Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributionally Robust Airport Ground Holding Problem under Wasserstein Ambiguity Sets

Haochen Wu, Alexander S. Estes, Max Z. Li

Abstract

Ground Delay Programs (GDPs) mitigate demand-capacity imbalances by holding flights on the ground when an airport's arrival capacity is reduced, thereby reducing costly airborne holding. A central challenge is that day-to-day demand-capacity balancing relies on accurate predictions of airport capacities. However, these predictions are deeply uncertain: forecast errors, operational disruptions, and climate change-driven shifts in weather severity can induce distribution shifts in capacity outcomes. Thus, policies optimized for a single predicted distribution may be brittle out of sample. We address this challenge by developing a \emph{distributionally robust} framework for the single airport ground holding problem (dr-SAGHP). We also propose a method integrates Kelly's cutting plane method with the integer L-shaped method, and that is applicable more broadly to two-stage distributionally robust integer programs with relatively complete recourse and continuous second-stage decision variables. Our method includes a novel dual bisection and primal recovery algorithm that makes use of the structure of the distributionally robust integer program in order to quickly generate subgradients required by Kelly's cutting plane method. In computational experiments, our proposed algorithm delivers up to two orders-of-magnitude speedups compared to solving the convex reformulation directly, while maintaining negligible optimality gaps. We generate capacity scenarios via Gaussian process regression and evaluate out-of-sample performance by perturbing the posterior mean and variance. The numerical experiment results show that dr-SAGHP delivers significant out-of-sample gains under moderate-to-severe shifts, improving the resilience and effectiveness of GDP decision-making under capacity uncertainty.

Distributionally Robust Airport Ground Holding Problem under Wasserstein Ambiguity Sets

Abstract

Ground Delay Programs (GDPs) mitigate demand-capacity imbalances by holding flights on the ground when an airport's arrival capacity is reduced, thereby reducing costly airborne holding. A central challenge is that day-to-day demand-capacity balancing relies on accurate predictions of airport capacities. However, these predictions are deeply uncertain: forecast errors, operational disruptions, and climate change-driven shifts in weather severity can induce distribution shifts in capacity outcomes. Thus, policies optimized for a single predicted distribution may be brittle out of sample. We address this challenge by developing a \emph{distributionally robust} framework for the single airport ground holding problem (dr-SAGHP). We also propose a method integrates Kelly's cutting plane method with the integer L-shaped method, and that is applicable more broadly to two-stage distributionally robust integer programs with relatively complete recourse and continuous second-stage decision variables. Our method includes a novel dual bisection and primal recovery algorithm that makes use of the structure of the distributionally robust integer program in order to quickly generate subgradients required by Kelly's cutting plane method. In computational experiments, our proposed algorithm delivers up to two orders-of-magnitude speedups compared to solving the convex reformulation directly, while maintaining negligible optimality gaps. We generate capacity scenarios via Gaussian process regression and evaluate out-of-sample performance by perturbing the posterior mean and variance. The numerical experiment results show that dr-SAGHP delivers significant out-of-sample gains under moderate-to-severe shifts, improving the resilience and effectiveness of GDP decision-making under capacity uncertainty.
Paper Structure (34 sections, 6 theorems, 65 equations, 5 figures, 6 tables, 3 algorithms)

This paper contains 34 sections, 6 theorems, 65 equations, 5 figures, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Literature Review
  4. Stochastic Air Traffic Flow Management
  5. Distributionally Robust Optimization
  6. Climate Change Impacts
  7. The Distributional Robust Single Airport Ground Holding Problem
  8. Deterministic and Two-Stage Stochastic formulations of SAGHP
  9. Wasserstein Ambiguity Set for Discrete Measures
  10. Decomposition Approach
  11. Preliminaries
  12. Cutting plane approach
  13. Calculating the worst-case distribution
  14. From LP Relaxation to Integer Program
  15. Numerical Experiments and Discussion
  16. ...and 19 more sections

Key Result

Proposition 4.1

Let $x$ be any point in $\mathbb{R}^{\mathbf{n}}$ such that $\mathbf{A}\mathbf{x} = \mathbf{b}$ and $\mathbf{x} \geq 0$. Then, where $\partial_{\mathbf{x}} h(\mathbf{x},\xi)$ denotes the subdifferential of $h(\cdot, \xi)$ at $\mathbf{x}$.

Figures (5)

  • Figure 1: In-sample performance of sp-SAHP and dr-SAGHP with various epsilons.
  • Figure 2: Out-of-sample performance comparison in expected costs between dr-SAGHP and s-SAGHP under different levels of mean reduction.
  • Figure 3: Out-of-sample performance comparison in CVAR between dr-SAGHP and s-SAGHP under different levels of mean reduction.
  • Figure 4: Out-of-sample performance comparison in expected cost between dr-SAGHP and s-SAGHP under different levels of capacity variance increase.
  • Figure 5: Out-of-sample performance comparison in CVAR between dr-SAGHP and s-SAGHP under different levels of capacity variance increase.

Theorems & Definitions (8)

  • Proposition 4.1
  • Proposition 4.2
  • Proposition 4.3
  • Proposition 4.4
  • theorem 1
  • theorem 2: Danskin's Theorem bertsekas1971control
  • proof
  • proof