一种基于Hub-Spoke结构航空公司机型指派的实用启发性算法

doi:10.16381/j.cnki.issn1003-207x.2021.2459

Abstract

Abstract:

The fleet assignment problem of Hub-spoke network airlines in making flight schedules is addressed. According to the demand distribution of passengers and resulting in the flight costs from the airline's historical data， an optimization algorithm by tabular operation method based on the flight cost model is designed， and an heuristic algorithm is proposed for flight planning specialist to facilitate manual calculation and to adjust aircraft types， which solves the airline fleet assignment 0-1 integer programming problem， The algorithm integrates the ideas of Hungarian algorithm and backtracking algorithm. Starting from the minimum cost of ?ight optimization， the algorithm searches the optimal value by the depth-first-search method subject to the optimization constraints， and backtracks in the nodes when the aircraft constraints are not met， finds the minimum flight cost that meets the aircraft side constraints， and obtains the optimal fleet assignment and hence gives a theoretical proof. The effectiveness of the heuristic algorithm is obtained through case study. The total cost of ten B737 and five B757 scenarios is found to be the lowest among all scenarios by manual calculation using the tabular method， reaching $409，860， which proves that a reasonable mix of aircraft types can make the company operate better. Compared with the traditional operations research algorithm this algorithm is straightforward in construction and natural in optimization mechanism， which is simple and practical， also easy to understand and master， especially for small airlines or branches to manually formulate and adjust flight schedules.

Key words: 0-1 integer programming, airline fleet assignment（FAM）, heuristic algorithm, tabular operation method, backtracking algorithm

CLC Number:

TP273

Guohua Wu. Based on Hub-Spoke Network a Practice Heuristic Algorithm Applied to Airline Fleet Assignment[J]. Chinese Journal of Management Science, 2024, 32(1): 158-167.

Figures/Tables 11

航班i	进(+)出(-)港	成本增量 $△ c i j$		机型指派（回溯调整）	飞机平衡		回溯调整
航班i	进(+)出(-)港	j=1	j=2	机型指派（回溯调整）	j=1	j=2	j=1	j=2
0					$G 0,1$	$G 0,2$
1	-	$△ c 11$	0	j=2		-1
2	-	0	$△ c 22$	j=1	-1
:
k	+	0	$△ c k, 2$	j=1	+1
k+1	-	0	$△ c k + 1,2$	j=1	-1
:
n-1	+	$△ c n, 1$	0	j=2		+1
					$G n, 1$	$G n, 2$

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航班	进出港	成本（成本增量）		指派机型	飞机数量(回溯调整)		机型调整	成本损失
航班	进出港	737	757	指派机型	737	757	机型调整	成本损失
					2	1
104	-	25258（671）	24587（0）	757	2(1)	0（1）	737	671
105	-	29755（2758）	26997（0）	757	2(1)	-1（0）
125	+	19557（0）	22902（3345）	737	(1)	（1）	757	3345
106	-	21862（0）	23377（1515）	737	(0)	( )
126	+	18489（0）	22785（4296）	737	(1)	( )
127	+	17737（0）	22757（5021）	737	(2)	（）
					2	1

航班	进出港	成本（成本增量）		指派机型	飞机数量(回溯调整)		机型调整	成本损失
航班	进出港	737	757	指派机型	737	757	机型调整	成本损失
					2	1
104	-	25258（671）	24587（0）	757	2(1)	0（1）	737	671
105	-	29755（2758）	26997（0）	757	2(1)	-1（0）
125	+	19557（0）	22902（3345）	737	(2)	（0）
106	-	21862（0）	23377（1515）	737	（1）	( )
126	+	18489（0）	22785（4296）	737	(2)	( )
127	+	17737（0）	22757（5021）	737	(3)	（）
					3	0

编号	LOS		SFO		MIA		ATL		ORD		IAD		BOS		JFK		总数		算法	总成本（美元）
编号	a	b	a	b	a	b	a	b	a	b	a	b	a	b	a	b	a	b	算法	总成本（美元）
1	2	0	2	1	0	2	0	1	1	0	0	0	1	0	3	2	9	6	文献[5]	415309
2	2	0	2	1	0	2	0	1	1	0	0	0	1	0	3	2	9	6	本文	415309
3	1	1	1	1	0	2	0	1	1	0	0	0	1	0	5	1	9	6	本文	410128
4	2	0	1	1	0	2	0	1	1	0	0	0	1	0	5	1	10	5	本文	411278
5	1	1	1	1	0	2	0	1	1	0	0	0	1	0	6	0	10	5	本文	409860
6	2	0	1	1	0	2	0	1	1	0	0	0	1	0	6	0	11	4	本文	411010
7	2	0	2	0	1	0	1	0	1	0	0	0	1	0	5	0	13	0	无	418260
8	0	2	0	2	0	1	0	1	0	1	0	0	0	1	0	5	0	13	无	448149

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Based on Hub-Spoke Network a Practice Heuristic Algorithm Applied to Airline Fleet Assignment

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