Article

Integrated locating of helicopter stations and helipads for wounded transfer under demand location uncertainty

a b s t r a c t

Health emergency medical service (HEMS) plays an important role in reducing injuries by providing advanced medical care in the shortest time and reducing the transfer time to advanced treatment centers. In the regions without ground relief coverage, it would be faster to transfer emergency patients to the hospital by a helicopter. In this paper, an integer nonlinear programming model is presented for the integrated locating of helicopter sta- tions and helipads by considering uncertainty in demand points. We assume three transfer modes: (1) direct transfer by an ambulance, (2) transfer by an ambulance to a helicopter station and then to the hospital by a he- licopter, (3) transfer by an ambulance to a predetermined point and then to the hospital by a helicopter. We also assume that demands occur in a square-shaped area, in which each side follows a uniform distribution. It is also assumed that demands in an area decrease errors in the distances between each two cities. The purpose of this model is to minimize the transfer time from demand points to the hospital by considering different modes. The proposed model is examined in terms of validity and applicability in Lorestan Province and a sensitivity anal- ysis is also conducted on the total allocated budget.

(C) 2016

Introduction

Helicopter Emergency Medical Service was first used in 1944 when the beach guard helicopters transferred blood plasma from New York to survivors from a massive explosion in New Jersey. Twenty years later during Korea War, about 20,000 injured were trans- ferred to hospitals by helicopters [1]. In Iran, HEMS was first used in 1981 to transfer trauma patients during Iran-Iraq War [2]. Injury and harm influence the performance of body and organs. Most of these inju- ries become serious without intervention, but quick and timely actions can help the wounded to survive. Emergency experts describe this time as “accident subsequent golden time”, during which half of the deaths occur.

In the regions without ground relief coverage, locating helicopter stations makes it easier to transfer emergency patients to medical cen- ters. Emergency helicopters can pass directly between two points, cover vaster area and also have more speed than ground ambulances. Thus, they can give better services to emergency injuries or the wound- ed with limited access to hospitals. Some points are geographically mountainous or have high population density that disturbs the helicop- ter landing process. So it seems critical to install helipads for the suc- cessful implement of HEMS [3].

* Corresponding author.

E-mail addresses: [email protected] (A. Bozorgi-Amiri), [email protected]

(S. Tavakoli), [email protected] (H. Mirzaeipour), [email protected] (M. Rabbani).

HEMS usually acts as follows: first, an emergency unit like an ambu- lance is sent to the incident location. After evaluating the situation of in- juries, a helicopter is requested to transfer the injured to the hospital if necessary. After that, the Ambulance transfers the injured people to the helipad which is appropriate for helicopters for landing and taking-off. At the same time, a helicopter is sent out to the helipad from the heli- copter station. Because of this complex structure, designing an efficient HEMS system requires more complicated decisions than the ground ambulance transfer system [3]. Generally, there are three assumed transfer modes as follows:

Transferring patients directly to the hospital by an ambulance from demand areas.
  • Moving patients to the helicopter station by an ambulance and then transferring them to the hospital by a helicopter deployed at the station.
  • Transferring patients to the helipad by an ambulance and then trans- ferring them to the hospital by a helicopter.
  • The purpose of this study is to find the optimal helicopter stations and helipad locations considering uncertainty in demand areas. The ne- cessity of assuming demands in an area form, instead of single point, is to decrease computational errors occurring when the distance travelled between cities or facilities in the area is assumed as the distance be- tween those areas’ center points [4]. Subject to the uncertainty of inci- dent points in the real world, in this paper, we assume that a demand occurs in a square demand area and its length and width follow a

    http://dx.doi.org/10.1016/j.ajem.2016.11.024

    0735-6757/(C) 2016

    uniform distribution. As we reviewed the most important studies in HEMS context, this paper is the first one which considers demand point in an area shaped type.

