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EFFICIENT USE OF AIRPORT RESOURCES: OPTIMIZING THE AIRPORT CHECK-IN COUNTER ALLOCATION PROBLEM Gerson Araujo Hugo Miguel Varela Repolho
EFFICIENT USE OF AIRPORT RESOURCES:OPTIMIZING THE AIRPORT CHECK-IN COUNTER
ALLOCATION PROBLEM
Gerson Araujo
Hugo Miguel Varela Repolho
EFFICIENT USE OF AIRPORT RESOURCES: OPTIMIZING THE AIRPORT
CHECK-IN COUNTER ALLOCATION PROBLEM
Gerson E. Araujo, Hugo M. Repolho Departamento de Engenharia Industrial
PUC-Rio - Pontifícia Universidade Católica do Rio de Janeiro
RESUMO
Este artigo apresenta uma metodologia para otimizar o problema de alocação de balcões de check-in num aeroporto
(ACCAP). O objectivo é determinar o número mínimo de balcões de check-in necessários por voo e por intervalo
de tempo, de forma a minimizar os custos operacionais e garantindo um determinado nível de serviço para os
passageiros. A metodologia proposta divide-se em três passos e combina técnicas de otimização com técnicas de
simulação. O passo 1 recorre a modelos de otimização determinísticos para obter o número ótimo de balcões
necessário para garantir um determinado nível de serviço definido em função do tempo de espera dos passageiros
e procurar o menor custo no uso de recursos do aeroporto. O passo 2 utiliza ferramentas de simulação para validar
os resultados obtidos no passo 1. O passo 3 recorre a modelos de otimização para forçar a restrição de adjacência
na alocação de balcões a cada voo. Este artigo foca principalmente no passo 1 ao apresentar dois novos modelos
de otimização do número mínimo de balcões de check-in, que têm em conta o nível de serviço oferecido e custos
operacionais. Os dois modelos propostos aplicam-se a um sistema de balcões comum e a um sistema de balcões
dedicado. Os modelos são testados e comparados num exemplo de teste.
ABSTRACT
This paper presents a methodology to optimize the airport check-in counter allocation problem (ACCAP). The aim
is to determine the optimal number, location and schedule of check-in desks to open for departing flights, such
that operational costs are minimized and a given service level is ensured. The methodology proposed is composed
of three steps that combine optimization and simulation tools as well as deterministic and stochastic approaches.
Step 1 recurs to a deterministic optimization model to determine the optimal number of desks in order to meet a
service level for each separate flight and minimize the cost related to the airport resources. Step 2 uses a simulation
tool to assess the results of the first step. Step 3 recurs to optimization models to enforce an adjacency constraint.
This paper focuses on the step 1 by presenting two new optimization models that take into account service level
for a common and a dedicated check-in system and operating costs. The models will be applied to a sample test
and compared between them.
1. INTRODUCTION
The air transport sector has been facing high growth rates over the last ten years benefiting from
economic development and from the organization of big international events such as the 2014
FIFA Soccer World CUP and 2016 Olympic Games. Within the next years, air transportation
in Brazil is expected to reach the same traffic levels as the ones existing in developed countries.
Indeed, air travels are expected to go from 0.3 to 0.7 per person per year, in the medium term
(MCKINSEY & COMPANY, 2010). In this context of growing demand for air travel, it is
crucial for airports to grow accordingly. Investments in expansion, modernization, construction
of new airports, and even efficient methods for using airport resources may be essential, if one
aims to ensure adequate operational capacity and a given level of service (according to
international airports regulations standards). Increasing airport’s operational capacity in an environment where competition is fierce, leads airports and airlines to pay attention to cost
effectiveness. At the same time, the companies have to deal with increasing service levels
requirements and reduce operational costs. Thus, identifying and reducing all superfluous
operational processes and underuse equipment is mandatory.
