How to Improve the Efficiency of Check-In Counter: A Counter-Sharing Method

. Improving the efciency of check-in counters is a signifcant concern for airport operation management departments and airline companies. However, the existing studies mainly optimize the counter allocation based on the number of counters and airport demands, which needs more exploration on improving the utilization rate of check-in counters under the condition of unchanged resource allocation. In this paper, we propose a counter-sharing method to improve check-in efciency by sharing the idle check-in counters in the adjacent check-in area. In the proposed counter-sharing method, we frst defne the passenger’s total walking distance and waiting time for queues as the metrics, then reassign the check-in areas and adjust the internal departure sequence of fights to maximize the counter-sharing rate. Te numerical results indicate that the proposed counter-sharing method can improve the efciency of check-in counters and reduce the passenger’s total walking distance and waiting time in the queue during the check-in process, which can enhance the airport’s operation efciency and competitiveness.


Introduction
Aviation transportation has rapidly developed in recent years. Te Airbus Global Market Forecast for 2019-2038 indicated that the annual air trafc growth rate would be 4.3% in the next 20 years [1]. However, the growth rate of airport facilities could hardly reach the same speed as air trafc since the expansion was a long-term and expensive project [2]. When the airport facilities cannot be added to enhance the airport service capacity, the increased aviation transportation will cause many problems (e.g., congestion, long waiting times for passengers in queues) in airport terminals.
Each fight has a check-in counter demand, and the efciency of check-in counters signifcantly impacts the airport's level of service and system performance [3]. Terefore, the check-in counter assignment problem has risen, and researchers have proposed many models and methods to study the management of check-in counters. For example, Ahn and Park [4] employed the passenger arrival distribution pattern to propose an optimization model for calculating the most appropriate number of check-in counters and the corresponding duration of each counter. Te model could ofer airlines a means of operating check-in counters with greater cost-efectiveness, thus enhancing customer service. Yan et al. [5] developed an integer programming model to assign the check-in counters and designed a heuristic method for solving their model. Tey later improved this study and formulated one 0-1 programming method to minimize the total inconsistencies in common-use counter assignments [6]. Van Dijk and Van der Sluis [7] proposed a method combining simulation with integer programming to minimize the number and opening hours of check-in counters. In order to balance the quality of service stipulated by the airport authority and the optimal allocation of resources to the check-in counters, Parlar and Sharafali [8] developed one stochastic dynamic programming model, which could optimize the number of check-in counters for opening the time window specifed.
Tang [9] developed a new network model for the optimization of common-use check-in counter assignments, which could minimize the number of counters required for daily operations. Hsu et al. [10] developed a model for the dynamic allocation of check-in counters with the target of minimizing the waiting time for passengers, and the feasibility of the developed model is validated by comparing actual data from the free selection of check-in counters by passengers and the dynamic assignment of passengers to check-in counters. Gao et al. [11] proposed a target optimization model for the purpose of putting a minimum of the equipment quantity and shortening passengers' onboarding time and employed the improved NSGA-II algorithm to solve the model and get the allocation plan of check-in counters. Lalita et al. [12] proposed an exact integer linear programming model for allocating variable check-in counters in airports, which solves the check-in counter allocation problem with deterministic inputs and variable counter allocation. Liu et al. [13] developed an associative decision integer programming model to quantitatively describe the total time of handling luggage in the collaborative work system, which could generate various allocation schemes of check-in counters to reduce the waiting time of passengers in queues. Te above studies provide practical methods for the efcient operation of check-in counter assignments and valuable means of developing efective longer-term solutions to the problem of passenger terminal congestion and delays.
