incident time distributions. We assumed that incidents are distributed in sub-areas random uniformly. After an incident occurs, the model measures the distance to each helipad and chooses the nearest helipad. If the nearest helipad has no helicopters to assign, the second nearest helipad is chosen and so on. Since the objective in our formulation is to minimize total distance traveled, each incident checks the helipads in ascending order to confront an idle resource.

3.1. Optimization Model

We developed a Mixed Linear Programming (MIP) p-MP resource allocation model which determines k helipads that should be activated out of n candidates with the objective of minimizing total distance traveled between each helipad and incidents assigned to it. As an input to our optimization model we use the number of incidents and helipads, as well as their locations, maximum number of helipads that can be activated, demand hours for each incident and maximum range a helicopter can operate. We pre-process the distance between each helipad and incident. In our formulation we assume that each helicopter has the same range and speed. Thus minimizing total distance leads to the minimization of total response time. In our constraints we ensure that at most k helipads can be activated among available n candidate helipads where n ≥ k. All incidents are responded from a helipad and sharing demand among multiple helipads is not permitted, that is, an incident can only be responded from a single helipad. Our constraints also ensure that helipads that are not activated cannot be utilized to satisfy demand. Besides, a helipad can response to an incident if it is within its

3.2.1. Simulation Settings

Intercepting an incident rapidly relates to distance and SAR resource’s capabilities. Thus, there are three objects in our model: • • •

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SAR helicopters, Helipads, Incidents.

Figure 2. Flow chart of simulation model 3.2.2. Simulation Outputs

We assume that we have a single type of helicopter that can be deployed to a helipad. Although in reality, different types of helicopters with various capabilities can conduct SAR operations, our assumption ease the difficulty in the adoption of operational constraints in the model. In addition, weather conditions that can have significant impact on helicopters’ operability and communication are not included in our model. We first used the locations of helipads and the number of helicopters assigned to each helipad that are derived from the analytical model. Next we tested the performance of selected helipad locations for different numbers of helicopters.

Output #

MO1

MO2 MO3 MO4

The area of interest could have a specific physical characteristic like coastline shape, islands, tide and drift that makes the event locations to generate difficult in a simulation model. In such cases, it is plausible to divide the whole area of interest into sub-areas determined by a grid system. This enables to determine more risky zones in terms of representing uncertainty. Note that the size of a sub- area is significant for better resolution in simulation validation. For each sub area, we assume that the incident arrival process is Poisson with a rate of time in minutes divided by the total number of incidents.

Model Outputs Average Total Distance Traveled (nm) Average Number of Incidents Generated Average Number of Incidents Responded Average Total Number of Incidents Stand in Queue

MO5

Average Degree of Proximity of Helipad

MO6

Average Total Demand Generated (hrs) Average Total Demand Satisfied (hrs)

MO7

Definition Average of sum of distances traveled from each activated helipad to its associated incidents. Average number of incidents generated in a run. Average number of incidents responded by helicopters Average number of incidents which cannot be responded due to helicopter unavailability. Such incidents enter the nearest helipads’ queue. Average degree of proximity which indicates the proximity of helipad to an incident (1 is the closest helipad to an incident and 5 is the furthest). Average total demand hours of incidents generated in a run period. Average total demand hours of incidents that could be satisfied in a run period.

Table 2. Simulation outputs.

In addition to the stochastic arrivals, location of incidents in a sub-area is assumed to be random and uniformly distributed.

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The simulation model is built using Micro Saint Sharp© version 3.7 [14]. As the objective is to minimize total distance traveled, main output of simulation model is the total distance traveled. With respect to measure of effectiveness, other outputs are total number of operations conducted, total number of incidents in queue, and total operation time and total demand (Table 2).

models. To generate demand in our analytic model we adopt the historical incident data 2014 of which operation time density graph is displayed in Figure 4. Figure 5 shows the locations of 716 incidents occurred in the region in this period. Candidate helipad locations, which are also inputs to the analytical model, are marked on the map. 500 393 400 300 181 200

11

10

5

3

2

1

36-40

41-45

46-50

28

31-35

60

100

26-30

The Aegean Sea, lying between the mainland of Turkey and Greece, is the only way for shipping to countries border the Black Sea and is also a great center of leisure and cruise tourism with a number of glamorous islands. On the other hand, all these characteristics bring out heavy marine traffic and risk in maritime safety.

21-25

Total Number of Incidents

4. CASE STUDY

22

800

50+

16-20

11-15

0-5

Maritime safety is an issue that has gained a lot of attention in the Aegean Sea region due to the dense maritime traffic, mainly caused by shipping, cruise tours, yachting, windsurfing and illegal-border crossing activities. Besides, according to [15], the risk associated with the maritime transportation in the area increased with the number of ships carrying hazardous cargo and the lack of designated shipping lanes, together with narrow and dangerous routes. Although lots of effort has been paid to enhance safety in the region, 1933 incidents occurred in the region between 2009 and 2014, and 716 of those were in 2014 [20]. Figure 3 shows the number of incidents occurred in the Aegean Sea between 2009 and 2014. The analyses in [24] regarding the political and sociological situation of the region reveal that the increase after 2012 is mainly caused by illegalborder crossing through the Aegean Sea due to the turmoil in the Middle East. These illegal activities brought out an obvious boom in number of incidents due to using incapable boats.