    Generally, novelties of this paper compared to other works are as follows:

    A new model for simultaneously locating helicopter stations and he- lipads for the transfer of the wounded.
  • Ways of considering demands in a uniformly distributed area, in- stead of single demand points.
  • Ways of considering rectilinear distance for ambulances and Euclidean distance for helicopter movement.
  • Ways of considering budget constraints for the establishment of facilities.
  • Implementing the model in Lorestan Province, Iran, as a real case study. The organization of this paper is as follows: first, we review the liter-
  • ature of HEMS and the transfer point problem. Then, we describe the

    problem and explain the possible modes and assumptions and also present the problem modeling. Afterwards, we represent a numerical example of the problem and perform sensitivity analysis on the param- eter of assigned budget. In the next step, the model case study (Lorestan Province) is represented. Finally, the conclusion and future suggestions are made.

    Literature review

    Studies on emergency medical service (EMS) stations widely emerged in 1970s [5]. Based on the literature, most researchers have been focused on the establishment of EMS stations, especially ambu- lance location problem. A comprehensive study on this subject is in [6, 7]. Helicopter location models have been less considered than ambu- lance location models. Hub-and-spoke models are most relevant to the transfer point problem and can be the basis of TPLP models. The aim of the hub location problem is to establish hub facilities and allocate demand nodes to hubs in order to route the path between origin and destination centers [8]. Goldman [9] proposed the first study in the area of hub location problem in the networks and reviewed the hub nodes optimizing features in Hakimi’s work. O’kelly [10] formulated the first known Mathematical model of hub location by studying pas- senger airlines. To consider a comprehensive review in hub location problems, the literature is summarized in Alumur and Kara [11].

    Berman et al. [12] defined the transfer point problem as follows: “the problem of selecting a location of a new facility which plays the role of a hub center and covers N demand points”.

    Although the transfer point location problem is in the category of hub location problems, it is different from this category in two main as- pects. First, hub location problems are often studied on the network, but the transfer point location problem is not limited to this topology. Sec- ond, in hub location problems, the demand exists between each pair of nodes and there is no backup facility, but in the transfer point prob- lem, these facilities play a substantial role in the model [8]. For the first time, Berman et al. [13] discussed transfer point location problem

    (TPLP), the purpose of which is to determine the transfer point location by considering predetermined facility location and assuming that the demand points can be serviced by transfer point. Berman et al. [14] also studied facility and transfer point location problem (FTPLP) in an- other work, which aimed to determine the location of facilities and the transfer points under such conditions that the location of facilities and transfer points were not predetermined and each demand point could be serviced from facilities by a transfer point and a heuristic ap- proach can also be presented to solve it. Berman et al. [15] also present- ed multiple location of transfer point (MLTP) problem with the purpose of determining the location of transfer points by assuming that locations of facilities and transfer points were predetermined and each demand point could be serviced from facilities by a transfer point. Sasaki et al.

    [16] extended the MLTP problem similar to the P-median problem and got the optimum values. They also presented a new model of FTLP prob- lem and provided an enumeration-based approach to solve single facil- ity problems. Berman and Drezner [17] studied P-median problem by considering uncertainty in a number of servers.

    Also in the field of locating helicopter stations, the most important works are as follows: Schuurman et al. [18] developed an approach to assign an additional helicopter station so as to maximize the demand coverage of regions without a helicopter station. They implemented their model in a real case where two hospitals with helicopter medical services existed. In their analysis, five years of critical care data from British Columbia Trauma Registry along with population and travel time data were employed. Branas et al. [19] presented a model that could simultaneously determine optimum locations of trauma centers and helicopter stations. They also suggested a heuristic algorithm to solve their model and implemented their model in many regions in the United States [20]. Fulton et al. [21] presented an optimization model under uncertainty in order to make decisions about the redesign and relocation of emergency service facilities such as helicopters and lo- cation of ground ambulances during military stability operations. The optimum location of helicopter stations, hospitals and helicopter paths were investigated in their model so as to minimize expected travel time over all the possible scenarios. Erdemir et al. [22] presented an HEMS in New Mexico where it was not necessary for demands to only occur at nodes and they can also occur at routes. Erdemir et al. [23] de- veloped a model for service facilities with demands on both nodes and paths to find the optimum location of helicopter stations in order to maximize covered demands. Erdemir et al. [24] suggested two covering models for the locations of ambulance, helicopter and transfer points. One of their models tried to minimize the sum of the establishment cost of these three facilities while covering all the demand points. The other model sought to provide the maximum coverage of demands within the given Total cost. Hosseinijou and Bashiri [8] modeled the TPLP problem of Berman by considering a uniform distribution for de- mand point and solving it. Kalantari et al. [25] modeled the TPLP model by Berman et al. via considering fuzzy uncertainty at demand points and solved it by a heuristic method. Furuta and Tanaka [3] pre- sented a developed P-median and P-center model for the location of joint helicopter and transfer points with deterministic demand points. In their model, Euclidean distance was considered in all distances.

