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Air taxi skyport location problem with single allocation
choice-constrained elastic demand for airport access
Srushti Rath and Joseph Y.J. Chow
C2SMART University Transportation Center
Department of Civil and Urban Engineering New York
University, NY, USA
Email: srushti.rath@nyu.edu, joseph.chow@nyu.edu
Abstract
Witnessing the accelerated commercialization efforts for air taxi services in across metropolitan cities,
our research focuses on infrastructure planning of skyports. We consider design of skyport locations for air
taxis accessing airports, where we present the skyport location problem as a modified single-allocation p-
hub median location problem integrating choice-constrained user mode choice behavior. Our approach
focuses on two alternative objectives i.e., maximizing air taxi ridership and maximizing air taxi revenue. The
proposed models in the study incorporate trade-offs between trip length and trip cost based on mode choice
behavior of travelers to determine optimal choices of skyports in a city. We examine the sensitivity of
skyport locations based on two objectives, three air taxi pricing strategies, and varying transfer times at
skyports. A case study of New York City is conducted considering a network of 149 taxi zones and 3
airports with over 20 million for-hire-vehicles trip data to the airports to discuss insights around the choice
of skyport locations in the city, and demand allocation to different skyports under various parameter settings.
Results suggest that a minimum of 9 skyports located between Manhattan, Queens and Brooklyn can
adequately accommodate the airport access travel needs and are sufficiently stable against transfer time
increases. Findings from this study can help air taxi providers strategize infrastructure design options and
investment decisions based on skyport location choices.
Keywords: urban air mobility (UAM); advanced air mobility (AAM); air taxi; skyport location; revenue
management; hub location problem.
Preprint to be published in the Journal of Air Transport Management
I.
INTRODUCTION
Major cities around the world are currently struggling with a common problem: traffic congestion resulting from
urban population growth and limited roadway capacity. Spikes in travel time across congested routes in a city can
have unpleasant consequences, e.g., not reaching the airport on time to catch a flight or delaying emergency vehicles
in delivering a critical patient to a medical center. Such concerns have pushed the development of new higher speed
transportation modes to avoid surface congestion altogether. eVTOL (electric vertical takeoff and landing) vehicles,
also known as electric ’air taxis’, are emerging as a promising option to improve urban mobility. While helicopter
services have been around for quite a long time in various metropolitan areas, (e.g., New York City, Los Angeles, Sa˜o
Paulo), the concept of urban air mobility (UAM) or advanced air mobility (AAM) for passenger transportation is
focused on providing on-demand shared mobility using technology-efficient, less noisy, affordable, environment
friendly and potentially automated aerial vehicles (i.e., air taxis). While air taxi services have not yet been launched
in any major city, multiple industry groups (including air manufacturers, large private companies, and smaller start-
ups) are actively working on projects to offer such services in the next few years (e.g., Uber, Hyundai, Toyota, EHang,
Volocopter, AirBus, Boeing, Lilium Jet, Terrafugia, Joby Aviation, Kitty Hawk and others).
In 2016, the transportation network company Uber released a comprehensive white paper (Holden and Goel,
2016) with a follow-up technical document (UberElevate, 2018) discussing their view on requirements of urban air
taxis to make UAM feasible as an affordable solution to commuters. It is estimated that producing high volumes of
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safe and reliable air taxis would drive down passenger costs per trip (Hornyak, 2020; Holden et al., 2018).
Furthermore, various technology requirements and regulatory steps associated with on-demand aerial mobility have
been discussed by NASA (Holmes et al., 2017; Johnson and Silva, 2018); these include the use of distributed electric
propulsion, concept vehicle design, power and energy requirements, noise and emission reduction, safety, and
reduction in operation and energy costs. In past years, major brands and other eVTOL start-ups have made tremendous
progress towards making the UAM concept a reality (Downing, 2019; Glon, 2020). NASA signed Space Act
Agreements with 17 companies in the aviation industry to conduct full field tests in urban environments. The UAM
Grand Challenge (Hackenberg, 2019) by NASA is the first in a series of technology demonstrations aimed at
evaluating different elements of UAM operations under various weather, traffic, and contingency conditions. A first
version of an UAM Concept of Operations was released by the Federal Aviation Administration (Bradford, 2020)
providing an initial road map on achieving high volume and safe urban air taxi operations. Such active interest and
serious funding supporting air taxi projects is indicative of its (potential) widespread adoption in the near future.
Identifying the UAM market and understanding customers’ preferences for on-demand eVTOL services is the
primary consideration for planning UAM operations. As a preliminary assessment of the impact of air taxi services,
several groups conducted surveys and analyses. For example, Rothfeld et al. (2018b) confirmed via simulations that
the reduction in travel time may strongly influence the adoption of air taxi services. Another survey conducted by
Airbus (Thompson, 2018) spanning three regions (New York City, Frankfurt and Shanghai) indicated that airport
access/transfers are the best use case for UAM adoption by commuters. Similar investigation by other studies
including Berger (2018); Goyal et al. (2018); Hasan (2019); Shaheen et al. (2018) suggests airport transfers as the
most promising early market for UAM technology; this market could extend to include other urban commute trips as
the density of demand for UAM increases with increasing fleet size and service area coverage (Goyal et al., 2018).
Some recent studies that focus on the use case of airport access via UAM investigate business model options
(Straubinger et al., 2021), economic feasibility (Lewis et al., 2021), demand estimation (Rimjha et al., 2021), and
flight scheduling (Roy et al., 2022) of UAM services. The white paper by Uber (Holden and Goel, 2016) identified
infrastructure development as a key challenge in enabling efficient UAM operations. In their paper, the term ’skyport’
or ’vertiport’ denotes the ground infrastructures required for air taxi operations (i.e., boarding, alighting of passengers,
eVTOL charging, take-off and landing operations). The air taxi service is multimodal in nature i.e., the end-to-end
trip would mainly involve use of ground transportation to and from the skyports (Goyal, 2018). Kreimeier et al. (2016)
found that the willingness to pay for such on-demand aviation services is greatly affected by the first mile and last
mile ground transportation distance. Thus, location of skyports based on travelers’ choices might be a crucial factor
in the overall adoption of this emerging mode of transportation.
Our study draws motivation from the key findings in the above studies. We focus on the problem of planning the
ground infrastructure for air taxi services for airport access/transfers in an urban city. In particular, we incorporate
travelers’ preferences for UAM services to determine optimal skyport locations in an urban city with an objective of
providing economically sustainable solutions to air taxi service providers. Given a large city with multiple
candidate skyport locations, it is non- trivial to select a small subset as skyports that attracts all customer groups
with different preferences, especially when the location choices and users’ decisions of using air taxi services are
closely interrelated.
Contribution: The broader market of mobility-on-demand and shared mobility has radically expanded in the
global urban mobility sector over the past decade, along with an increasing interest in sustainable transportation
solutions. Due to the rapid technological advancement (specifically regarding distributed electric propulsion and
battery storage (Kuhn et al., 2011; Rezende et al., 2018), the concept of on-demand UAM using eVTOLs has captured
much public attention and research interest in recent years as an energy-efficient, cost-effective, and competitive
solution in an emerging market to alleviate traffic congestion in large cities and urban areas (Shamiyeh et al., 2017).
It is important to identify and analyze the potential benefits, challenges and impact of UAM to successfully
implement and integrate eVTOLs into the existing transportation ecosystem. One of the major factors closely tied to
effective UAM operations is the ground infrastructure i.e., skyport locations in a city. Since the success of initial
UAM networks would most likely determine the future demand and evolution of such services in cities, initial
infrastructure planning and design of skyports is an important topic of research.
The contribution of this study is a proposed skyport location problem with elastic demand response and solution
methodology that can be used by air taxi service providers for determining skyport locations in cities considering
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short term and long term price scenarios. The problem is a variant of the classic hub location problem (HLP)
(Campbell, 1994b; O’Kelly, 1987). Given a set of fixed facilities (in our case airports) each serving various demand
points, the location-allocation problem optimizes subsets of demand locations to be assigned to different transfer
points (in our case skyports) for connection to multiple facilities (airports). We model the objective function in two
ways leading to two variants of the skyport location problem i.e., (1) revenue maximization problem and (2) ridership
maximization problem. Our method optimizes the skyport locations considering travel costs, transfer times, and user
demand for air taxis using a logit model. Typically, such a formulation would be nonconvex due to the logit model
constraint, but we show that under the single allocation model design we can formulate it as a linear model that can
be solved using linear programming solution approaches. We analyze the sensitivity of skyport locations under three
different pricing strategies (considering short-term and long-term price scenarios) and varying transfer times at
skyports, to study how these parameters affect the choice of optimal skyport locations in a city. To be clear, this is an
operational demonstration study; profitability analysis of air taxi services is beyond the scope of this study. Although
the results are demonstrated for NYC, this method is fairly general and can be applied to other cities selected for air
taxi operations. The findings of this study can provide insights that can be useful to manufacturing companies,
policymakers, and shared mobility providers on how they may want to design the UAM infrastructure within an
existing transportation network.
The remainder of this paper is organized as follows. Section II covers related work (including prior work on UAM
infrastructure, and location models in the broader hub location framework) and highlights research gaps that motivated
this study. The proposed methodology is described in Section III. This is followed by Section IV on the experiment
and results and we conclude in Section V.
II.
LITERATURE REVIEW
A.
Prior work on eVTOL and research gaps
We first describe the recent industry research surrounding UAM and eVTOLs followed by prior work on eVTOL
infrastructure planning.
Due to the rapid technological advancement, the concept of on-demand urban air mobility has captured much public
attention and research interest in recent years. eVTOLs have been an area of active investment for various air
manufacturers, service companies, and high-tech giants who have been pushing for its public acceptance. While the
development of a safe and efficient eVTOL is necessary for implementation of UAM, various challenges and barriers
to the future of UAM have been highlighted and addressed by companies, consulting services and regulatory agencies.
Some of the key challenges include public acceptance, market space, airspace integration, safety, noise, emissions,
air traffic management, regulations, certification, security, privacy, and pilot training (Deloitte Insights, 2019;
Holden and Goel, 2016; Pelli and Riedel, 2020; Thipphavong et al., 2018; Thompson, 2018; Merkert and Bushell,
2020; Bradford, 2020; Grandl et al., 2018; Holmes et al., 2017; Shaheen et al., 2018). Additionally, one of the crucial
factors identified was ground infrastructure (skyport) selection (Holden and Goel (2016)) to enable efficient air taxi
operations and link multiple modes of urban transportation for a complete end-to-end trip (Lineberger et al., 2009).
The multimodal structure of the air taxi service would include first mile access from origin location to the skyport,
followed by boarding on the eVTOL, flight leg (take-off and landing) on a landing pad, de-boarding, and last mile
transfer from the landing pad to nearest destination (Grandl et al., 2018; Lineberger et al., 2009). Due to limited space
availability in urban cities, utilization of existing helipads as well as rooftops of high-rise parking garages or buildings
for eVTOL operations is a topic of active interest (Duvall et al., 2019; Holden and Goel, 2016; Lineberger et al., 2019)
targeted at reducing the air taxi infrastructure cost. A recent study highlighting current research and development
in UAM (Straubinger et al., 2020) indicates ground infrastructure as a key determinant in successful adoption of
this technology.
