The Route Network Development Problem based on QSI Models
Assia Kamal Idrissi
1
, Arnaud Malapert
2
and R
´
emi Jolin
1
1
Milanamos, 1047 route des Dolines, Sophia Antipolis, France
2
Universit
´
e C
ˆ
ote d’Azur, CNRS, I3S, France
Keywords:
Airline Schedule Design, Route Network Development, Forecasting demand, Quality of Service Index,
Time-independent Model, Graph Database.
Abstract:
The growth of air passenger needs has forced airlines to improve their quality of service. Airlines have to
choose flight schedules by considering demand, passengers preferences and competitors. The problem of
allocating a new flight involves the route network development, and consists to determine a set of (Origin-
Destination) pairs to serve and then choose flight schedules with respect to the Quality of Service Index (QSI)
model. In this PhD project, we work with a software tool developed by the company Milanamos that helps
airline managers to make decisions about destinations to serve. As a starting point, we define the flight radius
problem related to this software. It is a sub-problem of the route network development problem and aims to
optimize the visualization of the pertinent network by showing only interesting airports regarding QSI model.
In this paper, we present the problem of allocating a new flight and formulate the flight radius problem as
a problem of finding maximal sub-graph. Our objective is to locate in the network what routes represent
business opportunities and are attractive regarding competition so it can be visualized. We construct the graph
from Milanamos the database using the time-independent approach and store it in Neo4j a graph database.
We describe the process of generating and storing the graph in Neo4j and sum up by outlining the expected
outcome.
1 RESEARCH PROBLEM
The growth of air passenger needs has forced airlines
to improve their quality of service. At best, the air-
lines should offer flights that match the expectations
of their passengers. In order to capture a large flow
of the passengers, the airlines should focus on airline
schedule design which is one of the important com-
ponents and evokes complex decisions. It takes the
airline passenger demand, airport and aircraft charac-
teristics and then generates a selection of flight legs
as outputs those maximize the airline company profit
subject to resource constraints (aircraft and airport
capacity, maximal working hours, minimal ground
time,...). A flight leg or segment is defined with three
attributes: Origin-Destination (OD) pair (an OD pair
is a couple of airports), arrival/departure time and air-
craft type (Hall, 2012). Airline schedule design aims
to answer the following questions:
• Where to fly?
• How frequently to fly?
• When to fly?
• How much capacity to provide on each flight?
• What are the competitive choices of flight sched-
ules?
It’s a process with making decisions at different stages
about opening new routes or adding new flights which
need a demand forecasting that is not always based
on historical data when airlines decide to include a
new destination. Therefore, demand is calculated
and the best decision is chosen to maximize their
profit. These decisions are very important for an air-
line, quality of service and prices influence the air-
line’s ability to attract travelers. However, we deal
with a multi-objective problem. The airline company
has to take into consideration the passengers choice.
In fact, it may consider criteria such as travel costs,
travel time and also the type of flight. For example,
a businessman may try to optimize his travel time, a
student wants to minimize his costs and a visitor may
wish to avoid connecting flight. So, at the end, users
have different preferences over the criteria and type
of flights is one of these criteria. There are three dif-
ferent kinds of flights: non-stop flight, direct flight
and connecting flight. A non-stop flight is a single
flight with no intermediate stops. It is the preferred
choice for most passengers. In the absence of such
flights, passengers must take either a direct flight or
Idrissi, A., Malapert, A. and Jolin, R.
The Route Network Development Problem based on QSI Models.
In Doctoral Consortium (DCORES 2017), pages 3-11
3

a connecting flight. A direct flight or through flight
is operated by the same aircraft and includes at least
one intermediate stop; passengers stay on board dur-
ing the trip. Note that the flight number remains the
same throughout the trip. A connecting flight requires
an aircraft change for passengers in a hub. Thus, the
trip includes at least two different planes with two dif-
ferent flight numbers. A Trip is a sequence of flight
legs taken by passengers to complete a journey.
The problem of allocating a new flight concerns
the first two questions of airline schedule design, that
is, determining a set of OD pairs and then choosing
the arrival and departure times for an aircraft, given
certain constraints, that minimize costs and maximize
the profit of an airline company.
Adding a new flight leg to the current network is
complicated and involves several decisions:
• Scheduling decisions must be made according to
all flight legs connected with the new addition
flight leg. They must decide which flight leg to
add after considering competitors.