    Table 1

    Summary of the most important studies on TPLP.

    Author(s)

    Parameter type

    Topology

    Objective function

    Solution method

    Explanations

    Berman et al. [13]

    Deterministic

    Plane/network

    Minisum/minimax

    Exact/heuristic

    Origination

    Berman et al. [14]

    Deterministic

    Network

    Minisum

    Heuristic

    FTPLP

    Berman et al. [12]

    Deterministic

    Plane/network

    Minisum/minimax

    Exact

    TPLP

    Berman et al. [15]

    Deterministic

    Plane/network

    Minisum/minimax

    Heuristic

    MLTP

    Sasaki et al. [16]

    Deterministic

    Network

    Minisum

    Exact

    FTPLP

    Hosseinijou et al. [8]

    Uncertain/stochastic

    Plane

    Minimax

    Exact

    TPLP

    Kalantari et al. [25]

    Uncertain/fuzzy

    Plane

    Minisum

    Heuristic

    TPLP

    Furuta et al. [3]

    Deterministic

    Network

    Minisum/minimax

    Exact

    FTPLP

    This paper

    Uncertain

    Network

    Minisum

    Exact

    FTPLP

    Table 2

    Summary of the most important studies on HEMS

    Author(s)

    Parameter type

    Topology

    Objective function

    Time horizon

    Solution method

    Schuurman et al. [18]

    Deterministic

    Plane

    Maximizing weighted demand coverage

    Strategic

    Exact

    Branas et al. [19]

    Deterministic

    Network

    Minimizing time average

    Strategic

    Heuristic

    Fulton et al. [21]

    Uncertain/scenario

    Network

    Minimizing time average regard to intensity of injury

    Tactical

    Exact

    Erdemir et al. [23]

    Deterministic

    Network

    Maximizing weighted demand coverage

    Strategic

    Exact

    Erdemir et al. [24]

    Deterministic

    Network

    Minimizing sum of establishment costs/maximizing weighted demand coverage

    Strategic

    Heuristic

    Furuta et al. [3]

    Deterministic

    Network

    Minimizing the maximum time/minimizing time based on weighted demand

    Strategic

    Exact

    Furuta et al. [26]

    Deterministic

    Network

    Maximizing weighted demand coverage

    Strategic

    Exact

    This paper

    Uncertain

    Network

    Minimizing time based on weighted time

    Strategic

    Exact

    They also introduced a doctor-helicopter system in another study, in which a doctor was delivered to the patients by a helicopter. The objec- tive function of their model was to maximize demand cover [26].

    Table 1 shows the summary of the most important studies in TPLP context and the comparison with our study. Table 2 shows the most im-

    portant studies on HEMS and the comparison with our work.

    the hospital, (rx, ry) is the coordinate of helipads and (sx, sy) is the coor- dinate of helicopter stations.

    The distance between helicopter station and hospital D1, distance between helipad and hospital D2 and also distance between helicopter station and helipad D3 are calculated as follows:

    D1 = q(ffiffihffiffiffixffiffi-ffiffiffiffiffisffiffixffiffiffi2ffiffiffiffiffiffiffiffi ffiffiffihffiffiyffiffi-ffiffiffiffiffisffiffiyffiffi ffiffi2ffiffi

    3. Problem definition and mathematical model

    )

    +

    (2)

    Prior to presenting our mathematical model, we explain different

    D2 = q(ffiffihffiffiffixffiffi-ffiffiffiffiffirffiffixffiffiffi2ffiffiffiffiffiffiffiffiffi ffiffihffiffiyffiffi-ffiffiffiffiffirffiffiyffiffi ffiffi2ffiffi

    (3)

    possible transfer modes to the hospital. In the first mode, the injured

    would be transferred directly to the hospital by an ambulance. Fig. 1 ex-

    )