Logistic practices involved in the flight check-in and the subsequent handling process are key
aspects in airports and flights management. Check-in counters are preponderant facilities where
all processes start. Moreover, usually check-in counters occupy a considerable area within the
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airport, which strongly affect airport costs. In fact, many international airports are already
operating in the capacity limits. In others, over dimensioning of counters is preventing the
airport to allocate space to profitable activities such as shopping areas. Efficiently using and
allocating check-in counters may therefore contribute to reduce airport costs and raise the
service level offered to customers. An efficient if not optimal planning of check-in capacities
is therefore required at various levels: at a daily level to determine the number of desks and
opening and closing hours for each individual flight, at a weekly level to allocate flight and
reservations, at a monthly level to negotiate contracts with airlines and finally at a yearly level
to determine the total desk capacity required. This paper proposes a methodology to get an
optimal check-in system at daily level, which minimizes operational costs and ensures a given
level of service.
1.1. Terminology
The terminology used in practice to describe the main features of check-in system can vary
among authors. A well-accepted reference guide regarding air transportation concepts is the
one provided by IATA-ADRM. We assume the following standard definitions:
a) Arrival pattern: represents the proportion of passengers’ arrival for check-in process
distributed by fixed time intervals. The arrival pattern displayed in Figure 1 exemplifies a
realistic arrival pattern reference obtained from a case study carried out by Joustra and Van
Dijk (2001) in the Amsterdam Airport Schiphol.
Figure 1: Arrival pattern
Source: (Joustra and Van Dijk, 2001)
b) Flight-open time: it is the earliest time before flight departure when check-in process starts.
c) Flight close-out time: it is the latest time before flight departure when check-in process ends.
After close-out no more passengers are allowed to check in and the flight is said to be closed.
d) Common check-in system: passengers can check-in for their flights at any available desk in
the period between his flight-open time and flight close-out time.
e) Dedicated check-in system: passengers have to check-in at the corresponding service position
desk assigned for each flight for a fixed period before the scheduled time of departure.
f) Constant desks allocation policy: each flight is allocated to a constant number of desks during
its entire check-in period.
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g) Variable desks allocation policy: each flight is allocated to a variable number of desks in
each time interval (e.g. hour or half hour) during its check-in period.
h) Service level: customer satisfaction in terms of waiting time or queues size. As mentioned
above the IATA-ADRM is a good reference for obtaining this data, but there are interesting
works in this topic to revise. For example, Correia et al. (2008) present the results of a field
work about overall level of service measures for airport passengers.
i) Departure flight schedule: departure flight information indicating the number of flights, the
number of passengers and the starting time interval for each flight. Table 1 represents an
example of a departure flight schedule based upon a flight realization at the Dutch airport
Schiphol presented in a study case performed by Van Dijk and Van der Sluis (2006).
Table 1: Departure flight schedule
Source: (Van Dijk and Van der Sluis 2006)
1.2. Outline
This paper is structured as follows. First, we discuss existing literature related to the airport
check-in counter allocation problem (ACCAP). Next, in Section 3, we describe the
methodology for optimizing the ACCAP. The methodology involves three main steps. For each
step we detail the OR tools required. Then in Section 4, we present two optimization models to
solve the ACCAP considering, respectively, a common and a dedicated check-in system and
taking into account service level. In section 5, we present a sample test that will be used to
analyze the two models formulated in section 4. Finally, in section 6 we present the conclusions
of this work and identify future directions of research.
2. LITERATURE
Despite the practical relevance of the topic, the ACCAP can be considered a novel problem in
Operational Research literature, as few optimization approaches have been developed to deal
with it. Chunk and Mak (1999) introduced an intelligent resource simulation system (IRSS) to
predict on a daily basis how many check-in counters should be allocated to each departure flight
while providing passengers with a given quality of service. The major contribution of their work
relies on the number of factors considered: 1) different services rates for different destinations,
airlines, or handling agents; 2) different passenger arrival rates for different times of the day or
days of the week; and 3) different requirements for different service levels. In the same way,
Krug (2002) used the combination of simulation and various search procedures, such as a
greedy or gradient search method, to optimize the resource allocation problem. The authors
implemented the procedures through software (for example, ISSOP). However, this automated
search optimization did not include more technical specific OR-techniques such as LP.