• Measuring Route ’Profitability’: determines eco-
nomic profitability of opening a new flight, if it
involves a new destination. The other costs must
be considered including the additional cost of the
airport and also calculate the prices in order not
to lose their passengers but to capture a new de-
mand. That depends on the existence of current
routes that could be connecting flight as well as
expected future competition.
In this work, we aim to determine a set of (OD) pairs
for allocating new flights. This problem evokes the
selection of routes to be flown but some operational
and economic considerations must be taken to op-
timize an airline network. A route is a sequence
of flights with unique flight numbers that begins at
the origin airport and ends at the destination airport.
Therefore, a forecasting demand is required to esti-
mate passenger demand for each route and then de-
termine the expected cost and finally compute flight
time and revenue. Forecasting demand is the key ele-
ment while an airline is planning to add a new flight.
An airline needs to estimate the total number of pas-
sengers who are willing to take this route, especially
if the route is already operated by other airlines. It
has to supply enough seats to satisfy the demand. On
the one hand, we deal with retrieving set of origin-
destination pairs. On the other hand, we look for the
best itineraries based on three principal criteria of QSI
models (Quality of Service Index) which let airlines
project potential market share impact on each deci-
sion. QSI model is a market share model that is used
to estimate the probability that a traveler selects a spe-
cific itinerary connecting an airport pair (Jacobs et al.,
2012). Two KPIs (Key Performance Indicator) are
considered in potential market share impact: number
of passengers and revenue for the airline company,
that is, adding a new flight by allocating capacities
to maximize the revenue.
1.1 State of the Art
The air transportation industry has evolved rapidly
over the last years. Route network development,
schedule design, fleet assignment, aircraft mainte-
nance routing and crew scheduling that represent the
five facets of the air transportation optimization prob-
lem (Rebetanety, 2006):
Route Network Development: deciding which set
of origin-destination pairs to serve. The network
design problem consists of determining where to
fly (Belobaba et al., 2015).
Schedule design : defining the frequency of each
flight. Scheduling determines where and when the
airline will fly.
Fleet Assignment: specifying the type and the size
of aircraft serving each flight in a given schedule
(Rebetanety, 2006).
Aircraft Routing: determining feasible aircraft
routes, sequences of flight legs flown by an air-
craft type under maintenance and time constraints
(Jacobs et al., 2012).
Crew Scheduling: assigning crews to the flights.
Airlines have the choice to create new routes or in-
crease/decrease the frequency of exiting routes with
respect to operational and economic constraints. The
latter does not require the route network develop-
ment since the route already exists. Note that cre-
ating a new route requires a lot of investment (Car-
mona Benitez, 2012). Relevant literature exists for
airline scheduling and routing. Most researches deal
with minimization of the airline cost. (Dobson and
Lederer, 1993) studied profit maximization with re-
spect to quality of service and modeled flight sched-
ules including company costs and consumer choice.
The objective was to maximize profit against fixed
schedules and prices for other airlines, demand was
calculated for each route as a function of the ser-
vice quality of all routes to attract passengers. They
used a heuristic algorithm to calculate optimal sched-
ules and prices with two classes of customers busi-
ness and non-business and solved a sample problem
with 12-period and 5-city which gives 120 flights and
20 (OD). The competition between airlines has in-
creased. In order to deal with competition, airlines
have to increase their market share. In this regard,
QSI criteria are integrated in our model to get poten-
tial market share impact for an airline. Figure 1 shows
DCORES 2017 - DOCTORAL CONSORTIUM
4

the criteria used in the QSI model:
Revenue
and costs
Time
Regret
Frequency
Distance
Type of
aircraft
Departure
Time
Capacity
Costs of
airport
Surcharge
Costs
Cost of
revenue
Brand
perception
Type of
flight
Type of
airlines
Figure 1: Criteria of QSI models.
The three principal criteria are highly correlated:
Revenue and costs consists to fix an attractive price
to capture more traffic. The price must be deter-
mined in comparison with other flights in respect of
the competition. Time is the elapsed flying time and
finally Regret is the regret compared to the optimal
duration and cost. Each of these criteria is related
to other factors that affect the estimation of poten-
tial market share: Brand perception is a factor in-
cluded in the category revenue and costs because the
airline market share of total forecast demand for the
new route depends on the existence of current and ex-
pected future competition. In addition, the Brand per-
ception of travel costs criteria fixes the price for routes
against competing airlines. Surcharge costs include
maintenance costs, fuel and others stuff. When the
route involves a new destination, additional costs of
the airport must be considered. Cost of revenue con-
cerns marketing and advertising. Moreover, time cri-
teria concerns both airline managers who must decide
which flight to schedule and passengers. Regarding
revenue and costs, the focus is solely on the airline
company. In fact, airline costs are driven by fleet and
flight schedule. Finally, the regret criterion focuses on
avoiding regrets that may result from making a non-
optimal decision of time or price when choosing a
low-cost airline or a connecting flight. The passen-
gers do not have the same regret of the same route.