    +

    3

    x

    x

    y

    y

    poses this mode. In the second mode, the injured would be transferred to the helicopter station by an ambulance and then to the hospital by a

    D = q(ffiffisffiffiffiffi-ffiffiffiffiffirffiffiffiffi)ffiffi2ffiffiffi+ffiffiffiffiffi ffiffisffiffiffiffi-ffiffiffiffiffirffiffiffiffi ffiffi2ffiffi

    (4)

    helicopter. Fig. 2 shows this mode. In the third status, the injured would be transferred to the helipad by an ambulance. At the same time, a he- licopter would be sent out to the helipad and, after the ambulance and helicopter arrived at the same location, the injured would be transferred to the hospital by a helicopter. This mode is shown in Fig. 3. The key de- cision factor to select each mode is the transferring time of the injured to the hospital which is determined by the shortest time of each mode’s transferring time (TD). T1, T2, T3 represent the transferring time from de- mand area to the hospitals by modes one, two or three, respectively.

    In this problem, it is assumed that each demand area has Pi=(Ui, Vi) coordination, in which Ui and Vi are independent stochastic variables with [a,b] uniform distribution. In other words, demand happens in a [a,b] x [a,b] square-shaped area.

    U; V ~uniform[a; b] (5)

    Because Ui and Vi are independent random variables with a uniform distribution in [a,b], so we have:

    TD = min(T1; T2; T3) (1)

    f U (u) = 1

    1

    ; f V (v) = ba

    (6)

    In this model, the ambulance distances are calculated by rectilinear distance. Also, the helicopter distances are calculated by Euclidean dis- tance because helicopters can travel directly between two points and do not face any obstacles. In this problem, (hx, hy) is the coordinate of

    ba

    Fig. 1. First mode of transferring the injured to the hospital.

    P = (U; V )?[a; b] x [a; b] (7)

    In fact, with the above-mentioned assumptions, we can consider that cities are square-shaped and the probability of incident at each point of this city is constant. To calculate the distance between the de- mand area and hospital di(hx, hy), the demand point and helicopter sta- tion di(sx, sy) and demand area and helipad di(rx, ry), we have:

    di hx; hy = |Uhx| + V hy (8)

    di sx; sy = |Usx| + V sy (9)

    di rx; ry = |Urx| + V ry (10)

    Fig. 2. Second mode of transferring the injured to the hospital.

    Fig. 3. Third mode of transferring the injured to the hospital.

    Now, we can calculate the expected value of distance between the helipad and the hospital as follows:

    Sets and parameters

    E di hx; hy = E |Uhx| + V hy = E[|Uhx|] + E V hy (11)

    I: Set of demand points indexed by i

    J: Set of candidate locations for helipads indexed by j

    We also have:

    +? b

    Z Z

    f (h ) = E[|Uh |] = |uh | f (u)d = 1 |uh |d

    (12)

    K: Set of candidate locations for helicopter stations indexed by k Ct: Establishment cost of each helipad

    Cs: Establishment and mobilization cost of each helicopter station

    B: Total budget of the plan

    x x x u

    -?

    8> –hx + a + b

    2

    u ba x u a

    hx <= a

    hi: Demand weight of each demand area i v: Helicopter speed

    w: Ambulance speed

    Decision variables

    >>< 2 2

    f (hx) =

    (hxa) + (hxb)

    2(ba)

    >>: hxa + b

    2

    a <= hx <= b (13)

    hx >= b

    xj: 0-1 location variable; 1 if helipad is established at node j, 0 otherwise

    yk: 0-1 location variable; 1 if helicopter station is established at node k,0

    f(hy), f(rx), f(ry), f(sx) and f(sy) is calculated as above.

    In this section, an integer mathematical modeling is developed to solve the problem. We assume that demand areas and hospital locations are pre-determined. Our objective is to determine the optimum location of helicopter stations and helipads in a way to minimize the transfer time from demand areas to hospitals under different transfer modes. In order to model the problem, we define these parameters and decision variables.

    otherwise

    ui: 0-1 allocation variable; 1 if demand i is met by the ambulance (first mode), 0 otherwise

    lik: 0-1 allocation variable; 1 if demand i is met by station k (second mode), 0 otherwise

    ?ijk: 0-1 allocation variable; 1 if demand i is met by the combination of transfer point j and station k (third mode), 0 otherwise

    Tijk: Auxiliary variable which is the maximum value between ambulance arrival time to helipad and helicopter arrival time from base to transfer point j

    Fig. 4. Candidate points for helicopter station and helipad.