In the academic research community, prior work on eVTOL infrastructure selection focus on operational and space
require- ments for UAM infrastructure while discussing several layout options for skyports (Alexander and Syms,
2017; Vascik and Hansman, 2017a,b,c, 2018). These studies highlight various factors that contribute toward
infrastructure planning of UAM (e.g., population density, income levels, long commute times to work, congestion,
tourism, and airport trips) and propose suitable locations for infrastructure (e.g., existing helipads, rooftops of existing
parking garages or high rise buildings, roadways, and open spaces in large intersections). Access to airports or other
major transport hubs was ranked the highest in a study by Fadhil (2018) (in terms of importance of factors in assessing
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ground infrastructure station selection); a GIS-based analysis was used for studying skyport placement options. Lim
and Hwang (2019) proposed selecting skyport locations by using a K-means clustering algorithm and demonstrated
results for the Seoul metro area. The clustering of trips to determine skyport locations (cluster centroids) was limited
to only three major routes within the city. In addition, there was no explicit optimization algorithm to minimize the
aggregate travel time based on the trips data, and the clustering approach was essentially a heuristic. Another similar
study is that of Rajendran and Zack (2019). They also looked at skyport placement, starting first with a comprehensive
analysis of the demand requirements for skyport siting before diving into analysis involving k-means clustering
approach. The authors only looked at demand within 1 mile of each skyport and ignored the access/egress times in
the computation of the switch to air taxi. Also, the air taxi eligible demand accounts for only the trips with air taxi
travel times at least 40% less than the ground trip duration. These approaches do not exploit the spatial structures of
multimodal paths (access, flight, and egress) connecting origins to destinations through different skyports located
across a city. Considering the importance of access and egress ground transportation in the willingness to pay for such
services (Kreimeier et al., 2016), it is essential to consider the trade-offs between the time savings and the service
cost in the skyport planning process.
In order to understand the user demand due to such factors (i.e., trip length and trip cost) and to be able to
incorporate effects of such factors on user behavior in the planning process, a discrete choice based demand model is
used. Based on multiple factors (individual specific, mode specific, attitudinal, social, psychological, and latent
variables), various studies have used discrete choice models to understand travel behavior and user adoption of UAM
services (Al Haddad et al., 2020; Balac et al., 2019a,b; Binder et al., 2018; Boddupalli, 2019; Fu et al., 2019;
Garrow et al., 2019; Ilahi et al., 2019; Roy et al., 2021). Some studies have also looked into users’ familiarity,
wariness of new technology (Winter et al., 2020), user perceived benefits of flying taxis (Ahmed et al., 2021), and
weather and ride related factors (Rajendran et al., 2021) affecting consumers’ willingness to fly such services. A
detailed market study by Booz-Allen and Hamilton, Inc. (Shaheen et al., 2018) estimated the potential demand of
UAM in several cities in the United States, such as New York City, Los Angeles, Washington, D.C., San Francisco
Bay area; we use their findings to calibrate the model in our case study. Using a demand model to incorporate traveler
decisions and choices for UAM services, we propose a more general and principled optimization framework based
on HLP for optimizing the locations of skyports in any given city. A survey by Thompson (2018) indicated that users
were willing to pay more for air taxi services to avoid the negative consequences of ground transportation congestion
leading to delays in airport transfers. Motivated by the survey results, we focus on airport access/transfers as a use
case and optimize skyport locations for (1) maximizing air taxi ridership and (2) maximizing air taxi revenue. The
advantage of modeling the skyport location problem using HLP structure with a mode choice model is that it is able
to capture access costs to the skyports along with transfer costs of switching between modes, and optimize the
locations based on the cost trade-offs to reflect user behavior.
B.
Related work on hub location problem and choice-constrained optimization
The problem setup in our study has fundamental connections with HLP. Hubs serve as transfer or switching points
in a many-to-many distribution network. The basic framework of the network HLP is to select the locations for hubs
in order to serve N demand points accessing a facility in a network such that they fulfill an objective (e.g., minimizing
distance or travel time between origin-destination pairs in a network, maximizing profit from the hub facility). The
potential locations for a hub facility are the trip origin locations (nodes) in the network.
The HLP can be applied to all areas where demand points need to be routed through some transfer locations or hubs
(such that several demand points can be collected together at these hubs) for distribution to facilities. For example,
this can be employed in an emergency aid system (Furuta and Tanaka, 2013) where patients can be transferred by
ambulance to heliports (hubs) to be flown to hospitals (facilities). Usually, this approach is used when the travel
distance (or time) from a hub to the facility is comparatively less compared to traveling directly from demand points
to the facility. Therefore, we use the concepts of HLP for locating multiple skyports to connect demand points in
a city to multiple airports.
Depending on the objective, there can be three major variations to the HLP (Campbell, 1994a, 1996):
1)
p-hub median (minisum),
2)
p-hub center(minimax), and
3)
covering problem,
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where p is the number of hubs (typically an input parameter). In the p-hub median problem, the objective is to
minimize the total transportation cost. This cost is defined in terms of the travel distance or the travel time from
origin to destination. The p-hub median problem is NP-hard; even if the hub locations are fixed, the allocation part
of the problem remains NP-hard (Kara, 1999). The problems which include service time are typically formulated as
p-hub center or hub covering problems. While the objective in p-hub center problems is to minimize the maximum
distance between origin and destination (O-D) pairs, the hub covering problem focuses on maximizing the service
coverage.
The first mathematical formulations of HLP were introduced by O’Kelly (1987). In the HLP literature, this
formulation is referred to as a single allocation p-hub median problem, where p is the number of hubs (typically an
input parameter). The first linear integer programming formulation of this quadratic model was proposed by Campbell
(1994b). Various linear models for HLP were later proposed by Ernst and Krishnamoorthy (1996) and Skorin-Kapov
et al. (1996). The hub facilities in the HLP are categorized as uncapacitated (where there is no capacity restriction,
Contreras et al., 2011; Klincewicz, 1996; Topcuoglu et al., 2005) and capacitated (where there is a limit to the
maximum flow passing through a hub) (Aykin, 1994; Ebery, 2001). Several studies consider hub location under
congestion effects, where the delay of accessing a hub is dependent on the flow entering the hub. Examples include
de Camargo and Miranda (2012); Marianov and Serra (2003); O
¨ zgu¨n-Kibirog˘lu et al. (2019). The reader may
refer to Alumur and Kara (2008); Campbell et al. (2002); Farahani et al. (2013) for a comprehensive review on
classification of various models and approaches to HLP. The classic HLP assumes the unit travel cost from a demand
point to the hub is the same as that of traveling directly to the facility, whereas the unit travel cost between hubs
(or from the hub to the facility (Berman et al., 2007)) is reduced by a discount factor ( i.e., 0 < < 1). Some
variants of HLP also allow direct connection from origin to the facility without being routed through a hub (Berman
et al., 2007, 2008; Hosseinijou and Bashiri, 2012). In line with these assumptions, our setup considers use of ground
transportation from demand points to skyports as well as for direct connections to airports, with air taxi connections
(faster speed) from skyports to airports. The discount factor and direct connections in the HLP are accounted for
in our skyport location model by mode specific travel costs in the multimodal setup.
Generic HLP problems are modeled mainly with an objective to minimize total network cost to satisfy all demand.
However, when the decision to allocate demand via hubs is dependent on trade-off between various decision variables
(as per user behavior), it is beneficial to define the model objective accordingly. For example, from a ridership
point of view, it may be more advantageous to locate skyports such that the air taxi demand (i.e., demand allocated
to skyports) is maximized. Similarly, from a revenue perspective, the total fare collected from the demand going via
skyports should be maximized. There are limited studies in the HLP literature focusing on maximization objectives.
One variant of HLP with such objective is the hub maximal covering location model introduced by Campbell (1994b)
where hubs try to maximize the demand coverage. Various extension to this model with different notions of coverage
were investigated by Hamacher and Meyer (2006); Hwang and Lee (2012); Kara and Tansel (2003); Tan and Kara
(2007); Wagner (2008). Alibeyg et al. (2016) introduced hub network design with profit and provided exact solution
for such problems (Alibeyg et al., 2018). The profit calculation is based on total revenue obtained from captured
flows minus the total cost of establishing hubs. Variations to this model setup can be found in Neamatian Monemi
et al. (2017) and Taherkhani and Alumur (2019).
In terms of incorporating choice behavior in network optimization models, earliest works by Algers and Beser
(2001); Andersson (1989, 1998) apply logit choice models to estimate buy-up and recapture factors at Scandinavian
airlines system hubs. Mar´ın and Garc´ıa-Ro´denas (2009) incorporate user decisions as a constraint to model the rapid
transit network for optimizing the location of the transit infrastructure. To address the additional complexity
introduced by non-linear constraints (resulting from the use of a mode choice model), authors use piece-wise linear
approximation for solving the network optimization model. The use of discrete choice models in revenue management
in the context of airlines can be found in Talluri and Van Ryzin (2004) and in mixed integer linear programs in
Paneque et al. (2021). These studies highlight the benefits and complexity of modeling user-based behavior in
solving network optimization and revenue management problems under elastic passenger demand.
The skyport location problem in our study aims to determine the optimal locations of skyports for origin-destination
(OD) pairs in a network, decide which subset of origin nodes to be served by the set of skyports to multiple
destinations, and make allocation decisions based on user demand model. We formulate our skyport location problem
with two different objectives: (1) maximizing air taxi ridership and (2) maximizing air taxi revenue. The hubs are
treated as uncapacitated while we incorporate a mode choice model to include elastic user demand of going through
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the skyports (to multiple airports) based on trade-offs between different factors (influencing user decisions). Because
the model is an uncapacitated HLP, the mode split is followed by a ”single allocation” (de Camargo and Miranda,
2012) of the demand to the shortest path connecting the OD pair via a skyport. The is analogous to an all-or-nothing
assignment in urban transportation modeling. By keeping the path selection deterministic to the shortest path with
single allocation, we avoid the messier non-linearity if dealing with multiple (stochastic) route choice. Furthermore,
the single shortest path means that path selection can be pre-processed for a given skyport location instead of having
to incorporate path selection variables within the optimization model. To illustrate this fundamental difference, in a
stochastic route choice (path endogenously selected) setting, flow would no longer be decided by a binary logit model
between air taxi and ground taxi but would be non-linear as a choice between multiple routes and taxi. This is
shown below, where would be flow on path (needed for the objective) for OD , is a binary decision
on whether a path is open due to there being a skyport open ( ), is a path-skyport incidence parameter,
is the set of links on path , the travel time on path , is a calibrated travel time coefficient, is the
corresponding coefficient for taxi based on shortest path
, and is the maximum demand.
In a single allocation model shown in the Methodology section below, we can avoid the non-linearity because only
the shortest path will be chosen for an OD pair taking air taxi at a particular skyport. This allows us to determine
flows per skyport and to select the flow that is minimal cost per OD pair.
III.
METHODOLOGY
We first provide a high level overview of our approach used to formulate the skyport location problem in Section
III-A; this is followed by the formal problem formulation in Section III-B.
A.
High level overview
For a given city characterized by a discrete set of locations and multiple airports associated with it, the air taxi
skyport location problem is formulated as a variant of the HLP. The skyport location problem in our study is defined
as an optimization model with two alternative objectives i.e., either maximizing air taxi ridership or maximizing air
taxi revenue (not as a multi-objective problem but as two alternative optimization models). The number of skyports
is a (budget) constraint in the formulation. Considering trip length and trip cost of the transportation mode as major
influencing factors in our setup, we only consider a major subset of airport travelers (i.e., regular taxi users) and
estimate the behavioral mode shift of these travelers towards air taxis using a mode choice model (McFadden et al.,
1973). The sensitivity of skyport locations to varying transfer time and trip cost is analyzed to study how these
parameters affect the choice of optimal skyport locations.
• no capacity constraint is considered; our study is based on a subset of air taxi demand (i.e., airport demand)
with explicit demand response, hence the formulation is uncapacitated (reader may refer Vascik and
Hansman (2019) that studies skyport capacity),
• single allocation refers to the assumption that the origin-destination demand is routed all-or-nothing
according to a single shortest path going through a single hub or hub pair, as a consequence of the
uncapacitated setting. This is a common assumption when congestion effects are negligible (i.e. taxi route
choices only negligibly impact road congestion compared to passenger travel), where the only stochastic
component is which mode the users will take,
• no fixed infrastructure cost is considered (number of skyports is considered as the budget constraint in
our setup),
• conditions for reduced travel cost from transfer points to facilities and direct allocation of demand nodes
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to facilities (as in HLP) are both reflected in the mode choice model integrated in our skyport location
problem that diverts a portion of the population of taxi passengers to air taxi,
• no congestion effects (see de Camargo and Miranda, 2012) are assumed at the skyports, and
• existing landing space for helicopters in airport zones are assumed to serve as landing zones for air taxis
in our setup.