A first attempt to solve a similar problem with a mathematical programming approach has been
provided by Atkins et al. (2003). They presented a combined stochastic and deterministic
approach with OR tools. This work employed simulation and integer programming tools to
improve passenger flows and customer service at Vancouver International Airport. Simulation
was employed to determine queue times and to meet the service criterion (the simulation was
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run until the minimum staffing level met the service criterion defined). LP was used to
determine minimum staff numbers and optimal shift schedules. Given a list of possible shifts,
they used a linear programming model to determine the optimal shift schedule that satisfied the
airport-wide staffing requirements in each time period.
An important approach of check-in desk assignment problem has also been addressed by Yan
et al. (2004). They studied a deterministic scheduling problem with a different assignment
problem. The objective was to determine an assignment on a monthly basis such that the total
passenger walking distance was minimized combined with a constraint of allowable
inconsistency. A flight assignment was considered consistent when the same flight number was
assigned to the same block of desks on different days. Since the model to determine an
assignment for one week becomes too large, they proposed a three-step heuristic where single
day assignment problems were solved.
Based on the work of Atkins et al. (2003), Van Dijk and Van der Sluis (2006) deepen the check-
in problem by proposing an integrated stochastic (simulation) and deterministic (mathematical
programming) approach. First, simulation was used to determine minimal numbers of desks in
order to meet a service level for each separate flight. Next, integer-programming formulations
were provided to minimize the total number of desks and the total number of desk hours under
the realistic constraint that desks for the same flight should be adjacent. Both cases with
constant and variable requirements are studied. According to these authors, simulation and
mathematical programming tools are widely available, but the combination of these tools can
be regarded as an illustration of a new practical OR-tool for optimization.
Finally, Bruno and Genovese (2010) proposed new mathematical models for the ACCAP based
on a deterministic scheduling problem. The aim is to decide the optimal number of check-in
counters to open for departing flights, such that operational costs and passenger waiting time at
the terminal are balanced.
3. METHODOLOGY: OPERATION RESEARCH TOOLS
The methodology to optimize the airport check-in counter allocation problem implies
essentially three main steps: STEP 1 - Airport Check-in Counter Allocation Problem (ACCAP);
STEP 2 - simulation tools; and STEP 3 - Adjacency constraint. A brief description on each step
will be given in this section.
3.1. STEP 1 – ACCAP
Step 1 involves a novel optimization approach for the Airport Check-in Counter Allocation
Problem (ACCAP) considering a variable desks allocation policy. This approach is based on
the model proposed by Bruno and Genovese (2010) with some modifications. We present two
optimization models, one for a common check-in system and the other for a dedicated check-
in system. The two models aim to determine the minimum number of check-in desks to be
opened in a time interval, such that operational costs and passengers waiting time are
minimized. Both models take into account a given service level. A detailed description on the
models is given in section 4. Step 1 is therefore a deterministic scheduling problem based on
the departure flights scheduling, reference arrival pattern and a rough check-in time.
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3.2. STEP 2 - Simulation tools
Step 2 recurs to simulation tools in order to assess if the results reached through Step 1 meet a
given service level in terms of waiting and queue size when considering real uncertainty
behavior. A pure deterministic approach ignores the essential stochastic aspects that are
intrinsically involved in the check-in process such as passenger arrival times and check-in
times. Therefore, Joustra and Van Dijk (2001) argued the importance of simulation tools in
order to capture the non-steady behavior (stochastic aspects) of check-in processes.
Simulation programs such as SIMUL8 and ARENAS are available simulation tools that allow
testing specific initial situations, different time intervals during which the desks are open,
different arrival patterns and different check-in times. When testing a sufficient numbers of
replications for the same initial conditions and by sampling from experimental arrival and
service distributions it is possible to obtain reasonable confidence intervals. For example,
Joustra and Van Dijk (2001) highlighted a special feature obtained by simulation in check-in
process, where the number of desk during the opening period does not need to be constant.
These authors demonstrated the advantage of the variable desk allocation over constant desk
allocation in order to reduce the number of desks hours. In this step, with variable desk
allocation as result of step 1, the main scenarios to be tested are the common and dedicated
check-in systems.