Recently, passenger's requirements for airport service quality have increased quickly, which has led researchers and aviation agencies to pay more attention to the airport service quality and passenger satisfaction. For example, Airport Council International defned the overall service quality as the overall level of passenger satisfaction measured by survey responses [14]. Fodness and Murray [15] empirically investigated passengers' expectations of service at airport terminals and found that passengers do not expect long waiting times for queues or long walking distances. Bezerra and Gomes [16] used the partial least squares structural equation modeling to analyze the drivers of passenger loyalty to the airport and found that passenger experience was critical to their loyalty to the airport. Kayapınar and Erginel [17] developed a bi-criteria cost function that involves the costs of opening check-in counters and the costs of modeling passengers' waiting time. Adacher and Flamini [18] considered passenger satisfaction and proposed a bi-criteria objective function to minimize operational costs and the passengers' discomfort in terms of waiting time in line. Batouei et al. [19] delved into passenger experience by analyzing the data of 377 passengers and found that a good passenger experience will bring an excellent reputation to airports and attract more passengers.
Te above studies indicate that developing efective passenger-oriented (the waiting time in queues and walking distances to access airport facilities) facility management strategies could increase passengers' satisfaction and spread positive word of mouth, which helps promote the airport's high-quality development.
Sharing is a new mode in the current social environment, and it has been applied in many commercial projects, such as bike sharing, portable battery sharing, and car sharing. Sharing can reasonably distribute resources and improve a system's efciency. As the optimization theories and airport hardware advanced, it became feasible to manage the check-in counters optimally using the sharing mode. In this paper, a counter-sharing method is developed to enhance the utilization rate of check-in counters by sharing the idle counters in the adjacent check-in areas. Integrating the sharing concept into the management of check-in counters in airports can enhance check-in efciency without additional operational costs. In the proposed counter-sharing method, the passenger's total waiting time and walking distances are taken as the metrics to evaluate the reassignment of check-in areas based on the departure fight schedule. Te reassignment of check-in areas based on the departure fight schedule needs to transform the solutions into vectors and improve the solutions. Te general idea behind the diferential evolution algorithm is the representation of a solution as a vector of decision variables, which fts our problem very well. Tus, we use the diferential evolution algorithm to solve the problem.
Compared with the existing studies, this paper has two contributions: (i) We explore the planning of check-in counters from the standpoint of airline companies and develop a counter-sharing method with the target of enhancing the efciency of check-in counters by sharing idle the check-in counters in the adjacent check-in areas; (ii) we reassign the check-in areas and internally adjust the departure sequence of airline fights to minimize the passengers' waiting time for queues and walking distances during check-in, which are important metrics reported in the literature. Te management of check-in counters from available research does not consider sharing mode explicitly, and we incorporate the concept of sharing into the management of check-in counters and provide exact solutions to real-world problems. Te feasibility of the counter-sharing method is validated by case analysis. Te results of the case analysis evidenced the superiority of the counter-sharing method in terms of shorter passengers' waiting times and walking distances and better utilization of check-in counters. Te remainder of this paper is organized as follows: the implementation of the counter-sharing method and related assumptions are introduced in detail in Section 2; then, case studies, which are employed to validate the proposed method, are presented in Section 3; and some conclusions are summarized in Section 4.

Problem Statement
In this section, we introduce some rules for check-in and propose the counter-sharing method and its implementation.

Rules for Check-In.
Today, the check-in process can be achieved in various ways: online, via self-service kiosks at the airport, and via the traditional check-in counters where airline representatives serve the passengers. Te traditional check-in counters where airline representatives serve the passengers are still the frst choice for passengers [20]. Tus, most passengers will frst visit check-in counters to get a check-in service when traveling by air; they use check-in counters to check luggage and choose, buy, or change a seat. Besides, each airline occupies a check-in area in the airport terminal to place check-in counters and rents the check-in counters in this area to serve all of its fights daily.
Te check-in counter system has the following three primary rules [5]: (1) It is an exclusive-use system with multiple counters and queues of passengers. Tese check-in counters will service only passengers booked for a specifc fight. Te check-in counters should meet the following rules: (1) Each counter has the same service rate. It should be noted that rule 2 of the check-in counters is the hard rule of some airports, which has been formulated to provide a good quality of service to the passengers during the check-in process [21].
Furthermore, we suppose that we have the following information: (1) Te layout of the terminal area (2) Te number of passengers on each fight and each fight's departure time (3) Te distances of passengers moving to the checkin areas (4) Te number of check-in counters that each airline sets at its check-in area.

Implementation of the Counter-Sharing Method.
Te utilization of the airport check-in counters is crucial since it determines the check-in efciency to a certain extent [22,23]. Sharing is a new mode in the current social environment, which could reasonably distribute resources and improve a system's efciency. Terefore, we propose a check-in counter management method based on sharing to improve the utilization of check-in counters, which could enhance check-in efciency.
To illustrate this counter-sharing method, we assume that we have a discrete search space X and a function F that assigns a value to each one of the elements in the search space. Te problem can be formulated as follows: where S i is feasible solution in the discrete search space X.
According to the previous studies [24][25][26][27], the passengers' walking distances and waiting time for queues should be taken as factors that determine the fnal value assigned by the function, since these two factors can better refect practical needs for improving airport operations in real life. Terefore, we construct a function based on passengers' walking distances and waiting time in queues. To unify the units of the two objective function values, we divide the passengers' walking distances (unit: meters) by 1.0 m/s and transform them into the passenger walking time (unit: seconds).
Te function based on passengers' walking distances and waiting time for queues can be defned as follows: where T total is a factor that measures passengers' waiting time for queues in the solution; D total is a factor that evaluates passengers' walking distances in the solution; and α 1 , α 2 are the weights of the corresponding factors. D total represents the sum of the walking distances of passengers on all fights to the corresponding check-in areas. Tus, we can defne D total as follows: where M is the number of fights; P i is the number of the ith fight passengers; and D i is the distance of the ith fight passengers moving to the corresponding check-in area. T total represents the sum of the queue time of all fight passengers at the check-in counters, and we can defne T total as follows: where T i is the total queue time of the ith fight passengers.
Te airlines will open the corresponding number of check-in counters according to the constraint that one check-in desk must be open for every 45 passengers, and the maximum number of check-in counters in a check-in area is typically 5 [21]. Tus, the passengers' total queue time at check-in counters is diferent for fights with diferent numbers of passengers. For fights with no more than 225 passengers, the passengers' total queue time should have two features: (i) when the number of passengers is balanced with the number of check-in counters, the passengers' total queue time equals the product of a fxed constant and the number of fight passengers; (ii) when the number of passengers is unbalanced with the number of check-in counters, the passengers' total queue time is less than that of balance and Journal of Advanced Transportation 3 increases as the number of fight passengers increases. Terefore, for P i ≤ 225, the T i,1 can be defned as follows: where T average is the average queue time of each passenger; I i is an integer calculated based on the number of fight passengers, which represents the fight size and can be defned as follows: where P min is the minimum fight parameter, which is a constant. For fights with more than 225 passengers, the passengers' total queue time shall equal the total queue time when the number of passengers and the number of check-in counters are balanced, plus additional delay time. Terefore, for P i > 225, the T i,2 can be defned as follows: where T service is the service time of check-in counters; K i,1 is the number of extra queues and can be defned as follows: Te counter-sharing method is intended to improve the efciency of check-in counters by sharing idle counters between airlines in adjacent check-in areas. Te actual operation of the counter-sharing method is as follows: Suppose the check-in areas of two fights are adjacent, and the check-in counters' opening hours for the two fights overlap. In that case, the fight with more passengers (more than 225 passengers) can borrow extra check-in counters from the fight with fewer passengers (fewer than 180 passengers) during the check-in counters' overlapping opening time. Terefore, the total queue time of the ith fight passengers under the counter-sharing method T sharing i can be defned as follows: For P i ≤ 225, For P sharing i > 225, where P sharing i is the number of the ith fight passengers under the counter-sharing method; B i is the maximum number of check-in counters that adjacent check-in areas of the ith fight can share. Te quantitative relationship between P 1 i and B i can be defned as follows: ρ i is the period that could share check-in counters, which can be defned as follows: where t i is the intersection of the opening time of the checkin counter of the ith fight and that of the adjacent checkin area. K i,2 is the number of extra queues under the countersharing method and can be defned as follows: To help better understand the counter-sharing method, we take an example as follows.
As shown in Figure 1, fight X in check-in area A has 140 passengers, and its boarding time is 10 : 00; for the rules to be respected, three check-in counters should be opened from 8 : 00 to 9 : 30. Flight Y in check-in area B has 315 passengers, and its boarding time is 10 : 35. For the rules to be respected, fve check-in desks should be opened from 8 : 35 to 10 : 05. Flight Z in check-in area C has 280 passengers, and its boarding time is 14 : 00; therefore, fve check-in desks should be opened from 12 : 00 to 13 : 30. In this case, between 8 : 35 and 9 : 30, Flight Y can borrow the two extra check-in counters from Area A to improve check-in efciency. Since there is no overlapping time between Flight X and Flight Z, Flight Z cannot borrow check-in counters from Flight X. Te "Y" in Figure 1 means Flight Y can borrow check-in counters from Area A, and the "N" in Figure 1 means Flight Y cannot borrow check-in counters from Area C.
Te counter-sharing method could (i) enable airlines with rich check-in resources to share their check-in counters to save costs; (ii) make airlines lacking check-in counters borrow additional check-in counters to reduce passenger waiting time in queues. Besides, the above weights could be given diferent values to assign a diferent priority to the parameters. Depending on the airport's requirements, these priorities will afect the selection of various feasible solutions. Furthermore, the functions used by this approach are not restricted to only two values; they could be extended to include more parameters depending on the particular case of research in question.

Restraint Condition.
Based on the above discussions, the counter-sharing method can be defned as a static optimization problem based on airports' check-in areas. Teoretically, the check-in areas can be reassigned based on the departure fight schedule to maximize the sharing of checkin counters among airlines. Here, the reassignment of the check-in areas based on the departure fight schedule refers to internally adjusting the departure sequence of airline fights which would alter the corresponding relationship between the original check-in areas and airlines. Reassigning the check-in areas based on the departure fight schedule can make the opening hours of check-in counters for fights in adjacent check-in areas overlap as much as possible and ensure maximizing the counter-sharing rate. Terefore, it is necessary to combine the reassignment of check-in areas based on the departure fight schedule with the countersharing method to maximize the utilization of check-in counters.
When we perform the redistribution of the check-in areas, we should consider the following constraints: (1) Check-in counters are opened in advance 2 h before the fight takes of. For all fights of m airlines, the vector used to represent the information can be defned as s � [a i , N 1 , N 2 , . . . N m ], where a i is an integer in (1, 2, ...α), which is used to indicate an assignment sequence of check-in areas; α is the check-in areas' total number of assignment sequences, which is equal to the numerical value of check-in areas' permutations  A(m, m). Te vector representing the fight information for the jth airline with n j fights is an integer within (1, 2, ...β), which is used to indicate a departure fight's sequence; β is the airline's total number of departure fight sequences, which is equal to the numerical value of fights' permutations A(n j , n j ); t o l represents the check-in counters' opening times for the lth fight.
Te reassignment of the check-in areas corresponds to the airlines, after one check-in area is assigned to an airline, the remaining check-in areas can only be assigned to other airlines. Te departure fight schedules are established sequentially in time slots, which take one fight at a time and look for the corresponding available time slot that satisfes the restrictions; once allocated, the schedules continue with the next fight on the assignment list. After all the fights and check-in areas are assigned, an initial solution is obtained.

Solution
Algorithm. Based on the above discussions, redistributing check-in areas based on the departure fight schedule need to transform the solutions into vectors and improve the solutions. Te diferential evolution algorithm, developed by Storn and Price [28], is a heuristic search algorithm based on population, and each individual in the group corresponds to a solution vector. Te general idea behind an evolutionary algorithm is the representation of a solution in the form of a vector of decision variables. Transforming the decision variables into a vector-like representation is an interesting and challenging problem. Once the decision variables have been represented in a vector, the optimization problem can be specifed. Tus, the diferential evolution algorithm is suitable for solving our problems. Table 1 shows the pseudocode of the diferential evolution algorithm.
One of the critical tasks in the diferential evolution algorithm is to properly represent the information with vectors, which will signifcantly infuence the algorithm's performance. In Section 2.3, we used vectors to represent the identifer of each fight, the number of passengers on each fight, and the check-in counters' opening times. Another task of the evolutionary algorithm is the crossover, which is the main operation for improving the current solutions. Te crossing is performed between the elements of two solutions (solution A (SolA) and solution B (SolB)). Tis study's check-in areas and departure fight schedules must be optimized. Hence, SolA and SolB should contain vectors representing the check-in areas and departure times of fights. Te algorithm will take one element from SolA and Journal of Advanced Transportation 5 randomly choose another one from SolB for the crossover. Figure 2 illustrates the crossing process; the light blue color denotes the elements of the solutions that the crossover operators have changed. During the execution of the algorithm, once a feasible solution is generated, it must be evaluated on a static basis using an objective function to improve the solution.
To maintain the consistency of the generated solutions, the algorithm will verify two aspects of the new solution:  (1, 2, ...β), it could include all the departure fight sequences for the ith check-in area. Terefore, the corresponding relations between the fights and the check-in areas can be ensured.
(2) Constraints should be ensured to meet consistency.
Te crossover will evaluate whether the solution violates the constraints in Section 2.3. If it does not, it will be kept as a feasible solution, which will be evaluated later with other feasible solutions.

Case Study
In this section, we use a case study with six check-in areas (A, B, C, D, E, and F) and twenty-four fights to test the countersharing method implementation and then perform sensitivity analyses of the weighting vectors.  1). Some parameter values can be defned in Table 2. Tables 3 and 4 represent the initial and optimal solutions, respectively. Te two departure schedules display each fight's identifer, the number of passengers on each fight, Return the best vector ∆;

SoIA SoIB
Crossover      Table 5 presents the numerical results of the optimal solution and initial solution. In the optimal solution, the total passenger walking time is 874,350 s, and the total passenger queue time is 1,105,948 s. Te weighted objective value, equal to the total walking time plus the total queue time, is 1,980,298 s. In the initial solution, the total passenger walking time is 880,350 s, with a gap of 6,000 s from the optimal solution; the passenger queue time is 1,205,562 s, with a gap of 99,614 s from the optimal solution; and the weighted objective value of the initial solution is 2,085,912 s, with a gap of 105,614 s from the optimal solution. Te numerical results show the efectiveness of the countersharing method, which could reduce the weighted objective value of passenger walking time and queue time and improve check-in efciency.
We test the convergence speed of the evolution algorithm. Figure 3 illustrates the evolution of the function value versus the number of iterations. It can be found that the evolution algorithm efciently solves our problem, which converges with a few iterations.
Te above results indicate that with our counter-sharing method, a high-quality assignment of check-in areas based on the departure fight schedule can be found, which could improve the utilization of check-in counters and reduce the passengers' walking distances and waiting time for queues.
Besides, we perform a sensitivity analysis on the weighting vectors, which are the basic inputs. Sensitivity analyses of other factors may be performed in a similar manner if needed.
As mentioned above, the weighting vector refects the relative importance of two objective functions (e.g., passengers' walking time and queue time). To evaluate the efects of various weighting vectors on the assignment of check-in areas and departure fight schedules, we test four scenarios with weighting vectors of (1/2.1), (1/10.1), (1.1/2), and (1.1/10). Te results are displayed in Table 6.
According to Table 6, when the weighting vector is (1/2 : 1), there is a weighted objective value of 1,434,292 s; when the weighting vector is (1/10 : 1), there is a weighted objective value of 991,022 s; when the weighting vector is (1 : 1/2), there is a weighted objective value of 1,570,355 s; and when the weighting vector is (1 : 1/10), there is a weighted objective value of 1,265,193 s. Tese results confrm the performance and stability of our proposed method. When the weight of the queue time decreases, the allocation of check-in areas and departure fight schedules tends to reduce the objective function value of passengers' walking time. When the weight of the walking time decreases, the allocation of check-in areas and departure fight schedules tends to reduce the objective function value of passengers' queue time.
It might be not credible and particle without considering the proportion of self-service check-ins and passengers that do not require luggage check-in, which needs to be further discussed. Terefore, we test four scenarios with proportions of self-service check-in and passengers that do not require luggage check-in of 10%, 20%, 30%, and 40%. Te results are displayed in Table 7.   Journal of Advanced Transportation According to Table 7, when the proportion of passengers who do not require check-in counters is 5%, the total passenger walking time is 1,008,175 s, and the total passenger queue time is 836,333 s. When the proportion of passengers who do not require check-in counters is 10%, the total passenger walking time is 962,174 s, and the total passenger queue time is 778,172 s. When the proportion of passengers who do not require check-in counters is 5%, the total passenger walking time is 873,699 s, and the total passenger queue time is 725,711 s. When the proportion of passengers who do not require check-in counters is 10%, the total passenger walking time is 785,223 s, and the total passenger queue time is 673,250 s. Tese results confrm that the counter-sharing method still performs well even if some passengers self-service check-in services or do not require check-in counters. When the proportion of passengers who do not require check-in counters increases, the weighted objective value decreases, and the decrease in passengers' total queue time is more signifcant than that of passengers' walking time.

Conclusions
Te aviation industry is expected to grow at a high pace in the coming future. Terefore, it is necessary to take resource management technology to support the rising demand for airport facility resources. In this paper, we develop a counter-sharing method to improve check-in counters' efciency by sharing idle counters between airlines in adjacent check-in areas, reassign the check-in areas and departure fight schedules to maximize check-in counter sharing, and take the passengers' waiting time for queues and walking distances as the metric. To solve the problem in a reasonable time, we use a diferential evolution. Trough numerical tests, our method is fexible enough to include a variety of constraints in the evolutionary algorithm to provide solutions that align with the objectives of airport terminals. Te results are efective in the feld of airport operations, which could help airport operators achieve a competitive advantage in marketing.
Nevertheless, this paper still has the following limitations: (1) We lack a real-life case study to verify the countersharing method (2) Te proposed evaluation function cannot completely refect all the demands of airport passengers (3) We do not compare the performance of the proposed algorithm with that of other algorithms.
Given these limitations, we will, in the future, do the following studies: (1) Collect data and conduct a real-life case study to verify the counter-sharing method (2) Incorporate more factors that passengers are concerned about and develop a more reasonable evaluation function (3) Compare our proposed algorithm with other algorithms regarding the computation time and numerical results.

Data Availability
Te data displayed in this paper are simulated by the frst author. If some readers need the data, contact the corresponding author via the e-mail listed in this paper.

Conflicts of Interest
Te authors declare that they have no conficts of interest.  Journal of Advanced Transportation 9