Regarding competition, departure time can be deter-
mined and then frequency. In fact, passengers have
preferences for routes. These preferences depend on
the QSI criteria typically the departure time desired.
The type of flight is either a principal criterion. In
fact, airlines may choose to serve the route with non-
stop flights rather than going through their hub espe-
cially, when they see a high demand for travel on this
route.
The route network development is considered as
the initial problem addressed by the airlines, our work
position in this research field. Airlines choose what
routes to serve and what prices to fix so that the pas-
sengers have the quality and the safety services, the
first issue to consider is forecasting demand for po-
tential new routes. Three common methods for fore-
casting air travel: trends, gravity models, and simu-
lation (Swan, 2008). Since no single model guaran-
tee accuracy, the most commonly used in literature
is the gravity model. (Sivrikaya, 2013) studied this
model to estimate the domestic air travel demand for
any city pair, two levels of forecasts were considered:
1. Microscopic model; airport specific or city pair
specific data. 2. Macroscopic model: region or coun-
try. The aim of the study is to analyze the determin-
ing factors in air travel demand, it is a semi-log linear
model based on geographic, demographic and socioe-
conomic variables such as population, GDP, distance,
travel Time. In addition, (Marwaha and Kokkolaras,
2015) used the gravity model to estimate OD demand
figures for Canada but in function of routes distances.
Modeling a flight network is similar to a railway
network which is smaller but more complicated than
road networks (junctions are nodes, streets are edges)
due to different operations constraints which rely on
some kind of periodic timetable. Timetable is a listing
of times at which events are intended to take place and
are the basis behind any flight models. The problem
can be solved by modeling the network as a simple
graph where edge weights represent travel times on
the corresponding connection. In order to model the
flight network and thus obtain a graph, there are many
approaches cited in the literature for route planning.
The time-expanded model includes the time depen-
dencies of the timetable in the graph where each node
represents an event of the timetable and edge con-
nects two consecutive events (Kirchler, 2013). This
approach allows modeling the time-dependent infor-
mation with more flexible modeling of additional con-
straints. Therefore, this approach yields a huge graph.
The condensed model is a time-independent model
where edges correspond to the aggregate of all avail-
able connections between two nodes. While the first
approach allows a more flexible model but constructs
a big graph, the latter uses only smaller inputs. A
key point is that the output graph contains a single
node per station rather than multiple nodes per station.
Thus, instead of applying routing algorithms to the
whole graph, we opt to choose the condensed model
in such a way that a routing algorithm does not nec-
The Route Network Development Problem based on QSI Models
5

essarily explore some useless parts of the graph.
Once the graph is generated, routing problems are ad-
dressed by finding itineraries that are satisfying time
constraints. The routing problem is modeled in litera-
ture in different ways. As an example, it was modeled
to find an optimal flight path that avoids geographi-
cal obstacles (Bast et al., 2015). Another work was
dealing with routing problems and researches were
interested to find the shortest path in the flight net-
works during a time period with respect to several
criteria (transfer, time...). As the shortest path algo-
rithm, (Delling et al., 2009) used Dijkstra algorithm
to solve the earliest arrival problem. It retrieves the
quickest connections according to multiple criteria.
Although, the railway model can be adapted to flight
timetables, they developed a new model that takes
into account check in and check out time and transfer
time when it’s a connecting flight; it was due to the
fact that the problem of instantaneous transfers has an
even greater impact on realism flights than on railway
queries. These researches studied the routing problem
related to passengers.
1.2 Our Contribution
In this paper, we aim to solve the problem of allocat-
ing a new flight. It is represented as the route network
development problem. We work with Milanamos,
a startup company specialized in air transportation.
Milanamos has developed a decision tool for airline
managers to analyze and simulate a new market. Our
problem derived from this application and targets new
destinations for a given (OD). We proposed this sub-
problem (Flight radius problem) which is related to
the route network development problem. It helps to
enhance the visualization of the application by show-
ing only interesting destinations. Therefore, it can
be implemented in the short term within the exist-
ing application and helps airline managers to make
decision about where to fly. The data are stored in
a NoSQL database. The first challenge is to generate
the graph from a missing and erroneous data since
the real-world data are generally incorrect inputted.