3.3. STEP 3 – Adjacency constraint
Step 3 involves a mathematical model in order to determine the minimum number of desks and
desks hours under the adjacent resource constraint, which stipulates that all desks for the same
flight should be adjacent. The mathematical model is valid for the constant and the variable
desks allocation policies. This step is a deterministic scheduling problem based on a given
required number of desks for each flight with variable desks allocation policy.
Once one have determined the required numbers of desk by time interval for each individual
flight (dedicated) or group of flights (common), it is possible to minimize the total number of
desks and desks hours under the adjacent resource constraint. As can be easily understood, the
adjacency constraint does not make sense for the common check-in system as there is no
distinction between flights. In a dedicated check-in system there is an adjacency constraint to
be met. Van Dijk and Van der Sluis (2006) explain clearly this theme, and state that without the
adjacency constraint, the minimal number of desks could be found easily by the Earliest Release
Date First (one rule of the Fixed Interval Scheduling). This process would indicate the
maximum number of desks required (Nmax) at the busiest time interval but does not guarantee
an optimal solution satisfying the adjacency constraint. Clearly, Nmax is always the lower
bound for the optimal number of desks required and the mathematical model in this step has to
guarantee an optimal desk allocation with no more than Nmax desks and satisfying the
adjacency constraint.
Based on a given required number of desks per flight and considering a variable desks allocation
policy we thus need to find the best possible, if not optimal allocation satisfying the adjacency
constraint. Duin and Var der Sluis (2004) explain the theory of Adjacent Resource Scheduling
and propose a mathematical model for this purpose. In the same way, Van Dijk and Van der
Sluis (2006) explain and propose a mathematical model for the same purpose. This last model
is briefly presented in sections 3.3.1.
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3.3.1. Mathematical model for Variable Allocation considering the Adjacent Constraint
proposed by Van Dijk and Van der Sluis (2004)
For each flight in a given planning horizon of discrete time intervals, the airport management
seeks a feasible variable assignment to adjacent desks with the objective of minimizing the total
number of involved desks. The variable assignment considers flights with resource needs
varying over a time interval (variable desks allocation policy).
We introduce the following notation:
• T: time window (usually a day or some hours);
• l: length of the considered time interval (usually an hour or 30minutes);
• f: representative index of the single flight;
• g: representative index of the single flight;
• t: representative index of the single time interval;
• N: set of intervals in T or the number of intervals in T (N = T/l);
• F: set of flights scheduled in T;
• : the time interval when the check-in process starts for flight f;
• : the time interval when the check-in process ends for flight f;
• : the time intervals when the check-in process is allowed for flight f ( = [ , ] );
• ,�: the number of desks required for the check-in process of flight f in ;
• BigM: big value.
The model considers three sets of decision variables:
• ,�: the largest desk number assigned to flight f in each time interval of ;
• , : binary variable with , = 1 when flight f is assigned to highest desk number than flight
g. And , = 0 in otherwise.
• Dmax: the total number of desks required.
Once parameters and variables have been illustrated, the mathematical formulation is then:
= � � (1)
S.t. � � � � ∀ ∈ �, ∀ ∈ [ , ] (2)
� + � � + ∗ , ∀ ∈ �, ∀ ∈ �, ∀ ∈ ∩ (3) � + � � + ∗ − , ∀ ∈ �, ∀ ∈ �, ∀ ∈ ∩ (4) � − �− max( , � − �− ) ∀ ∈ �, ∀ ∈ [ , ] (5) �− − � max( , �− − �) ∀ ∈ �, ∀ ∈ [ , ] (6) � � , � ∀ ∈ �, ∀ ∈ (7) , ∈ { , } ∀ ∈ �, ∀ ∈ � (8)
The objective function (1) minimizes the total number of desks needed for all flights. In this
way, let us assume that desks are numbered from 1 to Dmax. Constraints (2) ensure that the
desks assigned to a flight fall within the interval of 1 to Dmax. Taking into account the
adjacency restriction combined with the fixed time intervals and the number of desks assigned
to flight may change during each time interval t )( fIt , the assignment of a flight to desks
can be described by the variable ,� which denotes the largest desk number assigned to flight
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in t )( fIt . Constraints (3) and (4) ensure that two flights are not assigned to the same desk
at the same time. For that, it is used a binary variable , for rewriting the disjunctive
constraint: ( � + � � � + � �). Constraints (5) and (6) avoid that during the
check-in process of a flight desks are opened and closed at the same time. When there is an
increase in demand for desks ( ,� > ,�− ) then exactly ,� − ,�− desks are opened, and
when there is a decrease in the demand for desks ( ,� < ,�− ) then exactly ,�− − ,�
desks are closed. Constraints (7) and (8) define the domain of the decision variables.
4. MATHEMATICAL MODEL FOR THE AIRPORT CHECK-IN COUNTER
ALLOCATION PROBLEM (ACCAP) FOR VARIABLE DESKS ALLOCATION
From a corporate point of view the most common objective is the minimization of resource
costs while ensuring a fixed service level. With regard to check-in desks management this
objective can be translated into the determination of the minimum number of check-in desks to
be opened in a given time interval that ensures the service coverage. The number of desks
opened per flight can be made following a constant or a variable policy. The former establishes
a constant number of desks to be open during the all check-in period. The latter varies the
number of check-in desks opened per flight during the check-in time interval in accordance to
passengers’ affluence. Thus, peak hours will have more desks while off-peak will have less.
The variable policy seems more reasonable and can lead to a more optimized solution. We will
therefore focus on the variable desk allocation policy.
The ACCAP will be approached considering the two check-in systems defined in section 1.1,
the common and the dedicated check-in system. The ACCAP model regarding the common
check-in system will from now on be designated as CACCAP. The ACCAP model regarding
the dedicated check-in system will from now on be designated as DACCAP. It is important to
highlight that while the CACCAP model gives the total number of check-in desks per time
interval, the DACCAP model gives the number of check-in desks per flight per time interval.
Both models can be classified as pure deterministic scheduling models as the departure flight
scheduling and passengers arrival patterns are known in advance. Both models are based on the
following hypothesis:
a) Discrete time window: The time horizon (generally equal to a day) is divided in intervals
with constant width . All parameters and variables are then referred to each time interval . On
this basis, the problem becomes a discrete problem.
b) Arrivals distribution: Check-in service demand can be expressed in terms of passengers
arriving to the check-in desks and represented by a stochastic variable. The uncertainty in
passenger behavior does not allow forecasting the exact distribution of the arrivals to each desk
within the check-in time. Empirically, it is possible to observe that there will be intervals
characterized by arrival peaks and intervals with a low level of service demand. However, in
order to simplify the problem, it is possible to forecast arrivals to a check-in desk through the
analysis of historical data, defining service demand as a deterministic variable.
c) Desk service time: desk service time represents the time needed to process and accept a
passenger. This capacity has been assumed equal for each desk, and the value has been
calculated based on real check-in processes analyses. The reciprocal of this value can be
assumed equal to the capacity of a desk.
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d) Desk opening cost: The desk opening cost is the amount of money that is necessary to pay
employees and other operative expenses to make the desk work.
4.1. Notation
• : time window (usually a day or some hours);
• : length of the considered time interval (usually an hour or 30minutes);
• : representative index of the single time interval;
• : representative index of the single flight;
• : set of time intervals in T or the number of time intervals in T (N = T/l);
• : set of flights scheduled in T;
• �: average desk service time for flight j;
• �,�: service demand from passengers of the flight j in the time interval t;
• � : number of passengers of flight j waiting before desk opening;
• �: cost associated with opening a desk at the time interval t;
• ℎ�: cost associated with the queue related to flight j per passenger;
• �,�: JxN matrix; the coefficient �,� is equal to 1 in the time interval when passengers of a
flight cannot check-in and when there is no possible to leave passengers for check-in for the
next time interval (case of the last opened time interval for a flight); 0 in all other intervals.
• : average service time per desk at the time interval t;
• � = maximum percentage of the passengers in a queue at the end of the time interval t;
The model considers three sets of decision variables:
• �,�: number of passengers of the flights to be accepted in time interval ;
• �: number of desks to be assigned in each time interval ;
• �,�: number of passengers in a queue for flight at the end of time interval .
4.2. CACCAP Formulation
The CACCAP model can be formulated as an integer optimization model as follows:
= ∑ ∑ ℎ� �� �� + � � (9)
S.t. �� = � �− + �� − �� ∀ ∈ , ∀ ∈ (10)
∑ ���= ∗ �� ∗ � ∀ ∈ (11)
�� ∗ �� = ∀ ∈ , ∀ ∈ (12)
∑ ����= � ∗ ∑ �� ��= ∀ ∈ (13)
�� , �� ∀ ∈ , ∀ ∈ (14)
� ∈ � ∀ ∈ (15)
The objective function (9) minimizes the total cost given as the sum of two components: a) the
costs associated with passengers in queue; b) the costs associated with opening a desk.
Constraints (10) keep track of the passenger in the queue for each flight in each time interval.
The number of passengers in a queue for flight at the end of a time interval is the sum of
passengers in queue for flight j from the previous time interval plus the number of passengers
of flight arrived at the desk in minus the number of passengers that completed the check-in
at this time interval . Constraints (11) represent capacity constraints. Constraints (12) express
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the fact that all passengers of a flight j must be accepted by the closing time of the desk.
Constraints (13) can be considered the service level constraints in a common check-in system.
They state the most quantity of people that arrive in and can be processed at the time interval + . Finally, constraints (14) and (15) define the domain of the decision variables.
It is worthy to mention that if we replace �,� with ��,� and �,� with ��,�, we can interpret ��,�
as the external demand for an item at the time and ��,� as the production quantity for item
at time . In this way, the model (9)-(15) becomes perfectly equivalent to a very common
formulation of the well-known multi-item Capacitated Lot Sizing problem, which is known to
be NP-hard when capacity is not constant.
4.3. DACCAP Formulation
The DACCAP model differs from the CACCAP model since each open check-in desk is
allocated specifically to one flight at a time interval t. Thus the DACCAP model suffered some
minor changes with regard to the CACCAP. Let us consider the additional set of decision
variables � �,� that represents the number of check-in desks opened for flight in a time
interval .
The DACCAP model can then be formulated as an integer optimization model as follows:
H = ∑ ∑ (ℎ� �,� + �� �,� )�� (16)
S.t. (10), (12), (14) � ∗ �� ∗ � �,� ∀ ∈ , ∀ ∈ (17) �,� � ∗ �,� ∀ ∈ , ∀ ∈ (18) � �,� ∈ � ∀ ∈ , ∀ ∈ (19)
The objective function (16) has the same meaning of equation (1), i.e. it minimizes the total
cost given as the sum passengers in queue costs plus the costs associated with opening a desk.
Constraints (17) represent capacity constraints for each flight and for each time interval.
Constraints (18) ensure a given service level for the dedicated check-in system. Basically,
constraints (18) limit the number of people that arrive in a time interval t and that will process
their check-in only in the time interval t+1 for each flight. Finally, constraints (19) define the
domain of the new decision variables.
5. SAMPLE TEST
This example uses as input the flight schedule shown in Table 1. This information is based upon
a flight realization at the Dutch airport Schiphol presented in a study case performed by Van
Dijk and Van der Sluis (2006). This departure flight schedule indicates the number of flights,
the number of passengers and the starting time interval for each flight. Next, additional
parameters and assumptions are detailed:
a) Discrete time window: According to the flight schedule, the time horizon equals to ten time
intervals of one hour each time interval. It is important to state that the open check-in time for
any flight considers three time intervals. The width of the time interval can be an hour, half an
hour or some minutes. The optimal width of the time interval has to be analyzed in accordance
with the real situation of each particular case study.
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b) Arrivals distribution: this information is based on the arrival pattern from Figure 1. Thus,
taking into account the arrival pattern and the flight schedule, the parameter of demand or the
number of passengers arriving for check-in is defined by fixed time intervals. Table 2 shows
the demand for each time interval of the open check-in time for each flight. The number of
passengers listed as “before” are the passengers who arrive to airport before the open check-in
time (Ij .
Table 2: Demand from passengers
c) Desk service time ( �): A viable value can be assumed equal to 2 minutes per passenger.
d) Desk opening cost ( � : A viable value can be assumed equal to USD 150 per hour, taking
into account the payment of one employee and the rent of a check-in counter space.
e) Queue cost (ℎ� : A viable value can be assumed equal to USD 30 per passenger, taking into
account the minimum consumption per passenger at the airport.
f) : A viable value can be assumed equal to 50 minutes at time interval of one hour.
g) �: A viable value can be assumed equal to 10% or passengers in a queue at the end of the
time interval t.
With the parameters provide above, the sample test was run for CACCAP and DACCAP
models. The results for the number numbers of desks for each case (common and dedicated
check-in system) are given in Table 3. It is important to mention that the DACCAP result gives
the total number of desks required per time interval and also the number of desks required per
flight per time interval. As expected when considering a dedicated check-in system it is required
some additional desks. In this case we needed one additional desk in periods 5 and 9.
Table 3 also presents the result obtained by Van Dijk and Van der Sluis (2006) based on field
work and simulation tools. The comparison between the results obtained by both CACCAP and
DACCAP, and Van Dijk and Van der Sluis (2006) evidence the accuracy of these models in
order to get the minimal number of desks and desks hours. It is clear that the target of these
three proposals searches to obtain the optimal number of check-in counters for flights in each
time interval. But it is important to highlight that the two models proposed in this paper are
based on optimization models as OR tool with the additional target of balancing the service
level and his related operative cost. Meanwhile the third proposal is based on simulation as OR
tool and only focuses in meeting a service level.
Flight 1 2 3 4 5 6 7 8 9 10
Passengers 150 210 240 180 270 150 210 300 180 270
Before 7 10 12 9 13 7 10 15 9 13
1 46 64 72 54 82 46 64 90 54 82
2 75 105 120 90 135 75 105 150 90 135
3 22 31 36 27 40 22 31 45 27 40
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Table 3: Desk required number.
6. CONCLUSIONS AND FUTURE WORK
This paper proposes a methodology to optimize the airport check-in counter allocation problem
by minimizing operational costs such that a given service is ensured. The methodology
promotes the combination of deterministic and stochastic OR-approach for real world
applications. This combination of mathematical programming and simulation can be regarded
as an illustration of a new practical OR tool for optimization (Van Dijk and Van der Sluis,
2006).
The methodology involves three steps, of which we have focused on Step 1. Step 1 is a pure
deterministic scheduling problem that optimizes number of check-in desks to be opened for
departing flights. We have proposed two new optimization models that take into account the
service level (passenger waiting time at check-in areas) and his related operative costs (airport
resources). The first model is applied for a common check-in system while the second is applied
for a dedicated check-in system.
This work will serve to assess and improve the existing management check-in system of
Brazilian airports. Also, each airport represents a particular situation and this methodology
searches to give flexibility in order to fit in any scenario. In this way, different options such as
common or dedicated check-in system and different features to adjust such as the arrival pattern,
the service level, the desk service time, the length of time interval, the cost of airport resources,
let this methodology to be useful in the ACCAP task. The next idea is to apply this methodology
in different scenarios in Brazil and analyze the value of the features to adjust according the
dimension of the airports. At the same time, this work intends to promote the combination of
OR approach as an OR technique to optimize general planning and scheduling problems. Also,
this technique can be useful for optimization problems in other application areas such as: call
centers, manufacturing, transportation, health service and administrative logistics.
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Time Interval 1 2 3 4 5 6 7 8 9 10
CACCAP 2 6 11 14 10 8 12 15 8 2
DACCAP 2 6 11 14 11 8 12 15 9 2
Simultion study by Van
Dijk and Van der Sluis 3 6 12 14 11 8 13 15 8 2
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assignments. Transportation Research Part A. 38, p. 101-125.
Gerson E. Araujo ([email protected])
Hugo M. Repolho ([email protected])
Departamento de Engenharia Industrial, Pontifícia Universidade Católica do Rio de Janeiro - PUC-Rio
R, Marquês de São Vicente, 225, Gávea - Rio de Janeiro, RJ - Brasil
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