Scheduling of airport runway operations using stochastic branch and bound methods

• We present a solution methodology for the stochastic runway scheduling problem.
• The stochastic branch and bound algorithm is used find optimal/good sequences.
• A method to dynamically update the sample sizes for bound estimation is proposed.
• Algorithm gives solutions with 5–7% shorter makespan than deterministic model.

In this paper we present a solution methodology based on the stochastic branch and bound algorithm to find optimal, or close to optimal, solutions to the stochastic airport runway scheduling problem. The objective of the scheduling problem is to find a sequence of aircraft operations on one or several runways that minimizes the total makespan, given uncertain aircraft availability at the runway. Enhancements to the general stochastic branch and bound algorithm are proposed and we give the specific details pertaining to runway scheduling. We show how the algorithm can be terminated early with solutions that are close to optimal, and investigate the impact of the uncertainty level. The computational experiment indicates that the sequences obtained using the stochastic branch and bound algorithm have, on average, 5–7% shorter makespans than sequences obtained using deterministic sequencing models. In addition, the proposed algorithm is able to solve instances with 14 aircraft using less than 1 min of computation time.