بهینه سازی تخصیص مسافران به صندلی های هواپیما بر اساس بار قابل حمل  Optimization of assigning passengers to seats on airplanes based on their carry-on luggage

1. Introduction The total annual cost of airplane delays in 2007 in the United States alone was $29 billion (Ball et al., 2010). Jaehn and Neumann (2015) cite cost estimates of airplane delays ranging from $30 to $250 per minute. While some delays result from bad weather, mechanical issues, and congested airspace, as noted in Ball et al. (2010), other delays are due to the time to board passengers. To reduce the time it takes passengers to board their airplanes, Delta Airlines offered valet services on some flights to pre-load passengers’ luggage (i.e. bags) for them (Koeing, 2015). Clearly, methods that reduce the time to board airplanes would be advantageous for the airlines and their passengers. Skorupski and Wierzbinska (2015) determine the optimal time to wait for a late passenger to arrive at the gate. Many publications assume passengers are called to board in blocks or groups (e.g., Kuo, 2015; Bachmat et al., 2013; Bachmat and Elkin, 2008; Bazargan, 2007; Soolaki et al., 2012; Van den Briel et al., 2005) and that passengers board in a random sequence within a group. In an invited literature review, Jaehn and Neumann (2015) provide a broad overview of boarding methods and describe the 12 most relevant papers in detail. Of the methods they studied, the Steffen (2008) boarding sequence results in the fastest time to complete the boarding of all passengers. Boarding starts when the first passenger begins entering the aisle of the airplane in row 1 and concludes when all passengers have been seated. We assume a fully loaded airplane with 20 rows and three seats on each side of a single aisle. Fig. 1 illustrates the Steffen (2008) boarding sequence. If we assume that all passengers walk down the aisle at the same speed and there is always an empty row between them, then with Steffen (2008), the first set of 10 passengers to board the plane all begin storing their carry-on luggage, if any, at the same time and occupy a window seat in every other row. For instance, as indicated in Fig. 1, the 10th passenger to board the plane sits adjacent to the window in row 2 and begins storing his or her luggage in an overhead bin at the same time that the first passenger to board begins to store his or her luggage in row 20. The first group of 10 passengers is followed by a second group of 10 passengers sitting on the opposite side of the plane. As implied by Fig. 1, the process continues until the final 10 passengers to board (passengers 111e120) take their aisle seats in the 10 odd-numbered rows of the plane.