Hence, a data pre-processing step is required to fil-
ter our data. The result of the selection of routes will
be implemented to optimize the Milanamos applica-
tion (See section 3.3). We use the time independent
approach to model the flight network. The selection
of routes is based on QSI criteria to be competitive
against other airlines serving same (OD) pair. Thus,
the condensed graph constructed includes these crite-
ria. Once it’s done, we would like to apply the routing
algorithms to enumerate itineraries under certain con-
straints.
This paper is organized as follows. Section 2 de-
scribes objectives of this project. In Section 3, we ex-
plain the methodology and include formal definitions
of timetables, present the formalization of the prob-
lem discussed above and describe the database infor-
mation used in our research as well as the difficulties
encountered when industry data are missing. We con-
clude with the current research of our problem.
2 OUTLINE OF OBJECTIVES
The long-term goal of this PhD project is the opti-
mization of multimodal networks. Our first step is to
enhance the visualization in PlanetOptim. Hence,
for an airline managers, what is the relevant sub-
network related to a given flight? What are the pas-
sengers origins and destinations? This represents a
preliminary step before studying the allocation of new
flights, that is determining a set of (OD) pairs and the
arrival and departure times with respect to the QSI cri-
teria. The project is organized into five major steps.
The first two ones have already been performed and
their outcome is described in this document:
• Generation of the condensed graph and store it in
a graph database;
• Formulation of the flight radius problem for en-
hancing the visualization;
• Solving the flight radius problem in
PlanetOptim;
• Modeling and solving of the route network devel-
opment problem with respect to QSI criteria;
• Integration other transportation modes in a multi-
modal network.
3 METHODOLOGY
This section presents the formalization of the flight
radius problem, describes the flight database, and ex-
plain the construction of the condensed graph based
on the flight database. Network design and routing
problems often rely on graph theory. Therefore, we
first recall basic definitions of graphs.
3.1 Preliminaries
A graph G is a tuple G = (V,E) consisting of a fi-
nite set V of nodes or vertices and a set E ⊆ V ×V of
edges which are ordered pairs (u, v) if the graph is di-
rected. The node u is called the tail of the edge, and v
is called the head. Each edge (u, v) ∈ E has an associ-
ated non-negative weight w(u,v). In a directed graph,
DCORES 2017 - DOCTORAL CONSORTIUM
6

the edges point from one node to another. For in-
stance, airline networks are weighted directed graphs
where the weights represent the prices or the duration
of the flight. A direct flight from one city to another
does not necessarily imply that there is also a direct
return flight. A sub-graph G
0
= (V
0
,E
0
) of a graph G
where V
0
is a subset of V and E
0
is a subset of E. A
path is a sequence of nodes {v
1
,v
2
,..., v
k
} such that
for each 1 ≤ i < k the condition (v
i
,v
i+1
) ∈ E holds.
If additionally v
1
= v
k
, then the path is a cycle. The
length of a path is the sum of its edge weights along
the path and is denoted by:
δ(P) :=
k−1
∑
i=1
w(v
i
,v
i+1
).
A path in G is called elementary if no vertex oc-
curs more than once. A graph G is strongly con-
nected if there exists a path joining any two vertices.
A transportation network should be a strongly con-
nected graph.
3.2 Problem Formalization
The essence for each flight model is a timetable from
which we construct the condensed graph. A flight
timetable is defined by a 4-tuple (C , A, F ,T ) where
A a set of airports, F is a set of flights, T is the pe-
riodicity of the timetable and C is a set of elementary
connections. An elementary connection c ∈ C is a 5-
tuple c = ( f , o,d,t
s
,t
e
) which represents flight f ∈ F
departing from airport o ∈ A at t
s
< T and arriving at
airport d ∈ A at time t
e
< T . Concretely, an elemen-
tary connection corresponds to an event in a timetable.
Let cap(c) denote the capacity, let pax(c) denote the
number of passengers, and let r(c) denote the total
revenue. Let t(c) = t
e
−t
s
be the flight duration asso-
ciated with the elementary connection.
A passenger trip (c
1
,c
2
,. . ., c
n−1
,c
n
) is a sequence
of elementary connections, with the origin of an el-
ementary connection the same as the destination of
its predecessor in the sequence, and the elapsed time
between two successive connections at least as great
as the minimum connecting time:
o(c
i+1
) = d(c
i
) ∧t
e
(c
i
) + MCT (d) ≤ t
s
(c
i+1
)
∀1 ≤ i ≤ n − 1
Where MCT is the minimum connecting time at the
destination airport d.