    Fig. 5. Activated points for helicopter station and helipad.

    Mathematical model

    minX X X h u + ”

    f hx(i) + f hy(i) f sx(i) + f sy(i)

    w

    w

    i i

    i?I j? J k?K

    q ffiffiffihffiffixffiffiffiiffiffiffi-ffiffiffiffisffiffixffiffiffikffiffiffiffi ffiffi2ffiffiffi+ffiffiffiffiffi ffiffihffiffiffiyffiffiffiiffiffi-ffiffiffiffiffisffiffiyffiffiffikffiffiffi ffiffi2ffiffi#

    + v l

    ( ) ( ) ( ) ( )

    ik

    2 q ffiffiffihffiffixffiffiffiiffiffiffi-ffiffiffiffirffiffixffiffiffiffijffiffi ffiffiffi2ffiffiffi+ffiffiffiffiffi ffiffihffiffiffiyffiffiffiiffiffi-ffiffiffiffiffirffiffiyffiffiffijffiffiffi ffiffi2ffiffi3 )

    (14)

    xj?{0; 1}yk ?{0; 1}ui?{0; 1}lik?{0; 1}?ijk?{0; 1} i?I; j? J; k?K (22)

    The objective function (14) is the total weighted demand transfer time under different modes. Constraint (15) implies that demand i can be assigned to the second mode if a helicopter station is located at k. Constraints (16) and (17) together imply that demand i can be assigned to the third mode if a helipad is established at node j and a helicopter

    station is established at node k. Constraint (18) states that each demand

    s.t.

    +4Tijk +

    () ( )

    v

    () ( )

    5?ijk

    is assigned to only one of these three modes. Constraint (19) is the total budget constraint on the construction of helipads and helicopter sta- tions. Constraints (20) and (21) are used to linearize the objective func- tion in the third mode which represents that the ambulance’s and helicopter’s meeting time is equal to the maximum arrival time of each of these facilities to the helipad. Constraints (22) are the standard binary constraints.

    Numerical example

    In order to represent this model’s performance, first, a simple exam-

    ui + X lik + X X ?ijk = 1 i?I (18)

    lik <= yk

    i?I; k?K

    (15)

    ?ijk <= xj

    i?I; k?K; j? J

    (16)

    ?ijk <= yk

    i?I; k?K; j? J

    (17)

    k?K

    j? J k?K

    ple is given and, then, application of this model in a real case is discussed.

    X Ctxj + X Csyk <= B (19)

    j? J

    Tijk

    k?K

    >= f rx( j) + f ry( j)

    w

    i?I; j? J; k?K (20)

    q ffiffiffirffiffixffiffiffijffiffiffi-ffiffiffiffisffiffixffiffiffikffiffiffi ffiffiffi2ffiffiffi+ffiffiffiffiffi ffiffirffiffiyffiffiffijffiffiffi-ffiffiffiffiffisffiffiyffiffiffikffiffiffi ffiffi2ffiffi

    T

    >=

    ( )

    ( )

    ( )

    ( )

    i?I; j? J; k?K (21)

    ijk

    v

    Table 3

    Sensitivity analysis of assigned budget.

    Status

    Assigned budget (in billion Rial)

    Objective function of time

    Number of helipad points

    Number of helicopter stations

    Without implementing HEMS

    2.625

    With HEMS

    13

    1.577

    1

    1

    18

    0.715

    4

    1

    23

    0.537

    5

    1

    28

    0.432

    8

    1

    33

    0.432

    8

    1

    43

    0.418

    8

    2

    63

    0.418

    8

    2

    Fig. 6. Changing activated helipads and helicopter stations with increasing budget.

    Fig. 7. Changing objective function (time) with increasing budget.

    Table 4

    Population of important cities in Lorestan Province.

    Table 5

    Transfer mode of cities in Lorestan Province.

