Hub location of air cargo company in air alliance

Zhang Jin Yan Yan Tang Qiuyu

(1School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 611756, China)(2National Engineering Laboratory of Integrated Transportation Big Data Application Technology, Southwest Jiaotong University, Chengdu 611756, China)(3National United Engineering Laboratory of Integrated and Intelligent Transportation, Southwest Jiaotong University, Chengdu 611756, China)

Abstract：Based on the characteristics of the air alliance environment saving transport mileage, the hub location problem of the air cargo network was studied. First, the air alliance selection probability model was introduced to determine the alliance self-operation or outsourcing probability in different segments. Then, according to the location center rule, with the goal of minimizing the total cost, the hub location model was built. The improved immune chaos genetic algorithm was used to solve this model. The results show that the improved algorithm has stronger convergence and better effect than the immune genetic algorithm. When the number of hubs increases, the fixed cost increases, but the transportation cost decreases. The greater the discount factor, the fixed cost, and the self operating cost sharing coefficient, the higher the total network cost. The airline which joins the air alliance can greatly reduce the operating cost of airlines. Therefore, airlines should consider joining the alliance.

Key words：air alliance; air alliance selection probability; hub location; improved algorithm

With the transformation of economic growth mode and the upgrading of the industrial structure in China, air transport increases cargo transport volume, accelerates the construction of aviation infrastructures, and increases the level of hub airports. Although China’s aviation logistics has developed rapidly, it is still in the progression stage and has many shortcomings. Firstly, the scale is small, and the transport capacity is low. Secondly, the logistics enterprises have narrow business scope, mostly still engaged in a single air cargo or freight forwarding and so on. Air cargo volume and timelines have brought new requirements to the development of aviation division.

At present, most scholars focused on the evolution analysis of air cargo and air network[12], the location of air hub[35], and the optimization of air route networks. Most scholars adopted two methods in the location problem related to this paper. One is the index evaluation method, such as AHP, fuzzy clustering, fuzzy language and other multi-attribute decision-making methods. The other is to establish the location model by the gravity method, center method and linear integer programming. Campbell[6]first proposed to define decision variables based on the path between the starting and ending points. Based on this, a mixed integer programming model for the central hub problem was established, which increased the constraints of variables, simplified the model of the algorithm, reduced the difficulty of solving, and laid the foundation for the construction of a simple algorithm. Since then, most scholars’ research has been based on the idea of Campbell. Yang et al.[3]constructed a bilevel programming model to minimize the total transportation cost, and determined the location of the aviation hub and the assignment path of the flight segment. Mohri et al.[7]built a hub location model based on the capacity envelope function, and constructed a new adaptive large neighborhood search algorithm (ALN) to solve practical problems. da Gra?a Costa et al.[8]established a single hub location model with capacity constraints for hub nodes, and proposed a two-level standard method for solving the model. From the aspect of aviation alliance, the current research mainly focused on the impact on aviation users and airlines, the choice of alliance cooperation mode, the cost-benefit sharing of alliance, the analysis of alliance networks and the construction of alliance networks. Airlines participating in the alliance can reduce costs by sharing facilities, equipment and personnel. At present, there are few studies on the aviation network and hub location of aviation alliance. Wen et al.[9]set up an interactive route network multi-objective model based on the code sharing of aviation alliance, taking into account the factors of flight frequency and cost.

Alliances can create a competitive advantage, reduce costs, and expand the network reach for cargo carriers. Three global alliance clusters emerged, with founding partners located in the major geographic regions, and often already involved in bilateral partnerships with other founders. This study examines how global airline alliances form, with their related expansion of the network reach, resulting in an increase in the profitability for the founding members[1011]. In this paper, the selection probability of aviation alliance is determined by analyzing the revenue and cost under the competition of aviation alliance.

Hub carriers tend to charge higher fares to their passengers at their hubs. Using the fare data at the Hong Kong International Airport,this paper aims at empirically examining the factors affecting the hub premium for both economy and business class markets. The random effect models are employed in the analysis[12]. A new practical airline green hub location model with hub capacity decision is presented based on airport capacity envelope functions[7]. Therefore, this paper presents a solution to the problem of hub location based on capacity and quantity constraints.

In this paper, the hub location problem of the air cargo network is studied in the air alliance environment. According to the relevant influence of different airlines in the alliance environment, the choice of self-operation or outsourcing of airlines in different routes is analyzed, and the equilibrium probability function of alliance selection is determined. According to the location center rule and direct demand, the model of hub location is established. Considering the chaotic mapping, an improved immune chaotic genetic algorithm (ICGA) is designed to solve the localization problem.

1 Hub Points Location Problem with Descriptions

The location problem of air logistics nodes can be described as the location and demand of known OD points of freight demand, as shown in Fig.1(a). In order to minimize the cost, the location ofqtransit points is selected among thePalternative points inMdemand points of the aviation network, as shown in Fig.1(b).

Figs.1(a) and (b) illustrate our notation. The demand point is denoted byi,j∈[1,2，…,M]. The demand from origination to destination is represented asDij. The distance from origination to destination is represented asdij. When there is a transfer point from origination to destination, the distance of the transfer point from origination to destination isdikj=dik+dkj. In the formula,kis the transfer point belonging to [1,2,…,q];mis the alternative point of the transfer point belonging to [1,2,…,N].

(a)

We emphasize our assumption that the information is pertinent to air transport. Goods can only be transshipped once at most, since previous studies[7]have shown that two transshipments are almost non-existent. It did not consider the queuing problem of aircraft landing and time waiting costs in the transshipment process to simplify the model without considering the influence of time. The unit transportation cost of each section is the same during the course of transportation. Cargo between any two air nodes can only be transported along a route with the lowest transport cost.

Therefore, according to the hub points location problem, a hub location model is established. The hub location problem can be stated as a central location model problem with side constraints and capacity constraints. The hub location problem (HLP) can be modeled as follows:

(1)

s.t.

(2)

(3)

(4)

(5)

Xk={0,1}

(6)

Xij={0,1}

(7)

Xikj={0,1}

(8)

When the location model of the aviation hub is established, we need to depict the probability of alliance selection. Airlines choose to join the alliance, and the probability of operation choice on different routes is related to their freight volume and operation choice of other cooperative airlines.

When an airline chooses to self-operate its own alliance, its income isR1=Px[tdDij-(CP+CtdDij)]+(1-Px)[tdDij-(CP+αCtdDij)].When airlines choose outsourcing, the revenue isR2=Px[A4+tdDij-(βCtdDij)]+(1-Px)A8. Among them,A4andA8are the loss values when the airline business is abnormal.

According to the risk aversion problem studied by Rieger et al.[13], the proposed risk aversion prospect theory improves the loss effect.

The degree of risk loss is described by the weight function.

(9)

Using the improved value-at-risk function, the risk loss is depicted.

(10)

Therefore, the prospect theory model based on the value of risk loss is proposed.

V=∑v(x)π(p)

(11)

If the decision maker is more sensitive to losses, then ? is greater than 1, else it is less than or equal to 1.λ1andλ2denote the degree of concavity and convexity of the value function in gains and losses, 0<λ1,λ2<1.pis the probability.ξandτrepresent the degree of weight change, which also reflect the different attitudes of decision-makers towards returns and risks.

2 Solution Methodology and Algorithm Design

The problem to be solved in this section is to determine the point of the transit of goods based on a number of alternative points. Combining the immune algorithm, the genetic algorithm can effectively overcome the premature phenomenon. As the object of this study is large-scale population, it adopts the improved ICGA to effectively improve the calculation efficiency and optimization ability, which can obtain the optimal solution of the problem with a relatively high probability. The immune genetic algorithm (IGA) is an improved genetic algorithm, which improves the selection operation of the genetic algorithm according to the theory of somatic cell and immune network, so as to maintain the diversity of population and improve the global optimization ability of the algorithm. By adding the immune memory function to the algorithm, the convergence speed of the algorithm is improved. The IGA regards antigen as an objective function, antibody as the feasible solution of the problem, and affinity between antibody and antigen as the fitness of the feasible solution. The IGA introduces the concept of antibody concentration, and describes it with the information entropy to express the number of similar feasible solutions in the population. The IGA integrity method is based on the affinity between antibody and antigen and the concentration of the antibody. The antibody with high affinity and low concentration has a high selection rate, which can inhibit the antibody with high concentration in the population and maintain its diversity. Similar to the genetic algorithm, the combination of the immune algorithm and genetic algorithm is also suitable for solving nonlinear and NP hard problems. However, compared with the genetic algorithm, the IGA has higher efficiency and better results. The improved algorithm process steps are as follows.

Step1Encoding form and parameter initialization

In this paper, the decision variable is the location of transfer points, so the algorithms use the integer chromosome coding. The numberKrepresents that there are onlyKtransfer points in Fig.2. The gene of every chromosome indicates that which airport is selected as a transfer point. Four transfer points need to be selected. If the number of genes is [1,2,4,10], it represents that the transfer point is the airport of nodes 1,2,4,10.

Fig.2 Chromosomal coding of hub

Step2Generation of the initial antibody group

It generatesMindividuals randomly and picks upmindividuals to form an initial group from the memory bank, wheremis the number of individuals in the memory bank.

Step3Solving diversity assessment

Step4Forming a parental group

The initial population is arranged in a descending order according to the expected probabilityP. Then, the parent group from the formerMindividuals is formed, and is stored in the memory bank from the formermindividuals.

Step5Immune manipulation

A random number in [0,1] interval is generated. If the random number is less than or equal to the cumulative probability of the individual and greater than the cumulative probability of the individual 1, the individual is selected for the offspring population.

According to the crossover probabilitypc, the crossover operation is carried out by the single point crossover method. It inherits the excellent characteristics of the father generation to the offspring, thus forming new excellent individuals.

Step6Chaotic renewal strategy

Step7Generating new populations

After immunization and variation, a new population is obtained. Then, the individual with memory is extracted from the memory bank to form a new generation of population and go to step 3.

Step8If the maximum number of iterations is not reached, go to step 3; otherwise, output the optimal solution and terminate the algorithm.

3 Computational Examples

3.1 Basic conditions and parameter settings

Tab.1 Air cargo volume of S Airlines OD matrix partial data kg

3.2 Calculation results

We used MATLAB R2016b software to run the improved ICGA on Inter Core i7-8550U CPU @ 1.80 GHz, 8.00 GB memory computer. The specific parameters of the algorithm are as follows: The population sizeN=50; memory capacity is overbestΓ=10; crossover probabilitypc=0.5; mutation probabilitypm=0.4; the maximum iteration numberG=100; diversity evaluationps=0.95.

The convergence of the algorithm is shown in Fig.3. In the 36th generation, the algorithm converges, which indicates that the degree of convergence of the improved algorithm is strong. The result shows that the number of hub locations is (2,4,5,6,7,8), so the hub locations are Guangzhou, Chengdu, Shenyang, Beijing, Zhengzhou and Hangzhou. At the same time, the total cost is 701 768 yuan.

Fig.3 Convergence curve of the improved ICGA

3.3 Algorithmic comparison

In this paper, the ICGA is improved. Compared with the IGA, it has two main advantages. One is stronger iterative convergence and the other is a better fitness value. The algorithm comparison results are shown in Fig.4.

Comparing the improved algorithm with ICGA, IGA and CPLEX, it can be found that the improved algorithm in this paper has a faster calculation speed, and the difference between the calculation results and the solution is smaller, as shown in Tab.2. Therefore, in large-scale operations, the algorithm designed in this paper has certain applicability.

Tab.2 Algorithm comparison in large-scale operations

In Tab.3, the data of 38 cases is divided into 5 groups: (1,6,11,16,21,26,31,36), (2,7,12,17,22,27,32,37), (3,8,13,18,23,28,33,38), (4,9,14,19,24,29,34), and (5,10,15,20,25,30,35). The comparison between the calculation results and speeds of different algorithms in small-scale examples is shown in Tab.3. The solver solution in small-scale examples is obviously superior to the heuristic algorithm in terms of calculation speed, and the results are similar in terms of calculation results.

Tab.3 Algorithm comparison in small-scale operations

3.4 Sensitivity analysis

3.4.1 Transshipment cost coefficientθ

When the coefficient of transshipment costθbecomes smaller, the cost of transshipment chosen on behalf of airlines will become smaller. At this time, the cost affected by different transshipment coefficientsθ={0.7,0.8,0.9} is shown in Fig.5. As a result, when the coefficient of transshipment costθincreases, the total cost also increases. Therefore, the smaller the coefficient of transshipment costθ, the more frequent the transshipment of alliances, and the location of the transfer point remains unchanged.

Fig.5 Comparison of different transshipment cost coefficients

3.4.2 Number of transfer pointsq

Under the constraints of different numbers of transfer points, the results of the transshipment location of the airline freight network are shown in Tab.4. Whenq=6, the total cost is the lowest. Therefore, the optimal number of hub locations for S Airlines is 6. At the same time the total cost is 701 768 yuan. It shows that when the number of transfer points increases, the fixed cost of transfer points increases, but the variable cost including the transportation cost decreases with the increase in transfer points. The total cost decreases when the number of transfer points is increased.

Tab.4 Location results under different numbers of transfer points

3.4.3 Fixed cost on aircraft sectionCP

When the fixed cost of different segments of an aircraft changes, it affects the total cost of self-operation of the segment.The impact of fixed costCp={10 000,15 000,20 000,25 000，30 000} on the total cost is analyzed as shown in Fig.6. It can be seen that with the increase in the fixed cost in the flight segment, the total cost of the network increases.

Fig.6 Comparison of fixed cost of aircraft section

3.4.4 Cost-sharing coefficientαandβ

When the coefficients of alliance self-operation and alliance outsourcing change, the decision-making of S Airlines will also change.The optimal results with different values ofαandβare shown in Fig.7. It is found that the larger the cost of self-operationα, the smaller the probability of S Airlines choosing self-operation, the higher the total cost; the smaller the cost of outsourcingβ, the smaller the probability of S Airlines choosing self-operation, the higher the total cost.

3.4.5 Decision on whether S Airlines join an airline alliance or not

Aira lliance can increase the efficiency of a airline company due to the shortage of airlines and the small volume. When S Airlines do not join the air alliance, the total cost is obviously higher than that of joining it, as shown in Fig.8. The transportation cost of an aviation alliance is one third of self-operating aviation. However, the fixed cost of aviation alliance is similar to that of self-operating aviation. Therefore, the airline alliance is conducive to reducing the cost of enterprises. The S Airlines relying on the alliance can significantly reduce the cost.

Fig.7 Comparison of cost allocation coefficients of alliance self-operation and outsourcing

Fig.8 Comparison of alliance and non-alliance

4 Conclusions

1) The probability model of alliance selection that explicitly considers the wishes of policy makers is proposed. The probability of alliance self-operation or outsourcing on different segments are determined.

2) The improved ICGA increases the calculation efficiency and optimization ability, which can be used to solve large-scale nonlinear optimization problems. In the small-scale analysis, there is a certain gap between the calculation result and speed of the improved ICGA and the accurate algorithm.

3) The total cost is the lowest when the optimal number of hub location is 6. The guidance provides a basis for entrepreneurs’ decision-making. Decision makers can dentify better airline segment adopting self-operations. However, there is still a gap between the guidance of the improved algorithm and that of the precise algorithm.

4) The cost of airlines joining an airline alliance can be greatly reduced. Therefore, airlines should choose to join the alliance to reduce their own costs. If a company chooses to join the alliance, it needs to consider the influence of the alliance mechanism.