6-10

0

Operation Times/Demands(hrs)

Figure 4. Operation time histogram of incidents occurred in 2014.

716

Number of Incidents

700 600 451

500 400 300

240

200

174

185

2010

2011

167

Figure 5. Locations of incidents occurred in 2014 and candidate helipads.

100 0 2009

2012

2013

4.1. Input Values

2014

We used the key parameter values in Table 3 to solve our optimization model. There are a total of nine candidate helipad locations and we assume that at most five of them can be activated (a helicopter can be deployed). This rule reflects the budgetary constraint associated with the cost of activating a helipad.

Year

Figure 3. Number of incidents occurred in the Aegean Sea region between 2009 and 2014.

According to Turkish National SAR Plan, Turkish Coast Guard is responsible for coordinating and conducting SAR operations in the Aegean Sea coastline of Turkey. With the aim of enhancing the survival and success rate in an incident, we apply our analytic model to determine optimal locations for the SAR helicopters in the western region of Turkey and later test its performance with simulation

Parameters Value 9 Number of candidate helipads Maximum number of helipads that 5 can be activated Table 3. Key parameters for helipads.

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deployed to a helipad decreases in the simulation model. For lower numbers of helicopters per helipad, it is less likely for an incident to receive a response from its closest helipad. Hence such incidents are responded from other helipads such that the closest ones having the highest priority. If all helicopters are on task, the incident stands in queue.

In the simulation model we test the performance with respect to the performance metrics defined in section 3.2.2. The Aegean Sea has a particular geographical structure with more than 3000 islands. This characteristic makes the generation of random events/incidents at sea difficult in the simulation model. Thus, we divide the area of interest into 0.25x0.25 degree-sized histograms to reduce the effects of landscapes on the accuracy of model, Figure 6. In addition, it is clear that histograms with more incidents represent the risky regions in the area of interest.

Output

MO1 MO2

MO3

MO5

MO6 MO7

Figure 6. Grid structure and number of incidents in the area of interest.

Our optimization model results in an objective function value of 20,281 Nautical miles (nm) by activating five helipads, 1, 3, 4, 7, and 9. Number of incidents responded and total demand distribution are summarized in Table 3. Number of Incidents Responded

Demand (hrs)

Number of helicopters assigned

90

1155

2

3

185

1800

3

4

191

1800

3

7

179

1799

3

9

71

1559

3

Average Total Distance Traveled (nm) Average Number of Incidents Generated Average Number of Incidents Responded Helipad1 Helipad3 Helipad4 Helipad7 Helipad9 Average Order of Helipad Closeness Degree 1st 2nd 3rd 4th 5th 6th-Queue Average Total Demand Generated(hrs) Average Total Demand Satisfied (hrs)

Analytic Model Results

Simulation Model Results (A) (B) (C) Analytic 2 Helos 1 Helo Plan

20281

19879

22425

36744

-

718

716

715

716

717

715

678

90 185 191 179 71

100 185 206 177 49 1.05

-

677 40 -

102 185 197 169 62 1.20

578 129 7 1 -

114 161 172 145 86 1.86

305 221 102 36 13 1

8113

8150

8128

8120

8113

8112

8100

7671

Table 5. Simulation results. Scenario (A) is the same plan as analytic result. In scenarios (B) and (C) two and one helicopters are deployed to each activated helipad respectively.

4.2. Simulation Results

Activate d Helipad # 1

Performance Metrics

As mentioned in Section 3.1., the analytic model assumes an infinite helicopter supply, so we would expect to see the lowest value for the analytic model case. However, simulation model (A), where the performance of analytic model result is tested, performs approximately 2% better in terms of MO1. The difference is due to the assumptions in both models. Analytical model considers the exact incident locations in each sub-area and determines the real helipadincident distances, whereas in simulation, incident locations are determined by random uniformly at each sub-area. Due to this assumption a number incident locations fall on the landscape regions at particular grids and this yields an optimistic estimate of the total helipad-incident distances. MO2 and MO6 show that simulated incident data almost matches the analytic data in terms of number of incidents and total amount of demand hours generated.

Table 4. Key results of optimization model. Number of incidents responded and total demand distribution among the helipads.

MO3 shows the workload distribution among the five helipads. For all cases helipads 3, 4 and 7 seem to be satisfying most of the demand. That is because these three helipads are located at the mid-region of the area of

Detailed outputs of the performance metrics are presented in Table 5. As expected, MO1, the average total distance traveled, tends to increase as the number of helicopters

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interest, hence they have the capability of intersecting a greater number of incidents. MO4 is excluded in the table since the number of incidents which must be waited is significantly low. However, we observe that the average total number of incidents stand in queue increases as available resources decrease.

