不确定需求下的两阶段机型指派模型

中国民航大学学报

不确定需求下的两阶段机型指派模型

张春晓，石晓磊，臧其银

（1.中国民航大学 a.天津市民用航空器适航与维修重点实验室；b.理学院，天津 300300；2.山东航空股份有限公司太原营业部，太原 030001）

收稿日期:2014-05-07 修回日期:2014-06-12 出版日期:2015-08-22 发布日期:2015-09-24
作者简介:张春晓（1971—），女，青海西宁人，副教授，硕士，研究方向为民航统计与优化.
基金资助:
中央高校基本科研业务费专项（3122014D034）

Two-stage fleet assignment model with uncertain demand

ZHANG Chun-xiao,SHI Xiao-lei,ZANG Qi-yin

(1a. Civil Aircraft Airworthiness and Maintenance Key Lab of Tianjin;1b. College of Science,CAUC,Tianjin 300300,
China;2. Sales Department in Taiyuan,Shandong Airlines Co. Ltd.,Taiyuan 030001,China)

Received:2014-05-07 Revised:2014-06-12 Online:2015-08-22 Published:2015-09-24

摘要/Abstract

摘要：

针对航空公司新开辟航线的机型指派问题，由于缺乏历史运营数据，无法得到乘客需求的概率分布，因此将需求描述为不确定变量。建立带有机会约束的两阶段机型指派0-1 整数规划模型，第1 阶段为机族指派，第2 阶段对指定机族所属机型进行指派遥给定新航线需求的不确定分布袁将不确定整数规划模型转换成确定性模型，通过一个改进的分枝定界算法进行求解。算例采用某航空公司枢纽机场6 条新航线共20个航班的数据进行分析，结果验证了模型的可行性和算法的有效性。

关键词: 机型指派, 新航线需求, 不确定理论, 两阶段, 0-1 整数规划, 分枝定界算法

Abstract:

For the fleet assignment problem of a new opening airlin.the probability distribution of its demand cannot be obtained due to the absence of previous data. Therefore.the demands of new flights are assumed as uncertain variables. A binary integer programming model of two-stage fleet assignment with chance constrains is proposed.where the first stage makes family-assignment decision.and the second stage solves type-assignment problem for a certain aircraft family. Given the uncertain distribution form of new flight demand.the proposed model is converted into a deterministic programming model. An improved branch and bound algorithm is designed to solve this model. Finally.a numerical example considers the fleet assignment problem of twenty flights of six new opening routes in a hub airport.results indicate the proposed model and algorithm are effective in practice.

Key words: fleet assignment, new airline demand, uncertainty theory, two-stage, binary integer programming, branch and bound algorithm

中图分类号:

张春晓，石晓磊，臧其银. 不确定需求下的两阶段机型指派模型[J]. 中国民航大学学报.

ZHANG Chun-xiao,SHI Xiao-lei,ZANG Qi-yin. Two-stage fleet assignment model with uncertain demand[J]. .

参考文献

[1] 马苏德·巴扎尔甘. 航空公司运营与规划管理[M]. 邵龙，王美佳,译.北京：中国民航出版社，2006.

[2] ABARA J. Applying integer linear programming to the fleet assignment problem[J]. Interfaces，1989，19（4）：20-28.

[3] 朱星辉，朱金福，巩在武. 我国航空公司机型指派模型及算法研究[J].工业技术经济，2007，26（4）：75-77.

[4] 刘昕，白存儒，刘慧颖. 带时间窗的飞机排班问题优化[J].航空工程进展，2012，3（4）：517-521.

[5] LISTES O，DEKKER R. A scenario aggregation-based approach for determining a robust airline fleet composition for dynamic capacity allocation[J]. Transportation Science，2005，39（3）：367-382.

[6] SHERALI H D，ZHU X. Two-stage fleet assignment model considering stochastic passenger demands[J]. Operations Research，2008，56（2）：383-399.

[7] LIU B. Why is there a need for uncertainty theory[J]. Journal of Uncertain Systems，2011，5（1）：3-20.

[8] LIUB.UncertaintyTheory[M].2nded.Berlin：Springer-Verlag，2007.

[9] LIU B. Uncertainty Theory[M]. 3rded. Berlin：Springer Link，2010.

[10] 耿淑香.航空公司运营与管理方略[M].北京：中国民航出版社，2000.

[11] BERGE M E，HOPPERSTAD C A. Demand driven dispatch：A method for dynamic aircraft capacity assignment，models and algorithms[J].Operational Research，1993，41（8）：153-168.

[12] SHERALI H D，BISH E K，ZHU X M. Airline fleet assignment concepts，models，and algorithms[J]. European Journal of Operational Research，2006，172（1）：1-30.

[13] JACOBS T L，SMITH B C，JOHNSON E L. Incorporating network flow effects into the airline fleet assignment process[J]. Transportation Science，2008，42（4）：514-529.

[14] BARNHART C，FARAHAT A，LOHATEPANONTM. Airline fleet assignment with enhanced revenue modeling[J]. Operations Reserch，2009，57（1）：231-244.

[15] YEN C L，KUEI T F，BERTRAND L. A branch-and-bound algorithm for makespan minimization in differentiation flow shops[J]. Engineering

Optimization，2013，45（12）：1397-1408.