aerospace-05-00080.pdf - aerospace Article Robust Optimization of Airplane Passenger Seating Assignments R John Milne 1,† Mostafa Salari 2,† and

aerospace-05-00080.pdf - aerospace Article Robust...

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aerospace Article Robust Optimization of Airplane Passenger Seating Assignments R. John Milne 1,† , Mostafa Salari 2,†, * and Lina Kattan 2 1 David D. Reh School of Business, Clarkson University, 333 B.H. Snell Hall, Potsdam, NY 13699, USA; [email protected] 2 Department of Civil Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada; [email protected] * Correspondence: [email protected]; Tel.: +1-587-832-1368 These authors contributed equally to this work. Received: 26 June 2018; Accepted: 23 July 2018; Published: 1 August 2018 Abstract: We present a method that reduces the time it takes to complete the passenger boarding of an airplane. In particular, we describe a two-stage mixed integer programming (MIP) approach, which assigns passengers to seats on an airplane based on the number of bags they carry aboard the plane. The first stage is an MIP that assigns passengers to seats to minimize the time to complete the boarding of the plane. The second-stage MIP also determines seating assignments, while constraining the total boarding time to that determined by the stage-one MIP and maximizing weighted slack times to provide a more robust assignment. Numerical results show that this two-stage approach results in lower average boarding times than the one-stage approach, when the time it takes passengers to walk and sit in their seats is random. Experiments indicate that the magnitude of the improvement is not very sensitive to variations in the slack time weights. Keywords: airplane boarding; passenger luggage; mixed integer programming (MIP); slack times; robust optimization 1. Introduction Delays in airplane takeoffs cost $29 billion annually [ 1 ]. The costs of these delays have been estimated from $30 to $250 per minute [ 2 ]. The time to board passengers can contribute to these delays [ 3 5 ]. A number of researchers have created and investigated methods that board passengers by groups, with the group assignment depending upon their seat assignment [ 6 14 ]. For instance, Van den Briel et al. [ 12 ] shows that it is effective to board the passengers who will be sitting in window seats before the passengers who will sit in middle seats and to board the passengers who will sit in aisle seats last. This approach eliminates delays caused by seated passengers leaving their seats to make room for other passengers to sit down. A number of researchers have recently used stochastic simulation [ 15 22 ] and field tests [ 23 27 ] to compare the performance of boarding strategies. Schultz [ 28 ] estimates the improved boarding performance resulting from a “slip seat” configuration that enables aisle seats to temporarily move closer to the windows, thereby extending the aisle width, permitting passengers to pass others waiting ahead of them in the aisle.
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  • Fall '19
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