3. Basdemir, M. M. Locating search and rescue stations in the Aegean and Western Mediterranean regions of Turkey (No. AFIT/GOR/ENS/00M-03). Air Force Institute of Technology Wright-Patterson (2000). 4. Bezgodov, A. and Esin, D. Complex Network Modeling for Maritime Search and Rescue Operations. Procedia Computer Science, 29, (2014),2325-2335.

MO5 results reveal that as the helicopter resources are limited it becomes harder for an incident to be responded from a helicopter designated to its closest helipad. In case (A), almost all incidents receive the closest helipad. For case (C) the average is highest with a value of 1.86.

5. Caprara, A., Toth, P., & Fischetti, M., Algorithms for the set covering problem. Annals of Operations Research, 98(1-4), (2000),353-371. 6. Church, R. L. and ReVelle, C. S.Theoretical and Computational Links between the p-Median, Location Set-covering, and the Maximal Covering Location Problem. Geographical Analysis, 8(4), 1976,406-415.

MO6 and MO7 results are average total demand generated and satisfied. The generated demand outperforms the satisfied demand since some of the simulated incidents exist after the model execution ends.

7. Goerlandt, F., Torabihaghighi, F., & Kujala, P.. A model for evaluating performance and reliability of the voluntary maritime rescue system in the Gulf of Finland. 11th International Probabilistic Safety Assessment and Management Annual European Safety and Reliability Conference (2013),1-6.

5. CONCLUSIONS

Performance of search and rescue operations at sea has a direct impact on human life and therefore they should be well-planned. In this study, we built a mathematical model and a simulation model which work together to evaluate appropriateness of SAR helicopters’ base station locations. The mathematical model is a p-MP resource allocation model to seek optimum locations which minimizes the total station to incidence distances. The model finds p stations out of n candidate stations. After finding the optimal locations, we fed them to a simulation model which include some stochastic elements that the analytical model cannot, such as random incident time and locations.

8. Goldsman, D. and Goldsman, P Modeling and Simulation in the Systems Engineering Life Cycle, 103109. Springer, London, England, 2015. 9. Green, L. V. and Kolesar, P. J. Anniversary article: Improving emergency responsiveness with management science. Management Science, 50(8), (2004). 10011014. 10. Hakimi, S. L. Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Research, 12(3), (1964), 450-459.

The Aegean Sea is one of the active areas on earth in terms of the need for SAR operations at sea. We analyzed its historical incidence data and revealed hot areas and their inter-incidence time distributions. The distributions are used to generate incidents in the simulation model. Furthermore, the analytical model results, e.g. optimum number of helicopter stations, determined the resource levels used in experimental scenarios.

11. Krumke, S. O. On a generalization of the p-center problem. Information Processing Letters, 56(2), (1995), 67-71. 12. Kuronen, J. and Tapaninen, U. Maritime safety in the Gulf of Finland – Review on policy instruments. Publications from the Centre for Maritime Studies, University of Turku, Turku, Finland, A49/2009.

Simulation results extended the use of analytical model results in terms of revealing waiting times in response to incidences and work load distribution between helipads. The case study is an example of hybrid approaches in optimization with simulation.

13. Li, X., Zhao, Z., Zhu, X., & Wyatt, T.Covering models and optimization techniques for emergency response facility location and planning: a review.Mathematical Methods of Operations Research, 74(3), (2011), 281310.

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2. Afshartous, D., Guan, Y., & Mehrotra, A. US Coast Guard air station location with respect to distress calls: A spatial statistics and optimization based methodology. European Journal of Operational Research, 196(3), (2009),1086-1096.

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17. Nguyen, B. U., and Kevin, Y. K,. Modeling Canadian search and rescue operations, University of Ottawa, (2000). 18. Onggo, S. and Karatas, M. “Agent-based model of maritime search operations: A validation using testdriven simulation modelling”, Winter Simulation Conference, CA, USA, (2015), 254-265. 19. Pelot, R., Akbari, A., & Li, L. Vessel Location Modeling for Maritime Search and Rescue. Applications of Location Analysis, (1st ed., pp. 369– 402), Springer,2015. 20. Razi, N. and Karatas M. “A multi-objective model for locating search and rescue boats”, submitted for review, (2015) ,manuscript available on request. 21. ReVelle, C..Review, extension and prediction in emergency service siting models. European Journal of Operational Research, 40(1), (1989), 58-69. 22. Schilling, D. A., Jayaraman, V., & Barkhi, R.,. A Review of Covering Problems in Facility Location. Computers & Operations Research, (1993), 25-55. 23. Suzuki, A. and Drezner, Z. The p-center location problem in an area. Location Science, 4(1), (1996), 6982. 24. UNHCR, Global Appeal 2015 Update. http://www.unhcr.org/5461e5f80.html, 2015. 25. Wagner, M. R. and Radovilsky, Z. Optimizing Boat Resources at the US Coast Guard: Deterministic and Stochastic Models. Operations Research, 60(5), (2012), 1035-1049.

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