    No.

    City name

    City population

    Population weight (hi)

    No.

    Demand point

    Status

    Active helicopter station

    Active transfer point

    1

    Khorramabad

    354,855

    0.331

    1

    Khorram Abad

    First

    2

    Borujerd

    245,737

    0.229

    2

    Dorud

    Second

    Dorud

    3

    Dorud

    100,977

    0.094

    3

    Azna

    Third

    Dorud

    Aligudarz

    4

    Kuhdasht

    111,736

    0.104

    4

    Aligudarz

    Third

    Dorud

    Aligudarz

    5

    Aligudarz

    89,520

    0.083

    5

    Borujerd

    Third

    Dorud

    Borujerd

    6

    Nur Abad

    62,190

    0.053

    6

    Aleshtar

    Third

    Kuhdasht

    Aleshtar

    7

    Azna

    41,706

    0.039

    7

    Nur Abad

    Third

    Kuhdasht

    Farhad Abad

    8

    Aleshtar

    33,133

    0.031

    8

    Kuhdasht

    Second

    Kuhdasht

    9

    Pol Dokhtar

    32,594

    0.030

    9

    Pol Dokhtar

    Third

    Kuhdasht

    Pol Dokhtar

    Total population 1,072,448 1

    In Fig. 4, green squares represent demand areas which are distribut- ed in 2 x 2 dimension in a coordinate plane. Blue circles are helipads’ es- tablishment candidate points and orange triangles are helicopter stations’ establishment candidate points. The hospital is considered at the coordination origin point. There are 24 suggested points for helipads and 12 for helicopter stations.

    By considering 23,000,000,000 Rial as the budget, 2,000,000,000 Rial for each transfer point establishment, 10,000,000,000 Rial for each heli- copter station establishment, the helicopter speed of 200 km/h, and am- bulance speed of 40 km/h, the optimum value of the objective function was obtained as 0.537 by the GAMS software and points in Fig. 5 were activated.

    In Table 3 the comparison of transfer times in two modes is shown. According to Table 3, a noteworthy decrease in transfer time is observed by implicating HEMS and increasing budget. Also, we can see in Fig. 6 that by increasing the budget, the number of activated helipads and he- licopter stations increases; however, in some cases, this increase does not influence the number of activated helipads and helicopter stations. According to Fig. 7, the objective function, by increasing the budget, starts to decrease moderately; however, in some cases, particularly higher budgets, the objective function does not change.

    Case study – Lorestan Province

    Lorestan Province is one of the western provinces in Iran, with the area of 28,294 km2 and population of more than 1,700,000. According

    to the evidence, there are too many accidents happening on the roads of this province, and with respect to active faults in Zagros Mountains and potential flooding in the south part of this province, especially in Pol Dokhtar, Lorestan is among the 10 most accident-prone provinces of Iran. Therefore, it seems critical to implement a suitable emergency healthcare system in this province. In Table 4, the most important cities of Lorestan Province are listed based on their population and its related weight. “Shohada-e-Ashayer” Hospital is located in Khorramabad City which can respond to traumatic patients. The objective community of this research was the accident injured patients needing to be trans- ferred to Shohada-e-Ashayer Hospital as soon as possible.

    Each of these 9 cities in Table 4 is inscribed in a square with respect to their area (Fig. 8). Each city’s weight (hi) was calculated by dividing pop- ulation of each city by its total population. According to the comments of experts, these 8 points were considered as helicopter station candidate points: Azna, Aligudarz, Dorud, Borujerd, Aleshtar, Nur Abad, Kuhdasht and Pol Dokhtar. Also, these 18 points were considered as helipad sug- gested points: Beyranvande Junubi, Razan, Zargaran Olia, Dorud, Azna, Aligudarz, Borujerd, Oshtarinan, Varayeneh, Aleshtar, Firuzabad, Farhad Abad, Nur Abad, Sarab-e-Dowreh, Kuhdasht, Afrineh, Romeshgan and Pol Dokhtar.

    In addition, all the coordinates of the considered points were calcu- lated by Google Earth v. 6. The total budget for this plan was considered 130,000,000,000 Rial. Each transfer point establishment cost was esti- mated as 2,000,000,000 Rial and the cost of each helicopter station with its helicopter was 60,000,000,000 Rial.

