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Optimal boarding policies for thin passengers

Part of: Optimality conditions Operations research and management science

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 

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