The condensed graph is a time-independent represen-
tation of the flight network. Nodes represent airports
meanwhile the presence of an arc indicates that there
exists at least one elementary connection between the
two airports. Each arc is constructed by aggregating
all elementary connections between each pair of air-
ports. Let C
od
=
{
c ∈ C | o = o(c) ∧ d = d(c)
}
be the
set of elementary connections between two airports o
& d. The following labels are associated with the arc
(o,d) :
• F
od
= |C
od
| is the number of elementary connec-
tion between o and d;
• C
od
=
∑
c∈C
od
cap(c) is the total capacity in terms
of the number of passengers;
• P
od
=
∑
c∈C
od
pax(c) is the total number of passen-
gers;
• R
od
=
∑
c∈C
od
r(c) is the total revenue;
•
¯
R
od
= min
c∈C
od
r(c)
pax(c)
is the minimum revenue per
passenger;
• T
od
= min
c∈C
od
t(c) is the minimum flight dura-
tion;
• D
od
is the distance between the two airports.
Frequency, capacity and number of passengers are
the target market that determines for airlines what
routes to operate. We choose the sum aggregation for
these criteria since it indicates the importance of the
route so the airline decides to increase the frequency
or open new route. Concretely, a passenger trip is
a unique path p in the time-expanded graph whereas
many passengers trips are associated with the same
path in the condensed graph. The existence of a path
in the condensed graph is a necessary (but not suffi-
cient) condition to the existence of a passenger trip.
In addition, a path between o & d in the condensed
graph gives a lower bound on the cost and duration of
a passenger trip that goes along the same airports.
We aim to determine the set of (OD) pairs that
would be interesting for an airline manager. The prob-
lem is to identify flights and routes that represent busi-
ness opportunities and are attractive regarding com-
petition. But the flight network is so large that it
can’t be visualized. So, we aim to display only the
relevant airports with respect to the edge (o, d). It
means that there exists a route connecting these air-
ports passing through the arc (o, d) subject to time and
cost constraints. A naive algorithm could enumerate
all paths passing through the arc, but the number of
paths can grow exponentially. With this aim, let R
be a Boolean regret function defined on paths of the
condensed graph G. The problem consists in finding
a maximal sub-graph such that each node or arc sup-
ports a path accepted by the regret function.
Hence, the problem is formulated as follows:
Input: a graph G = (V,E), the arc (o, d), the regret
function R
Output: a subset E
0
⊆ E such that G
0
= (V
0
,E
0
) is a
sub-graph of G and that each node supports a path
accepted by the regret function.
The function is true if there exists a path between v
1
&
The Route Network Development Problem based on QSI Models
7

v
n
that passes by (o,d) and is shorter than the shortest
path between these nodes with a constant factor and
false otherwise. If such path exists then all vertices
of this one are added to the sub-graph. This func-
tion depends on the shortest path between v
1
and v
n
in terms of duration or cost and it’s defined for each
criterion: cost and time (duration). We fix a lower
bound for each criterion with a minimum stopover de-
sired. Let’s o & d represent two airports in the graph
G where the node o is the tail of the edge (o, d) and
d the head. The problem consists in finding an inter-
esting path for a given vertex o
1
regarding the edge
(o,d). That is finding at least one path from node o
1
to node d
1
that passes through the edge (o, d) such
that is shorter than the shortest path p
∗
between o
1
and d
1
plus a constant factor K. See Figure 2: ∃ a
path p = {o
1
,o
2
...o
k
,o, d, d
1
} where:
δ(p) ≤ δ
∗
(p
∗
) + K (1)
Then o
i
∈ V
0
, ∀o
i
∈ P \ {o, d} since {o,d} are al-
ready in V
0
.
o
o
1
d
d
1
o
2
d
2
Figure 2: The flight radius problem.
Figure 2 explains the flight radius problem. The
blue edge is the (o,d) connection and {o
1
,d
1
,o
2
,d
2
}
represent the set of candidate vertices meanwhile the
red dashed edge is the shortest path. The nodes o
2
and d
2
are not going since there exists a shortest path
between o and d
2
in the graph (respectively from o
2
to d).
Concretely, such a path that satisfies the regret
function exists if and only if exists a path reaching
o from o
1
or departing from d to d
1
acceptable to the
function R(p).