To be clear regarding the conditions above, we use the HLP model to design skyport locations that account for
the access, egress and transfer costs allowed in the air taxi market. The trade-offs in these costs at different skyport
locations are captured by an elastic demand function, modeled as a binary logit probability distribution applied at the
OD level, to determine the expected market share of airport taxi users to choose air taxi (see de Dios Ortu´zar and
Willumsen, 2011; Mahmoodjanloo et al., 2020). The elastic demand integration distinguishes this work from other
skyport design studies which have ignored the elasticity of demand. In the remainder of this paper, we use the term
hub and skyport interchangeably.
B.
Problem formulation
In the following subsections, we first describe our setup with formal notation, decision variables, and then the
optimization problem with associated constraints.
1)
Setup: Consider a discrete set
of locations spread across a given city. We consider trips
from a location
to an airport
, where
is the set of airports in the city (discrete set of size
). In other words, we only focus on trips which have an airport in set
as their destination. Two main modes
of commute to airports are considered, i.e., direct ground service (ground taxi) and aerial service (air taxi), as we
assume the air taxis would primarily compete with ground taxis. As such, the taxi user population is used as the market
from which users may shift to air taxi. Given such alternatives, we assume an individual’s choice of travel mode (to
a destination) is greatly influenced by trip length and price of the trip made by the mode (Fu et al., 2019). Since
the pricing of air taxi services would be adjusted based on market conditions over time, the focus is not on the
pricing decisions but how user responses to such decisions affect the choice of skyport locations. Therefore, in terms
of air taxi price, the estimates by Uber (Dickey, 2018; Holden and Goel, 2016) are assumed. Based on these values,
we consider three different price scenarios for our analyses:
• Short term (ST): Air taxi price is $5.73 per passenger mile
• Medium term (MT): Air taxi price is $1.86 per passenger mile
• Long term (LT): Air taxi price is $0.44 per passenger mile
In our setup, the originating airport demand at each origin node is fulfilled either via a skyport or via direct
ground transportation (as shown in Figure 1); the proportion distribution depends on the mode choice decisions by
users based on attributes such as trip length and trip cost to the destination airport as per commute options.
Travelers’ decisions to choose air vs ground taxi from an origin to a destination (OD) are reflected by a binary logit
model (as described in Section III-B5); each OD pair has one shortest path for the air taxi model for which attributes
are computed using the parameters described below.
2)
Decision variables: The decision variables are defined in Equations Error! Reference source not found. and
Error! Reference source not found..
(1)
(2)
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Fig. 1. Allocation of demand from an origin i to destination airport j as per commute options and decision
variables. The demand can be satisfied via a single skyport k (i.e., i allocated to k) using air taxi and via direct
ground transportation (i to j) using ground taxi. indicates trip time from point a to point b, while is the
corresponding distance, and denotes the associated trip fare.
3)
Parameters: The set of parameters to the proposed optimization problem (as shown in Figure 1) are defined
as follows:
• : ground transportation (access) trip time (minutes) between origin i and candidate skyport k with
and
• : ground transportation (access) trip distance (miles) from origin i to candidate skyport k with
and
•
: direct ground transportation trip time (minutes) from origin i to destination j with
,
and
•
d
i
j
: direct ground transportation trip distance (miles) from origin i to destination j with
,
and
•
d’
k
j
: ground trip distance (miles) from node k to destination airport j with
,
•
: aerial distance (miles) from candidate skyport k to airport j with
,
o
is a function of
d’
k
j
as explained in Section IV-A3
•
: fare associated with direct ground transportation trip (USD
1
) from origin i to destination j with
, and
o
is a function of
and
as explained in Section IV-A3
•
: fare associated with access ground transportation trip from origin i to candidate skyport k (USD)
with
and
o
is a function of
and
as
explained in Section IV-A3
•
: fare associated with air taxi commute (USD) from candidate skyport k to destination j with
o
is a function of
as mentioned in Section III-B1
•
: cost associated with end-to-end air taxi trip (USD) from origin i to destination j via candidate
skyport k with
1
United States Dollars
9
o
• : demand originating from i to destination airport j with
, = {1, 2, 3, 4, 5, . . .}
• p : number of skyports
4)
Incorporating transfer times: UAM use is a multimodal trip (shown in Figure 2). This involves some amount
of time (i.e., additional travel cost) to transfer to and from the skyports.
Fig. 2. Multimodal structure of air taxi service from origin i to destination airport j via a skyport k involves ground
access, transfer1, air taxi, and transfer2.
• transfer1 (): this refers to the time required to switch between ground transportation to air taxi along with
access time to the take-off zone of the skyport; we consider an equivalent in-vehicle (ground transportation)
time as α1,
• transfer2 (): this refers to the last mile transfer via ground transportation from a landing zone (e.g., existing
helipad located nearest to the destination airport) to the destination airport terminal.
In order to test the sensitivity of optimal hub locations and the demand for those hubs to transfer times, we include a
transfer cost in the air taxi service. This is reflected in the mode choice model to account for the impact of transfers on
users’ behavior. We essentially consider a transfer cost () associated with the total transfer time ( );
this value is captured in the total air taxi cost ( ) as shown in Eq. (3)
(3)
5)
Choice constraints: We integrate user mode choice behavior into our optimization problem. The demand for
air taxis is governed by a mode choice model, which determines the split of each OD demand to air taxi. Since we
consider a single allocation uncapacitated skyport location problem (which is a common problem in the literature:
e.g., Contreras et al., 2011; Klincewicz, 1996; Topcuoglu et al., 2005), this air taxi demand is then assigned to a single
shortest path that depends on which skyport location is selected. This way, user choices are explicitly taken into
account to include elastic user demand of going through the skyports to multiple airports.
We only consider airport travelers using regular taxi as the primary competition for air taxi and estimate the
behavioral mode shift of these travelers towards air taxis using a binary logit model (McFadden et al., 1973). A binary
logit model involves defining an utility function for individual n, associated with alternative a () from a binary
choice set A . The utility can depend on the attributes of alternatives and individual characteristics. has two
components i.e., a deterministic component () for the observable portion of the utility, and an error component
() assumed to be Gumbel distributed.
10
We adopt findings available from existing studies (and surveys) on user behavior in NYC to define the utility
functions of ground taxi and air taxi in our binary logit model. A detailed market survey on UAM by Booz-Allen and
Hamilton, Inc. (Shaheen et al., 2018) estimates a logistic regression model considering multiple individual and
alternative specific variables (including UAM trip distance and UAM trip cost) to predict users preference for air taxi
as a commute mode in NYC. The model is based on a stated preference survey of willingness to use UAM and does
not consider any other alternative modes. Another study by Ma et al. (2017) considers trip cost and trip time as
influencing variable to estimate a mode choice model comparing taxi (or for-hire-vehicles) along with other modes
for airport access in NYC.
Both the above mentioned demand studies (Ma et al., 2017; Shaheen et al., 2018) use survey data from NYC (which
is our study area). We define the utility components of the alternatives in our binary logit model as shown below.
• Ground taxi: Trip time (minutes) and trip cost (i.e., taxi fare in USD)
o
:
f
(
(parameters as in Section III-B3)
o
where =
and
• Air taxi: UAM trip distance (air miles) and UAM trip cost (i.e., air taxi fare in USD)
o
:
f
(
(parameters as in Section III-B3)
o
where =
and
Based on the above, the utility functions of ground taxi and air taxi are shown in Eqs. (4) - (5):
⇒
(4)
⇒
(5)
Based on the studies by Shaheen et al. (2018) and Ma et al. (2017), we assume the values for =
0.0313, = −0.0125 (Ma et al., 2017), and = 0.018, = −0.0213 (Shaheen et
al., 2018) respectively. For a binary logit model, there is typically a single alternative specific constant (ASC)
representing differences between the two alternatives that are not captured by any of the variations characterized by
the attributes. For air taxis and ground taxis, these differences may include: average population concerns about flying,
the interest in trying an emerging technology, the net difference in inconvenience not captured by attributes, etc. The
model from Shaheen et al. (2018) has an ASC = 1.25, which assumes that, without any other factors considered, 78%
of users of that survey would be willing to make a trip via UAM. However, their model is for willingness to make a
trip via UAM, absent of any other alternative modes and therefore does not inform on relative differences between
UAM and taxis. Without any data for estimating this with respect to taxis for the NYC case but given the
similarities in role of the air taxi and ground taxi, a conservative assumption is to set a net effect of ASC = 0 because
it assumes decisions between air taxi and regular taxi are governed only by quantitative factors like costs and distances.
Having a non-zero ASC would not change the optimal decision variables in the HLP since it’s uncapacitated (i.e.,
the optimal skyport locations would not change); only the objective value would change. This is similar to how all
the stochastic route choice models in the literature only look at differences in generalized travel costs without any
ASCs for specific routes (see Dial, 1971). In the future when operational data is available, an ASC can be calibrated
such that the input data like maximum demand for air taxis are better fit. Therefore, eqs. (4) and (5) can be
expressed as:
11
(6)
(7)
Applying eq. (3), the variable in eq. (7) can be expressed as the total cost of the multi modal trip (i.e, origin
to skyport via ground taxi and skyport to destination via air taxi, as shown in Figure 1) including transfer cost,
as shown in eq. (8).
(8)
Note that the trip length values via air taxi are smaller than the trip costs so the utility is generally negative
overall, and the positive trip length (i.e., travel time and travel distance) coefficients reflect user preferences such that
people farther away in distance prefer using air taxi and longer in time prefer ground taxi. Furthermore, both the
cost variables fi j and fik j are functions of corresponding ground trip times and trip distances (refer calculation
details in Section III-B3). Therefore, in a scenario where, for a given distance the ground trip time increases due to
congestion, there is a proportional increase in its trip cost which eventually affects the user choice behavior.
Essentially, the air taxi demand to the skyports is based on trade-offs between trip length and trip cost based on
user preferences. Based on the mathematical structure of the binary logit model (McFadden et al., 1973), eqs. (9) and
(10) denote the choice probabilities of air taxi and ground taxi.
(9)
(10)
The choice behavior of the origin population in Eq. (9) can be used to estimate the aggregate air taxi demand flow
originating from i to destination j that is routed via a skyport at location k. Therefore, we define population choice
behavior (based on ) as:
• : population choice probability of using air taxi service from origin i to destination airport j if routed
via skyport k with
.
Using eqs. (6) and (8) in eq. (9), can be expressed as eq. (11):
(11)
Eq. (11) can be used to estimate the probability of a regular taxi user switching to air taxi service for given attribute
values. Note that only one skyport is assigned to each location; under this assumption, the demand function Eq.
(11) need not be used as a constraint within the optimization model. Instead, we exploit the structure of the problem
to pre-compute all the probabilities of Eq. (11) to use as objective coefficients (e.g., with 150 (taxi) zones, 3 airports,
and 150 candidate skyport locations in NYC, there are 67,500 values) for an integer linear programming model.
6)
Optimization problems: Using Equations (1), (2) and (11), we develop an optimization model under two different
objectives. Due to the enumeration of the mode choice into an objective coefficient, we can formulate the skyport
location problem as an integer linear program.
• RDR model (maximize ridership): Equations (12)–(16) optimizes the skyport locations such that the total
air taxi ridership (i.e., total airport trips going via skyports) is maximized.
(12)
12
(13)
(14)
(15)
, (16)
• REV model (maximize revenue): Equations (17)–(21) optimizes the skyport locations such that the total
air taxi revenue (i.e., total air taxi fare collected from the airport trips made via skyports) is maximized.
(17)
(18)
(19)
(20)
, (21)
where (in Equations (12) and (17)) refers to the expression in Equation (11), which is pre-processed to use as
input to the models.
The objective function (12) maximizes the airtaxi ridership for each origin-destination pair, while the objective
function (17) maximizes the revenue generated by air taxi ridership for each origin-destination pair. Constraints (13)
and (18) allow single allocation (i.e., each origin node that passes through a skyport is allocated to only one
skyport), while constraints (14) and (19) ensure that demand for each destination j at an origin node i is satisfied
via the node at k if and only if a skyport is located at k. Constraints (15) and (20) denote that the total number of
skyports to be located is p. This is an indirect measure of the fixed cost; alternatively, if unit fixed costs are known
exactly with respect to the other costs in the objective, they can be added to the objective as a fixed charge term. In
our case, the budget constraint approach is used in combination with sensitivity analysis of the budget (see Tables III–
V) to give a decision-maker the flexibility to compare costs once they know the fixed costs. For revenue calculation,
we consider the air taxi operation model proposed by Holden and Goel (2016) where the end-to-end air taxi trip (i.e.,
ground transportation access to skyports and air taxi ride to airports) is provided by a single operator. Other air taxi
service operators planning to provide service only from skyports to multiple destinations may have different pricing
strategies. For example, the helicopter service by Uber in NYC (UberCopter, 2019) comprises of access and egress
ground trips along with aerial ride to the airport, and charges passengers for the end-to-end journey (average cost
ranges between $200 - $225). On the other hand, the BLADE helicopter service that transports passengers only from
helipads to NYC airports costs between $145 to $195 (Ott, 2019). The air taxi price values in our study is based on
estimates by Uber (Dickey, 2018), hence the revenue in our setup includes total revenue generated from end-to-end
multimodal air taxi trips.We provide additional analysis in Section IV-B which is a special case of the REV model;
here the revenue calculation is based only on the air taxi rides from skyports to airports.
We solve the model in Section III-B6 using the Gurobi optimization tool (Gurobi Optimizer 9.0). For integer
13
programming problems, Gurobi uses multiple solution methods to obtain an exact solution, e.g., parallel branch-and-
cut algorithms, non- traditional tree-of-trees search algorithms, cutting plane methods, and symmetry detection.
C.
Illustrative example
To illustrate the properties of RDR and REV models, the following example is used. Consider 7 origin locations (in
set and 2 destination facilities (in set distributed in a Euclidean space. Each origin has
direct connection to each destination (e.g., ground taxi connections); the aggregate demand from origin to destination
via direct connections are shown in Figure 3. The objective is to select 2 skyports (among 7 candidate skyport locations
in
to connect each origin to destination facilities via these skyports. Table I shows probability
of users (in O) choosing to go via a skyport (in
S
) to reach a destination (in D), while Table II shows the total fare
associated with such trips. The value corresponding to row i (e.g., O1) and column k − j (e.g., S1 − B) in Table I
represents the choice probability of users in origin i to go via a skyport at k to reach destination j (e.g., O1 − S1 −
B = 0.66); Table II follows a similar notation. The values displayed in Tables I and II are only for illustration purpose
in this example.
Table I. Air taxi choice probabilities () of users; each cell in the table shows user probability of choosing to
go via a skyport
from an origin location to a destination : for illustrative example.
S1-
A
S2-
A
S3-
A
S4-
A
S5-
A
S6-
A
S7-
A
S1-
B
S2-
B
S3-
B
S4-
B
S5-
B
S6-
B
S7-
B
O1
0.66
0.59
0.51
0.39
0.52
0.51
0.32
0.66
0.47
0.44
0.58
0.3
0.56
0.33
O2
0.58
0.66
0.42
0.35
0.41
0.21
0.5
0.63
0.62
0.37
0.4
0.44
0.38
0.46
O3
0.65
0.41
0.67
0.47
0.45
0.51
0.53
0.48
0.55
0.62
0.32
0.34
0.52
0.51
O4
0.6
0.53
0.53
0.68
0.31
0.4
0.39
0.39
0.37
0.54
0.68
0.54
0.44
0.35
O5
0.42
0.31
0.43
0.52
0.64
0.56
0.46
0.47
0.61
0.45
0.58
0.61
0.32
0.4
O6
0.5
0.57
0.37
0.45
0.55
0.65
0.31
0.39
0.57
0.45
0.65
0.58
0.69
0.43
O7
0.49
0.36
0.41
0.4
0.35
0.39
0.59
0.55
0.54
0.4
0.46
0.34
0.42
0.52
Fig. 3. Illustrative example showing 7 origin locations and 2 destinations; each link displays aggregate demand going
from origin to destination via direct connection.
14
Table II. Total fare (USD) associated with air taxi trip ) from an origin to a destination via a
skyport
including access cost from origin to skyport () and air taxi cost from skyport to destination
): for illustrative example.
S1-
A
S2-
A
S3-
A
S4-
A
S5-
A
S6-
A
S7-
A
S1-
B
S2-
B
S3-
B
S4-
B
S5-
B
S6-
B
S7-
B
O1
180
178
181
185
189
126
104
111
122
156
162
141
155
191
O2
115
118
112
184
114
100
166
119
115
186
138
142
100
174
O3
124
173
149
195
193
134
117
155
129
164
103
124
131
171
O4
149
166
195
101
145
191
135
133
179
173
111
196
175
105
O5
114
145
190
184
101
160
183
105
168
121
160
155
198
187
O6
103
193
200
180
194
162
125
192
172
117
157
178
182
189
O7
123
140
132
120
130
170
151
118
104
169
157
173
124
142
Using the values of demand, choice probabilities, and fare in this example, we define the parameters used in the
optimization models (Section III-B6) to determine optimal skyport locations. In this case, p = 2; Table I and
Table II provide and values respectively (where i denotes origin, k is skyport and j denotes
destination). The values of parameter are as per the numbers shown in Figure 3 for origin i to destination j.
Therefore, for a candidate skyport in set
S
, for example at location 3 (S3), the demand from origin at 2 (O2) to
destination A via skyport S3 is calculated by multiplying the user probability O2 −S3 −A from Table I by the
aggregate demand from location 2 to A in Figure 3. Therefore, 363 riders (0.42 × 863) from O2 would choose to go
via skyport S3 to destination A; the revenue generated from these air taxi riders is obtained by multiplying the ridership
with corresponding air taxi fare for O2 − S3 − A in Table II which gives $40, 656 (363 × 112). Also, for O2, this
means 500 out of 863 users directly go to A without using skyports.
Similarly, the air taxi demand from different origins to each candidate skyport (going to destinations A and B) are
computed to be used in the location-allocation decision process for obtaining an optimized set of skyport locations
based on the objective in Section III-B6. Substituting the parameter values considered in this illustrative example in
the RDR model (eqs. (12)-(16) the optimal choice of skyports are at location 1 and 4, whereas the REV model (eqs.
(17)-(21)) result in optimal skyport locations at 5 and 7. The skyport locations and allocation of origin demand to the
selected skyports for each destination (obtained using Gurobi) are shown in Figure 4. Therefore, the total air taxi
ridership (demand) at selected skyports (shown in Figure 4) obtained by RDR model is 5,363 compared to 4,802 by
REV model. The total estimated revenue from potential air taxi riders in this example are $677,831 and $742,621
as obtained from RDR and REV models respectively.
15
Fig. 4. Comparison of location-allocation solutions of RDR model in (a) and REV model (b). The figure shows
allocation of air taxi demand from each origin to the selected skyport locations (highlighted in black outlines); links
are color coded as per destination choices. Values on links connecting origin i to skyport k denote air taxi riders
originating from i going via skyport k to their respective destinations, while those connecting skyport k to destination
j is the aggregate air taxi demand allocated to k to be transport to j.
IV.
DATA SET AND EXPERIMENTAL RESULTS
We first describe the NYC data sets and tools used for our experiments, and then go over the results of our approach.
A.
Data set and tools
1)
Data set: The study area includes five boroughs in NYC (The Bronx, Manhattan, Queens, Brooklyn and Staten
Island) that are divided into 263 taxi zones (New York City taxi zones); each taxi zone has a unique zone ID. The
centroids of the taxi zones are the trip origin nodes (locations) while the trip destinations are the three major airports
in NYC, i.e., EWR (Newark), JFK and LGA (LaGuardia). The NYC taxi and limousine commission FHV (for-hire-
vehicles) trip record data from 2019 (July to December) are used (New York City Taxi Limousine Commission) on
our study. This is a publicly available data set, and the motivation for using FHV trips data for airport transfer is
derived from the study by Ma et al. (2017). Their study indicated that 65% of trips to JFK are via FHV and taxis.
Each trip record includes the origin and destination locations of the trip in terms of taxi zone IDs. For example,
taxi zone IDs for Newark, JFK and LaGuardia airports are: 1, 132 and 138 respectively. The data set contains
over 20 million trip records, and each trip record includes the start time stamp, origin taxi zone ID, end time
stamp, and destination taxi zone ID for the trip. All the trips with trip time (i.e., end time stamp - start time stamp)
greater than 120 minutes were disregarded from the dataset along with other outliers. Furthermore, to avoid distortion
in average or aggregate values, major holidays such as Independence day, Halloween, Thanksgiving, Christmas were
filtered out before performing any calculations.
Assuming the skyport operations are likely to schedule from 7 am to 6 pm (Goyal, 2018), we only consider the trips
during this period for demand calculation. The total airport demand and travel costs were calculated using a script
written in Python programming language (version 3.7.4). For each origin-destination ID pair in the FHV data set, the
total trips were added to obtain the total demand from the origin ID to the destination ID. The trips with destinations
as airports (i.e., with destination taxi zone IDs 1, 132 and 138) were selected and used to compute the demand Di j
from origin i to destination airport j. We found the average monthly trips originating from each of the taxi zones to
the three airports; we refer to this as Di j. Figure 5 shows the profile of daily (average) taxi trips to the three airports
in NYC.
2)
Data pruning: To further prune the data set, we filter out taxi zones which do not have significant demand to
airports. The filtering process was implemented using the demand data Di j (as obtained in Section IV-A1). For our
experiments, we excluded the taxi zones with the lowest fraction of trips (i.e., zones with less than 10 airport
trips in a month) and as a result focused on the remaining 149 taxi zones (i.e., the top 149 zones contributing to
the airport demand). Figure 6 shows a choropleth map of the candidate taxi zones generated using ArcMap version
16
10.5.1 (ArcGIS desktop). Hence, as per the notation defined in Section III-B1,
|
L| = 149 and
|
J| = 3 (i.e., three
airports).
Fig. 5. Daily (average) taxi demand to three major airports in NYC (originating from all taxi zones)
Fig. 6. Choropleth map showing the candidate taxi zones with taxi zone-wise demand for the three airports in NYC
with zone shading.
3)
Calculation of travel costs: The input to the skyport location problem is composed of total trips to each
airport from each taxi zone ( and the associated trip travel costs across taxi zones (including airports). The
travel costs include trip time, trip distance and trip cost (i.e., trip fare). For extreme case scenario, we consider
17
weekday rush hours in NYC (i.e., 4 - 7 pm)
2
to reflect on congested conditions for calculating the parameters
defined in Section III-B3.
The average peak hour ground travel time (cik, ck j) and average ground trip distance () across taxi zones and
airports were found using Google Maps Distance Matrix API and Python programming language; values were obtained
during 5pm-6pm (peak hours) on a weekday. The aerial distance (dk j) was calculated based on the relation between ground
miles and aerial miles (Goyal (2018)):
(22)
For trip fare calculations, we consider the ground transportation fare structure (used by taxi services in NYC)
associated with trip time and trip distance values; the cost components include a Booking fee (Base fee), a per
mile cost (), and a per minute cost (). Therefore, the ground taxi (access) fare from origin to candidate
skyport ( and direct ground taxi fare from origin to airport () can be written as:
(23)
(24)
Based on average market rates in NYC (Majaski (2019)), we consider the following values for
and
:
•
Base f ee = $3
•
= $1.5
•
= $0.3
•
Minimum ground taxi fare between taxi zones: $7
•
Minimum fare for ground taxi trip with pick up or drop off location in Manhattan: $8 and an additional
congestion charge of $2.75 (Hu, 2019)
Using the above values in Equations (23) and (24) the access taxi fares to skyports and direct ground taxi fares
to airports were computed for different values of trip times and trip distances (for each origin zone).
The flight leg fare of an air taxi trip i.e., was determined by multiplying the aerial distance (Eq. (22)) by
the price per air mile. It is possible that for passengers sharing the same destination, an air taxi serves more than
one passenger at a time, but for worst case analysis, we consider average passenger occupancy as 1. Therefore,
assuming one air mile is equivalent to one passenger mile, let the price per air mile be represented as Rairmile
such that: (25)
Based on ST, MT, and LT scenarios (as explained in Section III-B1), the values of Rairmile include:
•
= $5.73 for short term
•
= $1.86 for medium term
•
= $0.44 for long term
Using Equations (23) and (25) the total air taxi fare in Eq.(3) consisting of access fare, transfer cost, and flight
leg fare can be written as:
2
https://www1.nyc.gov/site/tlc/passengers/taxi-fare.page#
18
(26)
where tt = is the equivalent in-vehicle time for transfers to and from skyports.
For the total transfer time (tt), we base our assumption of on previous findings. For example, the transfer
time for rail transit was found to be valued at approximately 8 minutes of in-vehicle time (Wardman et al., 2001). For
the transfer time i.e., the last mile transfer between a landing zone (located nearest to a destination airport) and the
destination airport terminal, we consider existing helicopter services in NYC (Blade; UberCopter, 2019) that use
helipads near airports for landing and transferring passengers from helipads to the airport terminals via ground taxi or
shuttle (Taylor, 2019). For example, the average ground taxi time from heliport at JFK airport to the JFK terminal is
between 5 to 8 minutes
3
. Therefore, we assign tt as 15 minutes (i.e., = 8 minutes and = 7 minutes). Using
the values of tt and in Eq. (26), we computed air
taxi fares from each origin i to each candidate skyport
location k (
) to each destination airport j
) for different
scenarios i.e., ST, MT, LT (to be used for
demand estimation and revenue calculation in the optimization models explained in following Section IV-B).
4)
Tools: To solve the proposed optimization problems (as described in Section III-B6), Gurobi optimization tool
(Gurobi Optimizer 9.0) and Python programming language (version 3.7.4) were used. Based on 149 taxi zones and 3
airports, the optimization problem for NYC consisted of 66752 binary variables and zero continuous variables. Our
experiments were carried out on a computer with Intel i7 processor with 2 cores, 4 logical processors and 16 GB
RAM with an average computation time below 10 seconds (for solving an instance of the optimization problem in
Gurobi for the above data set).
B.
Optimization results
Using the data obtained for the 149 taxi zones to the 3 airports (as explained above), we pre-computed all
possible values of population air taxi choice probabilities ( in Eq. (11) for each origin zone to each candidate
skyport (going to multiple airports). Using the obtained values, we solved the proposed optimization models i.e.,
RDR and REV (described in Section III-B6). The objective value of RDR model provides average monthly air taxi
ridership, while the REV model objective value gives the average monthly air taxi revenue. We used these models to
find optimal skyport locations for three price scenarios (refer Sections III-B1 and IV-A3). For each case, we
obtained results (using our Gurobi implementation) for different values of (where p
is the number of skyports). Figure 7 demonstrates the demand allocation from different origin to multiple airports via
optimal skyports in NYC (obtained for the case of p = 5 in RDR model for LT scenario)
4
. The edges connecting
origin to skyport (for multiple airports) as shown in the figure are the outcome of the optimization models (i.e).
3
www.google.com/maps/dir/Heliport+at+JFK+Airport,+Queens,+NY/JFK+Airport,+Queens,+NY
4
Visualization was done using the kepler.gl tool
19
Fig. 7. Demand allocation showing connecting edges between origin taxi zones to three airports in NYC via p = 5
skyports (output of RDR model for long term scenario). The edges connecting trip origin locations to skyports are
color coded as per destinations.
Using the optimal skyport locations, it is possible to estimate the ridership for the REV model and revenue for RDR
model respectively. The air taxi ridership corresponds to the total trips to airports originating from different origin
taxi zones that are routed via optimal skyports from REV model (
). This is calculated by multiplying population
choice probability (from the demand model) with airport trips where
. Similarly, the air taxi revenue
for the optimal skyports from RDR model (
) is computed by multiplying air taxi ridership with the revenue
generated from the multimodal trips ( ) for
. Tables III-V summarize optimization results
obtained from RDR and REV models for short term, medium term and long term price scenarios; details of optimal
skyport locations are reported in Appendix. The ridership and revenue values are average monthly estimates. For each
choice of skyport budget p, the data in Tables III–V include the following:
• Air taxi market share: this denotes the proportion of regular taxi users that are estimated to switch to air
taxi service for airport access
• Flight leg revenue share: the total revenue generated from end-to-end air taxi trips in our study includes
revenue from ground transportation access to skyports plus revenue from air taxi rides (this constitutes the
flight leg of the multi-modal trip). Hence, the flight leg revenue share refers to the percentage revenue
generated only from the flight leg ) with respect to the total revenue ( )
• Increment in total revenue: this represents percentage increment in total revenue with increasing
skyport budget p (increment is measured with respect to baseline p = 1)
20
Table III. Optimization results for short term scenario
Budget
RDR model
REV model
number of
skyports
(p)
Airtaxi
market
share (%)
Flight leg
revenue
share (%)
Increment
in total
revenue (%)
Airtaxi
market
share (%)
Flight leg
revenue
share (%)
Increment
in total
revenue (%)
1
13.21
60.14
–
11.87
72.31
–
2
14.95
38.15
-
5.12
12.82
63.71
3.70
3
16.22
39.14
-
1.79
13.48
69.77
4.97
4
16.73
44.98
-
2.49
13.57
72.22
5.80
5
16.92
49.31
-
1.13
13.64
76.42
6.58
6
17.07
48.28
-
1.64
13.92
78.25
7.29
7
17.21
52.01
-
0.38
14.16
78.66
7.97
8
17.32
52.39
0.05
14.29
79.38
8.53
9
17.42
54.92
0.92
14.30
79.73
8.98
10
17.52
56.32
1.34
14.34
80.19
9.38
Table IV. Optimization results for medium term scenario
Budget
RDR model
REV model
number of
skyports
(p)
Airtaxi
market
share (%)
Flight leg
revenue
share (%)
Increment
in total
revenue (%)
Airtaxi
market
share (%)
Flight leg
revenue
share (%)
Increment
in total
revenue (%)
1
22.22
47.10
–
15.39
43.91
–
2
24.19
50.75
-
7.65
15.29
56.88
7.53
3
25.04
54.10
-
9.46
16.27
58.34
8.15
4
25.62
56.45
-
10.78
16.35
58.58
8.36
5
26.02
58.23
-
11.50
16.11
58.46
8.55
6
26.38
59.45
-
12.24
16.21
58.78
8.66
7
26.68
60.91
-
13.02
16.33
58.78
8.76
8
26.98
61.73
-
14.00
16.31
58.78
8.80
9
27.25
62.97
-
14.17
16.40
58.96
8.83
10
27.50
64.11
-
15.16
16.41
59.00
8.86
Table V. Optimization results for long term scenario
Budget
RDR model
REV model
number of
skyports
(p)
Airtaxi
market
share (%)
Flight leg
revenue
share (%)
Increment
in total
revenue (%)
Airtaxi
market
share (%)
Flight leg
revenue
share (%)
Increment
in total
revenue (%)
1
27.55
17.57
–
12.77
11.90
–
2
29.37
20.13
-
12.65
14.18
14.40
4.94
3
30.67
24.34
-
16.18
15.99
14.99
7.11
4
31.33
26.09
-
19.77
18.29
16.96
7.69
5
31.80
27.46
-
22.32
18.54
17.05
8.16
6
32.22
29.03
-
24.28
18.56
16.91
8.31
7
32.59
30.15
-
25.70
18.35
16.62
8.41
8
32.90
31.11
-
27.56
18.29
16.61
8.47
9
33.21
32.36
-
29.11
18.35
16.60
8.50
10
33.50
33.36
-
30.88
18.37
16.64
8.52
21
The output from our experiments clearly depicts the sensitivity of skyport locations to different objectives as well
as varying price scenarios. To get a sense of the placement of skyports, a visualization in Figure 8 shows optimal
skyport locations (for p = 5) in NYC obtained from RDR and REV models for ST, MT, and LT scenarios. While it
can be seen that the location choice is sensitive to the objective values considered in the models, there are common
zones that are optimal across different scenarios which can guide investment decisions for setting up skyports. For
example, for p = 6 (as shown in 8), the common skyport zones in NYC include midtown Manhattan and Flushing
(Queens) from RDR model, and Park slope (Brooklyn) and Elmhurst (Queens) from REV model. Lower Manhattan
area seems optimal for both RDR and REV model.
Fig. 8. Optimal skyport locations in NYC (for p = 6) for short term, medium, and long term scenarios. (a) RDR
model output (b) REV model output
Moreover, going from short term to long term, it can be seen that with each additional skyport in the budget, the air
taxi market share in both RDR model and REV model monotonically increases, although the proportion of market
share obtained from RDR model skyports is higher compared to REV model skyports. This is because the objective
of RDR model is to maximize the air taxi ridership, thereby resulting in higher values of air taxi market share.
Similarly, based on the objective, the total estimated revenue generated from REV model skyports are relatively
higher. However, the REV model results in an increment in total revenue from additional skyports, while an opposite
trend is observed in the RDR model output (especially for MT and LT scenarios, and at lower values of p for the ST
scenario). In this context, REV model shows relatively better performance; there is an increment in both revenue and
air taxi market share with increasing skyport budget p (which is desired). Furthermore, for the ST scenario, the REV
model output shows a major portion of the total revenue being generated from the flight leg of air taxi trips; the value
decreases for MT and LT scenarios due to the lower air taxi prices considered in these scenarios. However, given the
higher air taxi market share estimated during the long term, various revenue management strategies can be used to
ensure higher revenue from these services (Bitran and Caldentey, 2003; Chiang et al., 2007). As mentioned earlier,
we assume a single air taxi operator to provide ground taxi access to skyports with air taxi rides from skyports to
airports. For cases where an air taxi operator plans to provide only air taxi rides from skyports to multiple destinations,
the revenue calculation used in the REV model objective can be modified accordingly. We discuss this special case
of REV model below:
Special case (REV model): The air taxi revenue considered in the REV model objective (Eq. 17) includes
i.e., total estimated revenue from end-to-end multi-modal air taxi trips. Let this objective be denoted as
. For the special case, we assume the operator is interested in maximizing only the flight leg revenue (based on
the type of air taxi service it plans to provide). Hence, the revenue ( ) in Eq. (17) can be replaced by
(keeping constraints in Equations (18)-(21) the same). We refer to this modified objective as .For comparison
22
purpose (for ST scenario) we assume the same pricing strategy considered for the multi-modal air taxi setup in our
study. The choice of optimal skyport locations obtained from solving the REV model with is different from
those obtained using . However, a higher number of common skyport locations were found in both objectives
for higher values of p. The REV model with resulted in 7% lower air taxi ridership for (averaged across
different choices of The flight leg revenue generated using is comparatively higher
(10% on an average) for , however, a decreasing trend (with revenue lift of 3-4%) was noticed for higher
values of p. Assuming in the multi-modal air taxi setup (as considered in our study), the total revenue
generated from (by adding ground transportation access revenue with flight leg revenue from ) was
found to be 2% less than the total revenue obtained using .
C.
Demand distribution at skyports
As an outcome of the optimized skyport locations, we estimate the (incoming) demand at each skyport; this demand
corresponds to the trips to airports that are routed via a skyport from origin zones (allocated to that skyport). In this
subsection, we study the characteristics of such demand vis-a-vis the number of skyports. In particular, given a budget
(p) and the optimal skyport locations (k) obtained from RDR and REV models for ST and LT respectively, we compute
the total number of (allocated) incoming trips to each skyport. The demand distribution at different skyports is
computed using the connections between origin zones and skyports (for each airport) obtained as an outcome of the
optimization models (see Section IV-B). These values are then used to calculate the percentage (proportion) demand
allocated to each optimal skyport location (with respect to total estimated air taxi demand flow via set of optimal
skyports). For the case of Figure 9 shows the percentage of airport demand allocated to each
skyport. In the short term, an increase in the skyport budget (p) will result in some of the skyports in the RDR model
having much lower incoming demand relative to other locations. For example, for p = 8, the proportion of incoming
trips at one of the skyports is only 1%. For the same scenario (i.e., ST), the REV model skyport locations show
relatively fair distribution of air taxi demand. In the long term, however, the proportion of air taxi demand across
different skyports is noticed to be fairly distributed in case of both RDR and REV model.
Fig. 9. Airport demand distribution at optimal skyport locations in NYC. Each set of bars represents percentage of
demand allocated to each skyport location (given budget of p skyports) obtained from REV and RDR models.
Overall, comparing the outcomes from RDR model and REV model, the performance of the REV model is
observed to be relatively better in terms of fair demand distribution at skyports and higher revenue generation (see
Section IV-B). The distribution of air taxi demand to different skyport locations based on the choice of the
optimization model (and its output) can guide service providers to plan multiple skyport design options. For instance,
based on demand at optimal locations, companies can opt for smaller skyports (e.g., accommodating one to three air
taxis) at locations with limited demand or they can choose to build skyports with higher capacity and additional
facilities at locations with significant incoming demand.
23
D.
Sensitivity analysis (time savings)
We investigate the effects of varying total transfer time tt to analyze minimum skyport requirements that can
accommodate such variations. As the time spent in transfers is a critical part in the end-to-end trip of the air taxi
service, we base the decision criterion of our analysis on time savings (i.e., time saved by travelers commuting via air
taxi compared to ground taxi while going to the same destination). As discussed earlier in Section III-B4, we consider
a transfer cost associated with transfer time tt; this has a direct impact on user choice behavior and may affect the
location allocation of skyports. The transfer time mainly depends on the infrastructure design as well as on the
integration of multi modal operations by the service provider; depending on these factors the time spent in transfers
can vary. Therefore, it is important to understand the minimum skyport requirements to accommodate these variations.
Our analysis is limited to near term only, mainly because such variations are more likely to occur during the short
term or initial period while investigating proper integration of different modes and operations design of such new
services. Moreover, determining the minimum requirements in the long term would require considering various other
factors besides time savings such as competitive services, user experiences, and market evolution of UAM in a city.
Fig. 10. Comparison of percentage increment in time savings (tsinc) with respect to each additional skyport in budget
p (for different choices of transfer time in TT ).
For our analysis, we consider the REV model (because of its superior performance) and assume four possible
values of tt, i.e., 10, 15, 20 and 25 minutes. A study by Garcia-Martinez et al. (2018) suggests the first transfer in
a multimodal trip to be equivalent to 15.2 minutes of the trip in-vehicle time. Using this finding and the values
assumed in Section IV-A3, we consider different choices of (in range 8 - 15 minutes) and (in range 5 - 8
minutes) to define the transfer time set TT = {10, 15, 20, 25} for our sensitivity analysis. For each choice of transfer
time in TT and skyport budget p (where p
{1, 2, 3, … , 14, 15}), we compute the travel cost values (refer Section IV-
A3) and solve the REV model to get p optimal skyport locations. This is used to calculate the total time savings of
trips allocated to the selected skyports (for each p). Using these values, we compute the percentage increment in time
savings () with each additional skyport in budget p. Figure 10 illustrates the variation of with respect
to p for different choices of . As shown in the figure, the variation in (for a given value of p) across
different choices of tt is significantly higher for lower values of p. Such sensitivity to tt variations decreases as p
increases (with minimum variations observed at ). Therefore, based on the analysis above, the infrastructure
planning for air taxi services (in the near term) requires locating at least 9 skyports across NYC. As per the REV
model results (obtained for varying tt), the optimal choice includes one skyport each in Union Square, Financial
district, Diamond district, Flushing, Murray Hill, Park Slope, Theater District, and 2 skyports near midtown
Manhattan.
24
E.
Discussion and Insights
Our experiments based on the formulated air taxi ridership maximization and revenue maximization optimization
models (i.e., RDR and REV models) lead to several valuable insights that may be of interest to air taxi service
operators that are planning to start their service in a metropolitan city.
•
For a given skyport budget (p), the optimal set of skyports that seem attractive in the short term may not be useful
for generating enough revenue in the long run. For a value of p, the common zones that are optimal across different
price scenarios can guide infrastructure cost allocation decisions. For example, in NYC (refer Figure 8), the RDR
model results for p = 6 (for short term, medium term and long term scenarios) show common skyport zones near
lower Manhattan, midtown Manhattan, and Flushing (Queens). It would make sense to allocate more
infrastructure budget to design high capacity skyports in these zones.
•
It is likely that the service operators, in the near term, would want to gain more riders (to improve familiarity with
the technology and increase user adoption). In this context, the initial set of skyports can be planned based on the
RDR model. However, the RDR model (for short term scenario) performs well only upto a limited skyport budget
(i.e., for ). This is because for higher values of p (i.e., ), the proportion of trips allocated to
some skyports is very less and this may not be able to compensate for high infrastructure costs on such locations.
For example, in case of NYC scenario for p > 7 (i.e., = 7), the percentage of incoming trips at some skyports
are very low; for p = 8, one skyport has only 1% demand allocated to it ((see Section IV-C)).
•
From revenue aspect, the RDR model is not greatly beneficial in the long run compared to REV model. This
is because in the long run, the RDR model output does not result in higher revenue with increase in skyport
budget (p) although it results in increased ridership (refer Tables III–V).
•
In order for large scale air taxi operations to be sustainable in the long run, the operators would be more interested
in planning for maximizing the revenue. In this context, REV model approach can be used determine the skyport
choices. The fair demand distribution across different skyports obtained from REV model (see Section IV-C)
would ensure promising returns on infrastructure investments at such locations.
•
Variation in time savings based on different choices of transfer time could serve as a possible decision criterion
(besides budget constraint) for deciding minimum skyport requirements in a city. For example, as per the
sensitivity analysis conducted based on time savings (see Section IV-D), it was found that atleast 9 skyports are
required in NYC to accommodate variation in transfer times.
The above insights with respect to the incorporation of elastic demand for short term and long term analyses
of optimal skyport location choices in a city can facilitate the air taxi infrastructure investment decision and
planning process, however, a more in-depth analysis with consideration of various other user factors in the demand
model and operational factors in the optimization models is suggested as future work.
Effects of varying model parameters: An important aspect to consider while planning resource allocation to
different locations for the skyport network design is the sensitivity of the optimal skyports to varying pricing
scenarios. For example, consider the skyport locations obtained using the REV model for p = 9 (details in the
Appendix tables VI–VIII). For the short term and medium term scenarios, if we compare the different pairs of
skyports from each scenario (paired simply based on their spatial proximity), it is observed that on an average the
shift in skyport choices is within 6 miles distance. Therefore, based on the operational feasibility and the estimated
benefits, the optimal skyport locations for short term and medium term can guide planners in designing the skyport
network in the common regions (as per spatial proximity) that can sufficiently cater to both short term and medium
term needs. However, based on the price transition from medium to long term, it is observed that even though 3 out
of 9 skyport choices (obtained using the REV model for the two price scenarios) are common, the average shift is
about 15 miles, which is more sensitive compared to the price transition from short term to medium term. Therefore,
in the long run, the operator may need to expand the skyport network (either by including additional existing
infrastructure or designing new stations based on the budget constraint) to effectively cater to the long term needs.
These observations may vary based on the population characteristics and mobility needs in a city. Hence, the above
insights with respect to the incorporation of elastic demand for short term and long term analyses of optimal
skyport location choices in a city can facilitate the air taxi infrastructure investment decision and evaluation of
different pricing schemes in the UAM service deployment planning process. It should be noted that, in the long run,
operators may incur additional costs with respect to the increasing fleet size based on the skyport choices and user
adoption (Rajendran and Shulman, 2020; Roy et al., 2022), hence the trade-offs between the revenue and cost resulting
25
from increased ridership need to be considered in the planning process. Further information on UAM services from
pilot deployments in cities may be needed to better analyze the impacts of different parameters to the operator’s profit.
Moreover, it is possible that the user demand, travel time and other factors related to UAM adoption may change
over time and in response to the location decisions. With respect to uncertainties, stochastic variant of HLP models
have been studied in the literature (Snyder, 2006). However, to properly model the uncertain parameters into the
location-allocation decision process would require some knowledge on either the probability distributions or some
pre-specified intervals for the uncertain parameters. Due to the emerging technology aspect of UAM services,
obtaining such data is difficult since they have not been implemented yet. As more information becomes available
on the use and impact of UAM services in different cities, a more in-depth analysis with consideration of various
other user factors in the demand model along with incorporation of uncertainty and operational factors in the
optimization models is suggested as future work.
V.
CONCLUSION
We formulated the skyport location optimization problem for access to special destinations like airports as a variant
of HLP while incorporating elastic demand toward air taxi services. Our linearized formulation can be readily solved
using commercial software like Gurobi for scenarios like that of NYC; this can be easily extended to include healthcare
facilities, sports venues, and major transportation hubs in addition to airports. We formulated an optimization model
with two alternative objectives in our study i.e., RDR model with an objective to maximize air taxi ridership, and
REV model with an objective to maximize air taxi revenue. Depending on the objective, the model allocates demand
from different origin zones across optimal skyports (for each destination). The demand to the skyports is based on
trade-offs between trip length and trip cost based on user preferences. These preferences are incorporated in the
skyport location problem using a binary mode choice logit model. We consider different price scenarios (estimated
by Uber for air taxi services) in our analysis such as short term, medium term and long term.
The case study of NYC was presented considering airport access/transfers as a use case for air taxis. Using a dataset
from NYC TLC with over 20 million FHV trips to major airports associated with NYC (i.e., JFK, EWR, and LGA),
we obtained the optimal locations for skyports for air taxis using RDR and REV models for each price scenario.
Choosing the right objective and approach to locate skyports has a great impact on potential air taxi ridership as well
as on the returns gained from such services.
The choice of skyport location and allocation of demand at each skyports based on user behavior was used to study
the demand distribution at each skyports; it was found that the REV model results in fair distribution of demand across
skyports compared to RDR model. Also, from revenue aspect, the REV model shows relatively better performance.
Another important insight is around the choice of minimum number of skyports. In this context, we considered
variation in travel time savings (increment) across different choices of transfer time as a decision criterion. The
number of skyports in a city should be able to handle variations in transfer time; this is reflected via increase in travel
time savings with respect to skyport budget (p). The results of sensitivity analysis for NYC (based on optimal skyport
locations using REV model) show that at least 9 skyports would ensure good performance in the near term.
Although our study is based on a (major) subset of demand and selected (significant) decision variables reflecting
user preferences, the method used in the analysis of optimal skyport locations considering short term and long
term scenarios can help air taxi providers pursue various skyport design options based on infrastructure location
choices. In terms of future directions, the research can be further refined and elaborated along the following lines:
• the optimization problem can be augmented by considering different modes of access to skyports (e.g.,
bike, walk, e- scooters, public transit) and adding other eligible (mostly long commute) trips for
potential demand estimation,
• updating demand model with other competitive modes (see Fu et al., 2019; Sun et al., 2018) and with
additional influencing factors (e.g., individual specific decision variables capturing changes in perceptions
in post-pandemic scenario),
• considering aerial (flight) restrictions, regulations, and noise related factors pertaining to operations in
cities as per the city structure,
• considering access to medical facilities and daily long commutes as additional factors driving UAM
adoption,
26
• incorporating queue management using pricing schemes,
• modeling stochasticity in travel time and demand,
• using simulation based modeling approaches (see Rothfeld et al., 2018a) to study overall performance,
• considering capacity effects at skyports (see Vascik and Hansman, 2019); one way would be to assign
travelers to skyports with nonbinding capacities, which would also consider potential for transfers between
hubs,
• developing robust optimization methods with additional heuristics, and
• queue sensitive air taxi rebalancing (motivated by similar work for ground transportation by Sayarshad and
Chow (2017)).
Finally, although our results are focused on NYC, the methods are easily applicable to other cities as well.
27
REFERENCES
S. S. Ahmed, G. Fountas, U. Eker, S. E. Still, and P. C. Anastasopoulos. An exploratory empirical analysis of willingness to
hire and pay for flying taxis and shared flying car services. Journal of Air Transport Management, 90:101963, 2021.
C.
Al Haddad, E. Chaniotakis, A. Straubinger, K. Plo¨tner, and C. Antoniou. Factors affecting the adoption and use of urban
air mobility. Transportation research part A: policy and practice, 132:696–712, 2020.
R. Alexander and R. Syms. Vertiport infrastructure development. https://www.youtube.com/watch?v=k3nP0F5Mzw8, 2017.
[Online Video].
S. Algers and M. Beser. Modelling choice of flight and booking class-a study using stated preference and revealed preference
data. International Journal of Services Technology and Management, 2(1-2):28–45, 2001.
A. Alibeyg, I. Contreras, and E. Ferna´ndez. Hub network design problems with profits. Transportation Research Part E:
Logistics and Transportation Review, 96:40–59, 2016.
A. Alibeyg, I. Contreras, and E. Ferna´ndez. Exact solution of hub network design problems with profits. European Journal of
Operational Research, 266(1):57–71, 2018.
S. Alumur and B. Y. Kara. Network hub location problems: The state of the art. European journal of operational research,
190(1):1–21, 2008.
S.-E. Andersson. Operational planning in airline business—can science improve efficiency? experiences from sas. European
Journal of Operational Research, 43(1):3–12, 1989.
S.-E. Andersson. Passenger choice analysis for seat capacity control: A pilot project in scandinavian airlines. International
Transactions in Operational Research, 5(6):471–486, 1998.
ArcGIS desktop. Environmental Systems Research Institute. http://desktop.arcgis.com/en/arcmap/.
T. Aykin. Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problem. European Journal
of Operational Research, 79(3):501–523, 1994.
M. Balac, R. L. Rothfeld, and S. Ho¨rl. The prospects of on-demand urban air mobility in zurich, switzerland. In 2019 IEEE
Intelligent Transportation Systems Conference (ITSC), pages 906–913. IEEE, 2019a.
M. Balac, A. R. Vetrella, R. Rothfeld, and B. Schmid. Demand estimation for aerial vehicles in urban settings. IEEE Intelligent
Transportation Systems Magazine, 11(3):105–116, 2019b.
R. Berger. Urban air mobility, Focus. https://www.rolandberger.com/publications/publication pdf/roland berger urban air
mobility 1.pdf, 2018. [Online], Accessed June 25, 2022.
O. Berman, Z. Drezner, and G. O. Wesolowsky. The transfer point location problem. European journal of operational research,
179(3):978–989, 2007.
O. Berman, Z. Drezner, and G. O. Wesolowsky. The multiple location of transfer points. Journal of the Operational Research
Society, 59(6):805–811, 2008.
R. Binder, L. A. Garrow, B. German, P. Mokhtarian, M. Daskilewicz, and T. H. Douthat. If you fly it, will commuters come?
a survey to model demand for evtol urban air trips. In 2018 Aviation Technology, Integration, and Operations Conference,
page 2882, 2018.
G. Bitran and R. Caldentey. An overview of pricing models for revenue management. Manufacturing & Service Operations
Management, 5(3):203–229, 2003.
Blade. The sharpest way to fly. https://blade.flyblade.com. Accessed July 28, 2020.
S.-S. Boddupalli. Phd thesis: Estimating demand for an electric vertical landing and takeoff (evtol) air taxi service using
discrete choice modeling. 2019.
S. Bradford. Concept of operations for urban air mobility (conops 1.0). Federal Aviation Administration, 2020.
J. Campbell, A. Ernst, and M. Krishnamoorthy. Hub location problems. Facility location: application and theory, 2002.
J. F. Campbell. A survey of network hub location. Studies in Locational Analysis, 6:31–49, 1994a.
J. F. Campbell. Integer programming formulations of discrete hub location problems. European Journal of Operational
Research, 72(2):387–405, 1994b.
J. F. Campbell. Hub location and the p-hub median problem. Operations research, 44(6):923–935, 1996.
W.-C. Chiang, J. C. Chen, and X. Xu. An overview of research on revenue management: current issues and future research.
International journal of revenue management, 1(1):97–128, 2007.
I. Contreras, J.-F. Cordeau, and G. Laporte. Benders decomposition for large-scale uncapacitated hub location. Operations
28
research, 59(6):1477–1490, 2011.
R. S. de Camargo and G. Miranda.
Single allocation hub location problem under congestion: Network owner and user
perspectives. Expert Systems with Applications, 39(3):3385–3391, 2012.
J. de Dios Ortu´zar and L. G. Willumsen. Modelling transport. John wiley & sons, 2011.
Deloitte Insights. Consumer perception urban air mobility: Global automotive consumer survey, 2019. https://www2.deloitte.
com/us/en/pages/energy-and-resources/articles/consumer-perception-urban-air-mobility.html.
R. B. Dial. A probabilistic multipath traffic assignment model which obviates path enumeration. Transportation research, 5
(2):83–111, 1971.
M. R. Dickey. Here’s how much uber’s flying taxi service will cost. https://techcrunch.com/2018/05/08/heres-how-much-ubers-
flying-taxi-service-will-cost/, 2018.
S. Downing. 7 urban air mobility companies to watch. https://www.greenbiz.com/article/7-urban-air-mobility-companies-watch,
2019.
T. Duvall, A. Green, M. Langstaff, and K. Miele. Air-mobility solutions: What they’ll need to take off. McKinsey & Company,
2019.
J. Ebery. Solving large single allocation p-hub problems with two or three hubs. European Journal of Operational Research,
128(2):447–458, 2001.
A. T. Ernst and M. Krishnamoorthy. Efficient algorithms for the uncapacitated single allocation p-hub median problem. Location
science, 4(3):139–154, 1996.
D.
N. Fadhil. A gis-based analysis for selecting ground infrastructure locations for urban air mobility. inlangen]. Master’s
Thesis, Technical University of Munich, 2018.
R. Z. Farahani, M. Hekmatfar, A. B. Arabani, and E. Nikbakhsh. Hub location problems: A review of models, classification,
solution techniques, and applications. Computers & Industrial Engineering, 64(4):1096–1109, 2013.
M. Fu, R. Rothfeld, and C. Antoniou. Exploring preferences for transportation modes in an urban air mobility environment:
Munich case study. Transportation Research Record, 2673(10):427–442, 2019.
T. Furuta and K.-i. Tanaka. Minisum and minimax location models for helicopter emergency medical service systems. Journal
of the Operations Research Society of Japan, 56(3):221–242, 2013.
A. Garcia-Martinez, R. Cascajo, S. R. Jara-Diaz, S. Chowdhury, and A. Monzon. Transfer penalties in multimodal public
transport networks. Transportation Research Part A: Policy and Practice, 114:52–66, 2018.
L. A. Garrow, B. German, P. Mokhtarian, and J. Glodek. A survey to model demand for evtol urban air trips and competition
with autonomous ground vehicles. In AIAA Aviation 2019 Forum, page 2871, 2019.
R. Glon. 15 awesome flying taxis and cars currently in development. Digital Trends, 2020.
R. Goyal. Urban air mobility (UAM) market study. NASA Technical Report HQ-E-DAA-TN65181, NASA Headquarters, 2018.
R. Goyal, C. Reiche, C. Fernando, J. Serrao, S. Kimmel, A. Cohen, and S. Shaheen. Urban air mobility (UAM) market study.
Technical report, 2018.
G. Grandl, M. Ostgathe, J. Cachay, S. Doppler, J. Salib, H. Ross, J. Detert, and R. Kallenberg. The future of vertical mobility
sizing the market for passenger, inspection, and goods services until 2035. Porsche Consulting, 2018.
Gurobi Optimizer 9.0. Gurobi. http://www.gurobi.com/.
D. L. Hackenberg. NASA advanced air mobility (AAM) urban air mobility (UAM) and grand challenge AIAA. 2019.
H. W. Hamacher and T. Meyer. Hub cover and hub center problems. 2006.
S. Hasan. Urban air mobility (UAM) market study. NASA Technical Report HQ-E-DAA-TN70296, NASA Headquarters, 2019.
J. Holden and N. Goel. Uber Elevate: Fast-forwarding to a future of on-demand urban air transportation. Uber Technologies,
Inc., San Francisco, CA, 2016.
J. Holden, , E. Ellison, N. Goel, and S. Swaintek. Uber Elevate Summit. Uber Technologies, 2018. https://www.youtube.com/
watch?v=hnceMcSnjQ0&t=4722s.
B. J. Holmes, R. Parker, D. Stanley, P. McHugh, C. J. Burns, M. J. J. Olcott, B. German, and D. McKenzie. Nasa strategic
framework for on-demand air mobility. Technical report, NASA Headquarters, 2017.
T. Hornyak. The flying taxi market may be ready for takeoff, changing the travel experience forever. CNBC, 2020.
S. A. Hosseinijou and M. Bashiri. Stochastic models for transfer point location problem. The International Journal of Advanced
Manufacturing Technology, 58(1-4):211–225, 2012.
W. Hu. Your taxi or uber ride in manhattan will soon cost more. https://www.nytimes.com/2019/01/31/nyregion/uber-taxi-lyft-
29
fee.html, 2019.
Y. H. Hwang and Y. H. Lee. Uncapacitated single allocation p-hub maximal covering problem. Computers & Industrial
Engineering, 63(2):382–389, 2012.
A. Ilahi, P. F. Belgiawan, M. Balac´, and K. W. Axhausen. Understanding travel and mode choice with emerging modes: A
pooled sp and rp model in greater jakarta. Arbeitsberichte Verkehrs-und Raumplanung, 1448, 2019.
W. Johnson and C. Silva. Observations from exploration of vtol urban air mobility designs. 2018.
B. Y. Kara. Phd thesis: Modeling and analysis of issues in hub location problem. 1999.
B. Y. Kara and B. C. Tansel. The single-assignment hub covering problem: Models and linearizations. Journal of the Operational
Research Society, 54(1):59–64, 2003.
J. G. Klincewicz. A dual algorithm for the uncapacitated hub location problem. Location Science, 4(3):173–184, 1996.
M. Kreimeier, E. Stumpf, and D. Gottschalk. Economical assessment of air mobility on demand concepts with focus on
germany. In 16th AIAA Aviation Technology, Integration, and Operations Conference, page 3304, 2016.
H. Kuhn, C. Falter, and A. Sizmann. Renewable energy perspectives for aviation. In Proceedings of the 3rd CEAS Air&Space
Conference and 21st AIDAA Congress, Venice, Italy, pages 1249–1259, 2011.
E. Lewis, J. Ponnock, Q. Cherqaoui, S. Holmdahl, Y. Johnson, A. Wong, and H. O. Gao. Architecting urban air mobility
airport shuttling systems with case studies: Atlanta, los angeles, and dallas. Transportation Research Part A: Policy and
Practice, 150:423–444, 2021.
E. Lim and H. Hwang. The selection of vertiport location for on-demand mobility and its application to seoul metro area.
International Journal of Aeronautical and Space Sciences, pages 1–13, 2019.
R. Lineberger, A. Hussain, M. Metcalfe, and V. Rutgers. Infrastructure barriers to the elevated future of mobility. Deloitte
Insights, 2009.
R. Lineberger, A. Hussain, and V. Rutgers. Change is in the air. Deloitte Insights, 2019.
Z. Ma, M. Urbanek, M. A. Pardo, J. Y. Chow, and X. Lai. Spatial welfare effects of shared taxi operating policies for first
mile airport access. International Journal of Transportation Science and Technology, 6(4):301–315, 2017.
M. Mahmoodjanloo, R. Tavakkoli-Moghaddam, A. Baboli, and A. Jamiri. A multi-modal competitive hub location pricing
problem with customer loyalty and elastic demand. Computers & Operations Research, 123:105048, 2020.
C. Majaski. The difference between uber vs. yellow cabs in new york city. https://www.investopedia.com/articles/personal-
finance/021015/uber-versus-yellow-cabs-new-york-city.asp, 2019.
