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Optimal boarding policies for thin passengers

Part of: Operations research and management science Optimality conditions

Published online by Cambridge University Press:  01 July 2016

Eitan Bachmat ,
Daniel Berend ,
Luba Sapir  and
Steven Skiena
Eitan Bachmat*
Affiliation:
Ben-Gurion University
Daniel Berend*
Affiliation:
Ben-Gurion University
Luba Sapir*
Affiliation:
Ben-Gurion University and Holon Institute of Technology
Steven Skiena*
Affiliation:
Stony Brook University
*
∗ Postal address: Department of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel. Email address: ebachmat@cs.bgu.ac.il
∗∗ Postal address: Department of Mathematics and Department of Computer Science, Ben-Gurion University, Beer-Sheva, 84105, Israel. Email address: berend@cs.bgu.ac.il
∗∗∗ Postal address: Department of Industrial Engineering and Management, Ben-Gurion University, Beer-Sheva, 84105, Israel. Email address: lsapir@bgu.ac.il
∗∗∗∗ Postal address: Department of Computer Science, Stony Brook University, Stony Brook, NY 11794-4400, USA. Email address: skiena@cs.sunysb.edu
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Abstract

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We deal with the problem of seating an airplane's passengers optimally, namely in the fastest way. Under several simplifying assumptions, whereby the passengers are infinitely thin and react within a constant time to boarding announcements, we are able to rewrite the asymptotic problem as a calculus of variations problem with constraints. This problem is solved in turn using elementary methods. While the optimal policy is not unique, we identify a rigid discrete structure which is common to all solutions. We also compare the (nontrivial) optimal solutions we find with some simple boarding policies, one of which is shown to be near-optimal.

Keywords

Stochastic geometryairplane boardingoptimalityoptimal airplane boarding

MSC classification

Primary: 49K45: Problems involving randomness 90B06: Transportation, logistics
Secondary: 90B22: Queues and service 65K10: Optimization and variational techniques
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 4 , December 2007 , pp. 1098 - 1114
Copyright
Copyright © Applied Probability Trust 2007 

References

Aldous, D. and Diaconis, P. (1999). Longest increasing subsequences: from patience sorting to the Baik–Deift–Johansson theorem. Bull. Amer. Math. Soc. 36, 413–432.CrossRefGoogle Scholar
Arias-Castro, E., Donoho, D. L., Huo, X. and Tovey, C. A. (2005). Connect-the-dots: how many random points can a regular curve pass through? Adv. Appl. Prob. 37, 571–603. (Correction: 38 (2006), 579).Google Scholar
Bachmat, E. (2007). Discrete space-time and its applications. In Random Matrices, Integrable Systems and Applications, eds Baik, J. et al., American Mathematical Society, Providence, RI.Google Scholar
Bachmat, E. (2007). Average case analysis of disk scheduling, increasing subsequences and spacetime geometry. Algorithmica 49, 212–231.Google Scholar
Bachmat, E. and Elkin, M. (2007). Bounds on the performance of back-to-front boarding policies. Submitted.Google Scholar
Bachmat, E. et al. (2005). Analysis of airplane boarding times. Submitted.Google Scholar
Bachmat, E. et al. (2006). Analysis of airplane boarding via space-time geometry and random matrix theory. J. Physics A Math. General 39, L453–L459.CrossRefGoogle Scholar
Baik, J., Deift, P. and Johansson, K. (1999). On the distribution of the length of the longest increasing subsequence of random permutation. J. Amer. Math. Soc. 12, 1119–1178.Google Scholar
Deuschel, J. D. and Zeitouni, O. (1995). Limiting curves for i.i.d. records. Ann. Prob. 23, 852–878.Google Scholar
Ferrari, P. and Nagel, K. (2005). Robustness of efficient passenger boarding in airplanes. Transportation Res. Board Ann. Meeting, paper number 05-0405, Washington D.C. Available at http://gulliver.trb.org/am/ip/assembly_detail.asp?id=3705.Google Scholar
Logan, B. F. and Shepp, A. (1977). A variational problem for random Young tableaux. Adv. Math. 26, 206–222.Google Scholar
Marelli, S., Mattocks, G. and Merry, R. (1998). The role of computer simulation in reducing airplane turn time. Boeing Aero Magazine 1. Available at http://www.boeing.com/commercial/aeromagazine/aero_01/index2.html Google Scholar
Prahofer, M. and Spohn, H. (2000). Universal distributions for growth processes in 1+1 dimensions and random matrices. Physical Rev. Lett. 84, 4882–4885.Google Scholar
Van den Briel, M., Villalobos, J. and Hogg, G. (2003). The aircraft boarding problem. Proc. 12th Industrial Eng. Res. Conf. IERC, CD ROM, paper number 2153.Google Scholar
Van den Briel, M. et al. (2005). America West develops efficient boarding strategies. Interfaces 35, 191–201.Google Scholar
Van Landeghem, H. and Beuselinck, A. (2002). Reducing passenger boarding time in airplanes: a simulation approach. Europ. J. Operat. Res. 142, 294–308.Google Scholar
Vershik, A. and Kerov, S. (1977). Asymptotics of the Plancherel measure of the symmetric group and the limit form of Young tableaux. Soviet Math. Dokl. 18, 527–531.Google Scholar