Proof. Let p = {o
1
,. . ., o, d,d
1
} be the path from o
1
to d
1
that passes through the edge (o, d) and verify in-
equality 1. Then: δ(p) ≤ δ(p∗) + K
⇒ δ({o
1
,. . ., o, d,d
1
}) ≤ δ(p∗) + K
⇒ δ({o
1
,. . ., o, d} ∪ (d, d
1
)) ≤ δ({o1, d
1
}) + K
⇒ δ({o
1
,. . ., o, d}) + w(d, d
1
) ≤ δ({o
1
,d
1
}) + K
However, the shortest path satisfies the triangle in-
equality property:
δ({o1,d
1
}) ≤ δ({o
1
,d}) + w(d,d
1
)
Thus:
δ({o
1
,..., o, d}) ≤ δ({o
1
,d}) + K
In this paper, we start by modeling the flight radius
problem in the additive case and aim to study also the
multiplicative case which is more complicated.
3.3 Flight Database
We first present the software tool PlanetOptim and
the graph database proposed besides MongoDB and
conclude by describing the process of generating and
storing the condensed graph in Neo4j.
3.3.1 Description of PlanetOptim
Our inputs derived from PlanetOptim software de-
veloped by the firm Milanamos. It is a decision-
making tool that helps airline companies to analyze
market, scheduling flights and forecasting demand to
maximize revenue. PlanetOptim is composed of
three principal modules: Analysis market, Flight sim-
ulators and analysis of the hub and routes. We are in-
terested in the second module which is the flight sim-
ulator, it consists of simulating flight in function of
supply and demand. This one assists the user in eval-
uating and displaying for a specific flight departure
time the connections from 45 until 360 minutes after
the Minimum Connecting Time (Milanamos, 2016).
Especially when a company wants to add a new flight,
it looks for the best time of departure time in order
to maximize the connections and thus the number of
passengers traveling in that flight. PlanetOptim is
based on a NoSQL flight database named Optimode.
Milanamos uses MongoDB for this database to store
both structured and unstructured data without schema
constraints and thus no option join. In MongoDB, we
talk about collections and documents rather than ta-
bles and rows in relational databases. We are inter-
ested in these collections while generating the con-
densed graph, data are monthly:
• Capacity: Includes data about equipment, origin,
destination, airlines. All data about frequency,
seat per operation, capacity.
• O&D: It contains all information about passen-
gers itinerary: origin, destination, connecting
points, duration, number of passengers, revenue...
• Schedule: Schedule is composed of individual
flights between two airports. We distinguish be-
tween the two types of schedule: Rotations and
routing. A routing is a set of aircraft routes. How-
ever, Rotations are routing which begin and end at
the same airport. (Barnhart et al., 2003) Schedule
collection contains information related to fleets,
(OD) pairs, flight numbers...
DCORES 2017 - DOCTORAL CONSORTIUM
8

• Segment: Contains all data of only flight legs: ori-
gin, destination, number of passengers, revenue,
distance, type of aircraft.
In the air transportation management, the O&D mar-
ket is defined by a passenger’s point of entry and exit
from the airline system and it’s important to the air-
lines because it let’s them know how many passengers
travel between the two cities during a certain time pe-
riod. However, Segment market information gathered
for a specific route operated by an aircraft from a point
of origin and a destination when it’s a non-stop flight
(Milanamos, 2016). We are based on these collec-
tions from which we extract information to construct
the condensed model. Basically, we are interested in
the segment collection since it provides all informa-
tion for each segment typically the number of passen-
gers traveled from origin to a destination rather than
O&D collection which only gives the number passen-
gers for the whole route and not for each sequence or
segment of the route.
In optimode, data are collected monthly so it is
worthwhile to keep this frequency rather than aggre-
gate to high frequency (e.g. yearly). Note that this
make most sense for a monthly result when the orig-
inal data covers a whole number of months: in par-
ticular aggregating a monthly data to yearly starting
in February does not give a conventional yearly data.
Moreover, it provides a better analysis of evolution
traffic per month and then gives a more accurate re-
sult. Besides, database does not use graph structure
and stores data in disconnected way.
That needs for compact structure to regroup data,
store and visualize the graph.
3.3.2 Graph Database
The graph was implemented using the Neo4j graph
database. It is one of the popular graph databases
stands for Cypher query language. It is used in many
use cases, typically network routing.
Neo4j Graph Database follows the property graph
model to store and manage its data. It has the fol-
lowing characteristics (Robinson et al., 2013): Repre-
sents data in nodes, relationships and properties. Both
nodes and relationships contain properties. A rela-
tionship connects a pair of nodes, it has a direction,
type, a start node and an end node.
We use Neo4j as another alternative that repre-
sents a data structure to store the condensed graph.
