Summary of Research Report

The slot scheduling problem has recently received a great deal of consideration in the literature due its size and complexity. As demand for air transportation rises but opportunities for the expansion of infrastructure remain limited, demand management measures are fundamental to help balance supply and demand. Supply side solutions, through airport capacity expansion or enhancement, are capital intensive and require a long term horizon for implementation. Such operations are also often subject to physical or political constraints. Instead, demand management is recognised as the principal instrument to deal with delays in air transport since such solutions are immediate and easily implementable. Slot scheduling is a method of managing demand through best allocating scarce airport resources.

Prior to the summer or winter scheduling season, airlines request slots at an airport; a slot allows them to use all of the infrastructure necessary for landing and take-off. For airports who are designated as `coordinated’, due to supply-demand imbalances, a coordinator is responsible for allocating slots. Currently slot schedules exhibit large deviations from requested slot times. Airport capacity is usually expressed in terms of the number of available slots and the demand for these slots often exceeds capacity, but this capacity is rarely used optimally. Slot scheduling models aim to best use capacity so that all airlines are allocated slots as close to their requests as possible, subsequently slots are used more efficiently and delays are minimised. There is large room for improvement in the current slot allocation process.

The first mathematical model to be compliant with scheduling regulations was proposed in 2012. This model aims to minimise the distance between requested and allocated slot times subject to an artificial measure of capacity and turnaround time constraints, at a single airport. This ensures capacity is not exceeded, so delays are minimised, and allows the aircraft sufficient time on the ground to prepare for the next flight. Using this simple formulation, the resulting schedule demonstrates large improvements on current procedures. Following from this, other models have been developed to also incorporate fairness and accessibility restrictions. These encourage flights to remotely located airports and aim to ensure no airline suffers greater displacement from their requested slots. This means all airlines are treated equally and all airports, regardless of size, are accessible. Other models aim to minimise similar objectives, but consider a network of airports. This means that dependencies between airports are accounted for in order to avoid the multiplier effect of delays once one flight is interrupted. Considering a network of airports creates a larger and more complex problem, but this helps to formulate a more realistic representation of the situation at hand.

This report reviews the current slot allocation procedure, detailing each stage necessary to formulate a slot schedule. Additionally, we discuss different allocation models in the surrounding literature, at the single and network level, and use computational results to compare them to the existing methods, as well as one another. Finally, we aim to identify any gaps in the research that present interesting ideas for future investigation.

Further Reading

The models I focussed on for this report are taken from the following papers:

• Zografos, K. G., Salouras, Y., and Madas, M. A. (2012). Dealing with the efficient allocation of scarce resources at congested airports. Transportation Research Part C: Emerging Technologies, 21(1):244- 256.

• Zografos, K. and Jiang, Y. (2016). Modelling and solving the airport slot scheduling problem with efficiency, fairness, and accessibility considerations.

• Castelli, L., Pellegrini, P., Pesenti, R., et al. (2011). Airport slot allocation in europe: economic efficiency and fairness. International journal of revenue management, 6(1-2):28-44.

• Corolli, L., Lulli, G., and Ntaimo, L. (2014). The time slot allocation problem under uncertain capacity. Transportation Research Part C: Emerging Technologies, 46:16-29.

Alexandre Jacquillat opened the STOR-i Annual Conference 2020 in early January. I thoroughly enjoyed his talk on Analytics for Operations, Scheduling and Pricing in Air Transportation so I decided to write an overview of the work he delivered. Alexandre demonstrated applications of both Statistics and Operational Research methods to the transportation industry. I had not witnessed such an application prior to this and I really appreciated this practical use of two topics I am currently studying. To find out more about the STOR-i conference, please read my post that details the event and all of the talks.

Alexandre is an Assistant Professor of Operations Research and Statistics at the MIT Sloan School of Management. His research applies to areas in transportation with the aim to promote efficient scheduling, operations and pricing practices. Alexandre is the recipient of several research awards, including the George B. Dantzig Dissertation Award and the Best Paper Prize in Transportation Science and Logistics from INFORMS.

This talk focussed on work that lies at the interface between analytics and transport, both of which are dynamic and growing industries. Specifically, the air transportation industry currently faces many challenges because they operate at or above capacity in order to avoid wasting any resource or time. This approach leads to flight delays and incurs costs for the airline provider. As the volume of flights increases, there is likely to be more delays set against more sales and profit. However, with fewer flights and hence fewer sales, it is likely that the number of delays will decrease. Using various results from analytical projects, Alexandre explained how they aim to support operations, scheduling and pricing practices in air transportation. In turn, this will improve the efficiency, reliability and profitability of the industry as a whole.

Operations

Alexandre started by discussing how his work has supported operations within the air transportation industry. This involves ensuring making the best use of available capacity. I mentioned above that airports operate at maximum capacity in order to avoid wasting any resource, but this often leads to delays and becomes costly. Alexandre proposes modeling this as an optimisation problem, this aims to minimise flight and passenger delays subject to flight, passenger and capacity constraints. Previously, passenger delays were not accounted for in this problem. When considering a network of flights, there is not a one-to-one correspondence between passenger and flight delays because passengers often travel through connecting flights. Therefore, a minor flight delay may cause a passenger to miss their connection and results in a major overall passenger delay once they reach their final destination. Including a new layer of passenger delays to the model proves to make flight operations more consistent.

Scheduling

Secondly, Alexandre presented ideas to optimally schedule flights. Airlines request a time slot for each of their flights and often they are allocated to a different slot because the demand for a specific slot tends to exceed the capacity. In order to minimise the overall displacement from an airline’s request, Alexandre presented a large-scale optimisation approach to slot allocation. By breaking the large-scale problem into smaller chunks, this delivered high quality, fast solutions compared to the current process. This method delivered optimal, or near-optimal, solutions at some of the largest schedule-coordinated airports. Additionally, Alexandre proposed an integrated model of both scheduling and operations that optimises scheduling in a network of airports but also captures the interdependencies between flight schedules and air traffic flow management.

Pricing

Lastly, Alexandre focussed on tackling the pricing practices in the industry. Often, flights between two destinations are priced the same even though one flight is direct and another has some number of stops for a significant length of time. This means that prices are not competitive. Alexandre outlined an experiment conducted with a global airline to assess a new, competitive pricing strategy. This demonstrated that making some minor changes to the baseline pricing practices results in a significant increase in revenue.     

Alexandre concluded with some ideas for future research prospects, to read more about Alexandre’s research feel free to visit his . I really enjoyed this talk and it encouraged me to read some more into the area, consequently, I have decided to write my first STOR-i research project on ‘Mathematical Models and Algorithms for Allocating Scarce Airport Resources’. The main focus of this project is to review relevant literature, therefore I intend to further investigate aspects of Alexandre’s research.

Future Reading

I have included a couple of papers by Alexandre that I have found interesting relating to the slot scheduling problem in air transportation

• Jacquillat, A. and Odoni, A.R., 2015. An integrated scheduling and operations approach to airport congestion mitigation. Operations Research, 63(6), pp.1390-1410.
  Available at:
• Jacquillat, A. and Vaze, V., 2018. Interairline equity in airport scheduling interventions. Transportation Science, 52(4), pp.941-964.
  Available at: