Modeling optimal air traffic rights resource allocation

doi:10.23919/JSEE.2025.000070

Abstract

Abstract:

International freedom of the air (traffic rights) is a key resource for airlines to carry out international air transport business. An efficient and reasonable traffic right resource allocation within a country between airlines can affect the quality of a country’s participation in international air transport. In this paper, a multi-objective mixed-integer programming model for traffic rights resource allocation is developed to minimize passenger travel mileages and maximize the number of traffic rights resources allocated to hub airports and competitive carriers. A hybrid heuristic algorithm combining the genetic algorithm and the variable neighborhood search is devised to solve the model. The results show that the optimal allocation scheme aligns with the principle of fairness, indicating that the proposed model can play a certain guiding role in and provide an innovative perspective on traffic rights resource allocation in various countries.

Key words: air transport, air traffic right (ATR), genetic algorithm, variable neighborhood search, mixed integer programming formulation

Zhishuo LIU, Yi’nan CHENG, Yanhua LI, Danyang SHEN. Modeling optimal air traffic rights resource allocation[J]. Journal of Systems Engineering and Electronics, 2025, 36(3): 778-790.

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Type	Notation	Description
Set	P	Set of passengers’ origins, $ p\in P $
	Q	Set of passengers’ destinations, $ q\in Q $
	R	Set of carriers, $ r\in {{R}} $
	K	Set of flights, $ k\in K $
	C_n, V_n	Sets of HS and FS airports in the nth region, respectively
	C	$C = {C_1} \cup {C_2} \cup \cdots \cup {C_{{N_{{r}}}}}$
	V	$V = {V_1} \cup {V_2} \cup \cdots \cup {V_{{N_{{r}}}}}$
Parameter	l_pj	Distance between origin p and HS airport j
	l_ji	Distance between HS airport j and FS airport i
	l_iq	Distance between FS airport i and destination q
	p_j	Volume of transit passengers at airport j
	β_r	Competitiveness of carrier r
	θ_rj	Market share of carrier r at airport j
	ω₁, ω₂, ω₃	Weight of the multiple objective functions
	D_r	Operational capacity of carrier r (i.e., the maximum number of flights it can put into operation per week)
	M_pq	Number of passengers from origin p to destination q
	a_n	Restriction on the number of flights operated per week for the nth region (i.e., the route capacity)
	L⁺, L⁻	Maximum/minimum passenger load of each flight
	N	Limit on the number of enabled carriers
Variable	w_r	w_r =1 if carrier r is enabled; otherwise, 0
	x_jirk	x_jirk =1 if flight k is operated by carrier r to fly the route j → i; otherwise, 0
	z_pqjirk	Integer variable, number of passengers (whose trip’s origin is p and whose destination is q) taking flight k operated by carrier r to fly route j → i

Perspective	Objective	Objective function formulation	Explanation	Principles to respond
Passengers	To enable passengers to travel more efficiently and conveniently	$ \min \displaystyle\sum {{z_{pqjirk}}\left( {{l_{pj}} + {l_{ji}} + {l_{iq}}} \right)} $	Minimizing passengers’ total travel time and distance	Maximizing public interests
Airports	To build international aviation hubs	$ \min \displaystyle\sum {\frac{{{x_{jirk}}}}{{{p_j}}}} $	The higher hub status an airport has, the more ATR resources it obtains	Promoting hub construction
Carriers	To sustain large network carriers	$ \min \displaystyle\sum {\frac{{{x_{jirk}}}}{{{\beta _r}{\theta _{rj}}}}} $	The more competitive the carrier and higher market share a carrier holds at an airport, the more ATR resources it obtains	Guiding orderly and moderate competition among carriers; maximizing ATR resource use; enhancing comprehensive carrier competitiveness

Air route	Carrier	Number of flights	Region
PEK-CDG	CA	27	1
CAN-CDG	CZ	12	1
PVG-CDG	MU	21	1
CTU-CDG	CA	4	2
KMG-CDG	MU	9	2
XIY-CDG	MU	5	2
SZX-CDG	CZ	3	2
PEK-NCE	CA	1	3
PVG-NCE	MU	1	3
PVG-LYS	MU	1	3

Region	Capacity	Residual		Carrier	Air route	Number of flights
Region	Capacity	Plan A	Plan B	Carrier	Air route	Plan A	Plan B
1: PEK/PVG/CAN to CDG	60	0	0	CA	PEK-CDG	27	21
				CZ	PEK-CDG	0	7
				CA	PVG-CDG	0	7
				MU	PVG-CDG	21	18
				CZ	CAN-CDG	12	7
2: HS airports except PEK/PVG/CAN to CDG	31	8	4	CA	CTU-CDG	4	3
				MU	KMG-CDG	9	3
				MU	TAO-CDG	0	3
				MU	NKG-CDG	0	4
				HU	XIY-CDG	0	3
				MU	XIY-CDG	5	0
				HU	CKG-CDG	0	2
				HU	KWE-CDG	0	1
				HU	SZX-CDG	0	3
				CZ	SZX-CDG	3	0
				MF	FOC-CDG	0	5
3: HS airports to FS airports except CDG	35	30	28	CA	PEK-NCE	1	3
				FM	PVG-NCE	0	4
				MU	PVG-NCE	1	0
				MU	PVG-LYS	1	0

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