V. Marianov and D. Serra. Location models for airline hubs behaving as m/d/c queues. Computers & Operations Research,
30(7):983–1003, 2003.
A
´ . Mar´ın and R. Garc´ıa-Ro´denas. Location of infrastructure in urban railway networks. Computers & Operations Research,
36(5):1461–1477, 2009.
D. McFadden et al. Conditional logit analysis of qualitative choice behavior. 1973.
R. Merkert and J. Bushell. Managing the drone revolution: A systematic literature review into the current use of airborne
drones and future strategic directions for their effective control. Journal of air transport management, 89:101929, 2020.
R. Neamatian Monemi, S. Gelareh, S. Hanafi, and N. Maculan. A co-opetitive framework for the hub location problems in
transportation networks. Optimization, 66(12):2089–2106, 2017.
New York City Taxi Limousine Commission. Taxi trip record data. https://www1.nyc.gov/site/tlc/about/tlc-trip-record-data.
page. Accessed May 20, 2020.
New York City taxi zones. NYC Open data. https://data.cityofnewyork.us/Transportation/NYC-Taxi-Zones/d3c5-ddgc.
Accessed May 20, 2020.
M. E. O’Kelly. A quadratic integer program for the location of interacting hub facilities. European Journal of Operational
Research, 32(3):393–404, 1987.
G. Ott. Blade review: $145 for a helicopter to nyc airports. https://www.godsavethepoints.com/review-blade-helicopter-service-
ny-airports/, 2019.
C¸ . O
¨ zgu¨n-Kibirog˘lu, M. N. Serarslan, and Y. ˙I. Topcu. Particle swarm optimization for uncapacitated multiple allocation hub
location problem under congestion. Expert Systems with Applications, 119:1–19, 2019.
M. P. Paneque, M. Bierlaire, B. Gendron, and S. S. Azadeh. Integrating advanced discrete choice models in mixed integer
linear optimization. Transportation Research Part B: Methodological, 146:26–49, 2021.
U. Pelli and R. Riedel. Flying-cab drivers wanted. https://www.mckinsey.com/industries/automotive-and-assembly/our-insights/
30
flying-cab-drivers-wanted, 2020.
S. Rajendran and J. Shulman. Study of emerging air taxi network operation using discrete-event systems simulation approach.
Journal of Air Transport Management, 87:101857, 2020.
S. Rajendran and J. Zack. Insights on strategic air taxi network infrastructure locations using an iterative constrained clustering
approach. Transportation Research Part E: Logistics and Transportation Review, 128:470–505, 2019.
S. Rajendran, S. Srinivas, and T. Grimshaw. Predicting demand for air taxi urban aviation services using machine learning
algorithms. Journal of Air Transport Management, 92:102043, 2021.
R. N. Rezende, E. Barros, and V. Perez. General aviation 2025-a study for electric propulsion. In 2018 Joint Propulsion
Conference, page 4900, 2018.
M. Rimjha, S. Hotle, A. Trani, N. Hinze, and J. C. Smith. Urban air mobility demand estimation for airport access: A
Los Angeles international airport case study. In 2021 Integrated Communications Navigation and Surveillance Conference
(ICNS), pages 1–15. IEEE, 2021.
R. Rothfeld, M. Balac, K. O. Ploetner, and C. Antoniou. Agent-based simulation of urban air mobility. In 2018 Modeling and
Simulation Technologies Conference, page 3891, 2018a.
R. Rothfeld, M. Balac, K. O. Ploetner, and C. Antoniou. Initial analysis of urban air mobility’s transport performance in sioux
falls. In 2018 Aviation Technology, Integration, and Operations Conference, page 2886, 2018b.
S. Roy, M. T. Kotwicz Herniczek, B. J. German, and L. A. Garrow. User base estimation methodology for a business airport
shuttle air taxi service. Journal of Air Transportation, 29(2):69–79, 2021.
S. Roy, M. T. Kotwicz Herniczek, C. Leonard, B. J. German, and L. A. Garrow. Flight scheduling and fleet sizing for an airport
shuttle air taxi service. Journal of Air Transportation, 30(2):49–58, 2022.
H. R. Sayarshad and J. Y. Chow. Non-myopic relocation of idle mobility-on-demand vehicles as a dynamic location-allocation-
queueing problem. Transportation Research Part E: Logistics and Transportation Review, 106:60–77, 2017.
S. Shaheen, A. Cohen, and E. Farrar. The potential societal barriers of urban air mobility (UAM). NASA Technical Report, 2018.
M. Shamiyeh, J. Bijewitz, and M. Hornung. A review of recent personal air vehicle concepts. In Aerospace Europe 6th ceas
conference, volume 913, pages 1–18, 2017.
D. Skorin-Kapov, J. Skorin-Kapov, and M. O’Kelly. Tight linear programming relaxations of uncapacitated p-hub median
problems. European Journal of Operational Research, 94(3):582–593, 1996.
L. V. Snyder. Facility location under uncertainty: a review. IIE transactions, 38(7):547–564, 2006.
A. Straubinger, R. Rothfeld, M. Shamiyeh, K.-D. Bu¨chter, J. Kaiser, and K. O. Plo¨tner. An overview of current research and
developments in urban air mobility–setting the scene for UAM introduction. Journal of Air Transport Management, 87:
101852, 2020.
A. Straubinger, J. Michelmann, and T. Biehle. Business model options for passenger urban air mobility. CEAS Aeronautical
Journal, 12(2):361–380, 2021.
X. Sun, S. Wandelt, and E. Stumpf. Competitiveness of on-demand air taxis regarding door-to-door travel time: A race through
Europe. Transportation Research Part E: Logistics and Transportation Review, 119:1–18, 2018.
G. Taherkhani and S. A. Alumur. Profit maximizing hub location problems. Omega, 86:1–15, 2019.
K. Talluri and G. Van Ryzin. Revenue management under a general discrete choice model of consumer behavior. Management
Science, 50(1):15–33, 2004.
P. Z. Tan and B. Y. Kara. A hub covering model for cargo delivery systems. Networks: An International Journal, 49(1):28–39,
2007.
E. Taylor. Everything you wanted to know about taking an uber copter. Vogue, 2019.
D. P. Thipphavong, R. Apaza, B. Barmore, V. Battiste, B. Burian, Q. Dao, M. Feary, S. Go, K. H. Goodrich, J. Homola,
et al. Urban air mobility airspace integration concepts and considerations. In 2018 Aviation Technology, Integration, and
Operations Conference, page 3676, 2018.
M. Thompson. Panel: Perspectives on prospective markets. In Proceedings of the 5th Annual AHS Transformative VTOL
Workshop, 2018.
H. Topcuoglu, F. Corut, M. Ermis, and G. Yilmaz. Solving the uncapacitated hub location problem using genetic algorithms.
Computers & Operations Research, 32(4):967–984, 2005.
UberCopter. Introducing UberCopter. https://www.uber.com/blog/new-york-city/uber-copter/, 2019.
UberElevate. Uberair vehicle requirements and missions, 2018. https://s3.amazonaws.com/uber-static/elevate/Summary+
Mission+and+Requirements.pdf.
31
P. Vascik and R. J. Hansman. Thesis report: Systems-level analysis of on demand mobility for aviation. https://dspace.mit.
edu/handle/1721.1/106937, 2017a.
P. Vascik and R. J. Hansman. Evaluation of key operational constraints affecting on-demand mobility for aviation in the
Los Angeles basin: Ground infrastructure, air traffic control and noise. 17th AIAA Aviation Technology, Integration, and
Operations Conference, 2017b. doi: 10.2514/6.2018-3849.
P. Vascik and R. J. Hansman. Constraint identification in on-demand mobility for aviation through an exploratory case study
of los angeles. 17th AIAA Aviation Technology, Integration, and Operations Conference, 2017c. doi: 10.2514/6.2017-3083.
P. Vascik and R. J. Hansman. Scaling constraints for urban air mobility operations : Air traffic control, ground infrastructure, and
noise. 18th AIAA Aviation Technology, Integration, and Operations Conference, 2018. doi: 10.2514/6.2018-3849.
P. D. Vascik and R. J. Hansman. Development of vertiport capacity envelopes and analysis of their sensitivity to topological and
operational factors. In AIAA Scitech 2019 Forum, page 0526, 2019.
B. Wagner. Model formulations for hub covering problems. Journal of the Operational Research Society, 59(7):932–938, 2008.
M. Wardman, J. Hine, and S. Stradling. Interchange and travel choice-volumes 1 and 2. TRANSPORT RESEARCH SERIES,
2001.
S. R. Winter, S. Rice, and T. L. Lamb. A prediction model of consumer’s willingness to fly in autonomous air taxis. Journal
of Air Transport Management, 89:101926, 2020.
APPENDIX
Tables VI–VIII report optimal skyport locations obtained from our experiments (for different pricing scenarios).
Table VI. Optimal skyport locations in NYC for short term scenario
Budget
RDR model
REV model
number of
skyports (p)
skyport locations
(taxi zone IDs)
skyport locations
(taxi zone IDs)
1
[157]
[170]
2
[10, 260]
[198, 234]
3
[10, 114, 129]
[114, 160, 161]
4
[7, 10, 92, 211]
[114, 161, 162, 198]
5
[7, 10, 92, 161, 211]
[92, 161, 162, 181, 249]
6
[7, 10, 92, 114, 129, 161]
[92, 161, 162, 181, 230, 231]
7
[7, 10, 92, 114, 129, 161, 162]
[92, 161, 162, 170, 181, 230, 231]
8
[7, 10, 92, 114, 118, 129, 161, 162]
[48, 92, 161, 162, 170, 181, 230, 231]
9
[7, 10, 92, 114, 118, 129, 161, 162, 230]
[48, 92, 161, 162, 170, 181, 230, 234, 261]
10
[7, 10, 25, 92, 114, 118, 129, 161, 162, 230]
[48, 92, 161, 162, 170, 181, 230, 234, 239, 261
Table VII. Optimal skyport locations in NYC for medium term scenario
Budget
RDR model
REV model
number of
skyports (p)
skyport locations
(taxi zone IDs)
skyport locations
(taxi zone IDs)
1
[170]
[257]
2
[92, 161]
[70, 87]
3
[92, 125, 161]
[70, 231, 236]
4
[92, 125, 161, 162]
[70, 231, 236, 257]
5
[92, 125, 161, 162, 230]
[7, 24, 70, 231, 257]
6
[92, 125, 161, 162, 181, 230]
[7, 24, 70, 231, 257, 261]
7
[92, 125, 161, 162, 181, 230, 236]
[7, 24, 70, 231, 243, 257, 261]
8
[92, 125, 161, 162, 170, 181, 230, 236]
[7, 24, 70, 129, 231, 243, 257, 261]
9
[48, 92, 161, 162, 170, 181, 230, 231, 236]
[7, 24, 70, 129, 143, 231, 243, 257, 261]
10
[7, 48, 92, 161, 162, 170, 181, 230, 231, 236]
[7, 24, 70, 118, 129, 143, 231, 243, 257, 261]
32
Table VIII. Optimal skyport locations in NYC for long term scenario
Budget
RDR model
REV model
number of
skyports (p)
skyport locations
(taxi zone IDs)
skyport locations
(taxi zone IDs)
1
[170]
[204]
2
[92, 161]
[135, 204]
3
[92, 161, 231]
[135, 204, 261]
4
[92, 161, 162, 231]
[70, 135, 204, 261]
5
[92, 161, 162, 230, 231]
[70, 123, 135, 204, 231]
6
[92, 161, 162, 230, 231, 236]
[70, 123, 135, 204, 257, 261]
7
[92, 161, 162, 227, 230, 231, 236]
[70, 98, 123, 135, 204, 257, 261]
8
[48, 92, 161, 162, 227, 230, 231, 236]
[44, 70, 98, 123, 135, 204, 257, 261]
9
[48, 92, 161, 162, 227, 230, 231, 236, 252]
[44, 70, 98, 118, 123, 135, 204, 257, 261]
10
[48, 92, 161, 162, 170, 227, 230, 231, 236, 252]
[44, 70, 98, 118, 123, 135, 204, 231, 257, 261]