    Fig. 8. Lorestan Province’s helicopter stations and helipad candidate points.

    Fig. 9. Transfer modes from demand areas to hospitals.

    The problem was solved by the GAMS software on a computer with these specifications: Intel Core i5 – 2.4 GHz CPU and 4 GB RAM. In the mathematical model, the objective function was equal to 32.4 min. The model activated two helicopter stations and five helipads. The po- tential cities for establishing helipads were Aligudarz, Borujerd, Aleshtar, Farhad Abad and Pol Dokhtar. Also, Dorud and Kuhdasht were nominated for establishing helicopter stations. For instance, if an injury occurred in Khorramabad, it was better to use ground ambulance for transferring the patients to the hospital. Also, if any injury occurred in Dorud, the fastest way to carry patients to the hospital was the second mode which was carrying patients by an ambulance to the Dorud heli- copter station and, then, to the hospital by a helicopter. If any injury oc- curred in Azna, it was better to use the third mode where the ambulance and helicopter both arrived at the Aligoudarz helipad and, from there, the patient was carried to the hospital by a helicopter. Table 5 shows how each demand area is assigned to each of the three modes.

    Fig. 9 shows each demand area’s transfer mode in this province ac- cording to Table 5.

    Conclusions and recommendations

    In this paper, an integrated helicopter station and helipad location model was developed by considering uncertainty. Some points were geographically located in mountainous areas or those with high popula- tion density, which could make helicopter landing procedure difficult. Thus, it seemed necessary to establish helipads. There were three modes to transfer injuries to the hospital. The first mode was to transfer injuries directly to the hospital by an ambulance, the second was to transfer them to the helicopter station by an ambulance and, then, to the hospital by a helicopter and the third was to transfer them to heli- pad by an ambulance and, then, to the hospital by a helicopter. In this paper, the demand area followed a uniform distribution. Demand areas were considered for decreasing computational errors occurring when the distance travelled between cities was assumed as the distance between their areas’ center points. The model objective function attempted to minimize the sum of transfer times from demand areas to the hospital. To evaluate the model, a simple numerical example was set and its results proved the advantages of the HEMS system in comparison with the traditional system. In addition, based on the case study performed in Lorestan Province, optimum places to establish

    helipads and helicopter stations were determined and allocation type of each facility to demand regions was also specified. Future studies can (1) consider a capacity for each emergency facility, (2) implement the HEMS system by assuming disruption in the network, (3) study more comprehensive cases at various points, different modes and more realistic conditions, (4) consider the distribution of the ambu- lances in the demand areas and its impact on the model and (5) consider uncertainty on the time of ground EMS services due to geographic issues.

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      Ali Bozorgi-Amiri received his B.S., M.S. and PhD degrees in Industrial Engineering from Iran University of Science and Technology, Tehran, Iran. He is currently an Assistant Profes- sor in the School of Industrial Engineering at College of Engineering, University of Tehran, Iran. His research interests include: disaster relief supply chain management, emergency/

      humanitarian logistics and uncertain programming. He has published several papers in re- lated filed in refereed journals and conferences.

      Shayan Tavakoli is a M.Sc. student at the school of Industrial Engineering, University of Tehran, Tehran, Iran. He obtained the undergraduate degree from Khajeh Nasir Toosi Uni- versity of Technology (KNTU) in Industrial Engineering, Tehran, Iran. His research interest is disaster and emergency planning.

      Hossein Mirzaeipour is a M.Sc. student at the school of Industrial Engineering, University of Tehran, Tehran, Iran. He obtained the undergraduate degree from University of Yazd in Industrial Engineering, Yazd, Iran. His research interest is emergency planning and facility location under uncertainty.

      Masoud Rabbani received his M.S. degree in Industrial Engineering from Iran University of Science and Technology and then his PhD degree in Industrial Engineering from Amir Kabir University of Technology, Tehran, Iran. He is currently a professor in the School of In- dustrial Engineering at College of Engineering, University of Tehran, Iran. His research in- terests include: graph theory, nonlinear optimization, production management, supply chain management & logistics. He has published several papers in related filed in refereed journals and conferences.

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