It is an open source project with more utilities besides
NoSQL database (MongoDB). Neo4j represents a graph
structure that regroups data contained in collections
and helps to visualize the graph and also the result
of queries. As an example: See what happens if we
allocate a new flight to the network which it’s real-
ized by adding a new edge to the graph. It makes
a lot of sense to store it there since relationships de-
scribe if there is at least flight between an OD pair
in contrast with MongoDB which requires updating all
related collections. Moreover, we can do our query
easily without any join now that it’s provided free by
the graph. This graph database response perfectly to
our needs since it performed well on the graph traver-
sal. (Holzschuher and Peinl, 2014). With Neo4j, we
are able to implement algorithms and then store them
as a stored procedure to use it in Cypher. It is easy to
handle it by the user in PlanetOptim.
We are working in a business context. Aviation data
are highly connected and grows day over days and
Neo4j performs well and handles this. Actually, we
are studying different models to store our data in
Neo4j:
• Store all information in a single relationship be-
tween an (OD) pair;
• Store monthly data per relationship;
• Construct relationship per criterion between each
pair of nodes.
The latter two models generate a huge graph since
we duplicate relationships per month but allows to
quickly access information. We are benchmarking
response time of the following questions (and many
others):
• What is the path between an OD pair with the min-
imum transfer?
• What is the average capacity since 2015?
• What is set of O-D for a period 2016 with capacity
greater than a certain value?
• If I want to fly from Paris to New York. Check-
ing for direct flights or check for flights with a
stopover at some airport.
The second model is more flexible for several reasons.
Firstly, data are monthly collected so it makes sense
to create relationship per period which is a month of
the year. Secondly, adding a period is realized by
adding a relationship. However, it consists to fetch
and get the relation and then set the properties in the
first models even for the deletion is the same thing.
Thirdly, the existence of a ’null’ value does not pre-
vent the calculation of an average or a sum and finally
response time is so fast.
The graph in Neo4j is represented as an adjacency
list. To test the existence of a relationship between a
couple of nodes, the time response is not constant in
contrary to adjacency matrix.
3.3.3 Extraction Process
We get into some issues while extracting data as a part
of collecting real world data. We estimate that at least
10% of data are erroneous. Besides, missing data of
The Route Network Development Problem based on QSI Models
9

certain airports such as: distance, region...and about
some flights such as: Departure time, arrival time, du-
ration.
The graph was generated based on three collec-
tions: Segment, Capacity and Schedule. The data are
extracted as follows: firstly, we get the information
about revenue, number of passengers and distance for
each month and (OD) pair by aggregated the monthly
data then a first join is set to obtain the frequency and
the capacity corresponding to this month and (OD).
Finally, a second join between Segment and Sched-
ule collection to fetch the duration. Another issue en-
countered is the distance. Both tables Schedule and
Segment contains this information. The first one is
collected from booking service. However, the sec-
ond is calculated by our formula. After a comparison,
we conclude that we don’t have the same distance for
routes matched between collection. The problem is
due to erroneous geographic coordinates of airports,
the distance is recalculated using the correct coordi-
nates. The process of extracting data is as follows:
• Step 1: Aggregate the frequency and seat per op-
eration for each (OD) pair in capacity collection
using the aggregation functions cited in 3.2;
• Step 2: Aggregate duration of schedule collection;
• Step 3: Aggregate the revenue and the number
of passengers in segment collection and then use
the function join to get the attributes aggregated
in step 1 & 2 for that (OD) pair.
Note that we use python to do join since this op-
tion is absent in NoSQL MongoDB. Python works per-
fectly with MongoDB via the pymongo api. The fol-
lowing figure 3 describes the process of generating
condensed graph:
Since we opt to monthly frequency, we aggre-
gate data per (origin, destination, month of the year):
(O,D,Y
M
). After the process of extracting data, we
store the graph in Neo4j using the driver py2neo.
Nodes represent airports, relationship per period (a
month of year) and properties regroup the labels of
the condensed graph. The graph was generated over
the last year (2015) and has 11,668 nodes and 608,812
relations.
4 STAGE OF THE RESEARCH
The overall airline scheduling design process involves
hierarchical steps starting with the route network de-
velopment and ending with crew assignment. Route
network development is especially important with re-
spect to timing and costs for airlines. In this paper,
we focus on allocating a new flight problem that con-
sists of determining a set of OD pairs and then choos-
Mongo collection
• Segment
• Capacity
• Schedule
Aggregation
(O, D, M )
Join
(O, D, M )
Data Query
Graph Neo4j
pymongo
py2neo
Figure 3: The process of constructing the graph.
ing the arrival and departure times for an aircraft. We
presented a sub-problem of this problem (Flight ra-
dius problem) which helps airline managers to visual-
ize the interesting sub-network of such a flight based
on QSI models. The result can be implemented in the
short term within the existing application in order to
improve the visualization of flight network and thus
help airline managers to make routing decision about
set of (OD) pairs to serve and also choose schedules
that maximize revenue. We formulated the problem as
finding a maximal sub-graph such that each edge sup-
ports a valid path. Such path depends on regret func-
tion that model the passengers preferences regarding
the cost and the duration and then showed how to con-
struct graph from a real data which it’s stored in a
DCORES 2017 - DOCTORAL CONSORTIUM
10

NoSQL database and presented an alternative to store
the graph.
Our research aims to solve the problem of allo-
cating a new flight which is a sub-problem of route
network development problem based on QSI method-
ology that is most used by airlines in trip choice.
Regarding future work, it would be interesting to
choose a shortest path algorithm to solve the flight
radius problem and as mentioned in section 3 ’Outline
of Objectives’, the next step in this research is to solve
the allocating a new flight since the first two of the five
objectives outlined have already been accomplished.
We may extend our recent work on the flight route
planning to multimodal route planning.
5 EXPECTED OUTCOME
The final outcome of this research is to help airline
managers to make rational decisions by improving the
application PlanetOptim. We aim to define a new
problem of modeling expert decision-making in air
traffic and then solve it by using our expertise in graph
theory; apply algorithms that have already studied in
the literature but also propose new one adaptable to
graph database. Moreover, our objective is to study
the complexity of these algorithms in the case of the
graph databases that are little studied in academic area
especially that they don’t stand for adjacency matrix.
REFERENCES
Barnhart, C., Belobaba, P., and Odoni, A. R. (2003). Ap-
plications of operations research in the air transport
industry. Transportation science, 37(4):368–391.
Bast, H., Delling, D., Goldberg, A. V., M
¨
uller-Hannemann,
M., Pajor, T., Sanders, P., Wagner, D., and Werneck,
R. F. (2015). Route planning in transportation net-
works. CoRR, abs/1504.05140.
Belobaba, P., Odoni, A., and Barnhart, C. (2015). The
global airline industry. John Wiley & Sons.
Carmona Benitez, R. (2012). The Design of a Large Scale
Airline Network. TU Delft, Delft University of Tech-
nology.
Delling, D., Pajor, T., and Wagner, D. (2009). Engineer-
ing time-expanded graphs for faster timetable infor-
mation. In Robust and Online Large-Scale Optimiza-
tion, pages 182–206. Springer.
Dobson, G. and Lederer, P. J. (1993). Airline scheduling
and routing in a hub-and-spoke system. Transporta-
tion Science, 27(3):281–297.
Hall, R. (2012). Handbook of transportation science, vol-
ume 23. Springer Science & Business Media.
Holzschuher, F. and Peinl, R. (2014). Performance op-
timization for querying social network data. In
EDBT/ICDT Workshops, pages 232–239.
Jacobs, T. L., Garrow, L. A., Lohatepanont, M., Koppel-
man, F. S., Coldren, G. M., and Purnomo, H. (2012).
Airline planning and schedule development. In Quan-
titative Problem Solving Methods in the Airline Indus-
try, pages 35–99. Springer.
Kirchler, D. (2013). Efficient routing on multi-modal trans-
portation networks. PhD thesis, Ecole Polytechnique
X.
Marwaha, G. and Kokkolaras, M. (2015). System-of-
systems approach to air transportation design using
nested optimization and direct search. Structural and
Multidisciplinary Optimization, 51(4):885–901.
Milanamos (2016). User Manual of PlanetOptim.
Rebetanety, A. (2006). Airline schedule planning in-
tegrated flight schedule design and product line
design. University Karlsruhe (TH). PhD thesis,
PhD thesis, 2006. Available at http://www. iks. kit.
edu/fileadmin/User/calmet/stdip/dip-rabentanety. pdf.
Accessed 2013 January 30.
Robinson, I., Webber, J., and Eifrem, E. (2013). Graph
Databases. O’Reilly Media, Inc.
Sivrikaya, O. (2013). Demand forecasting for domestic
air transportation in turkey. The Open Transportation
Journal, 7(1):20–26.
Swan, W. (2008). Forecasting air travel with open skies. In
joint EWCKOTI Conference.
The Route Network Development Problem based on QSI Models
11