Joint optimization of capacity expansion timing and increment in airport terminals: addressing stochastic demand and logistic growth

Abstract

Airport terminal capacity expansion planning is important yet challenging due to the stochastic factors inherent in long-term passenger demand growth. Existing studies often assume exponential demand growth, which can oversimplify real-world dynamics. For instance, passenger demand at Phoenix Sky Harbor International Airport (PHX) initially experienced exponential growth, but the demand growth rate has slowed. This trend is more accurately captured by a stochastic logistic growth process. In this paper, we propose a framework that jointly optimizes two related decisions: the expansion timing and the capacity increment, to maximize expected cumulative cost savings under stochastic logistic demand growth. Recognizing that airport authorities hold an “option” to invest in capacity expansion, granting them the right but not the obligation to do so, we adopt a real options approach. Numerical experiments for PHX validate the approach, revealing a congestion effect where added capacity initially reduces congestion and increases cost savings; but as demand approaches the expanded capacity, cost savings decline. Additionally, findings suggest interrelations between variables: a higher demand growth rate correlates with a smaller trigger demand but a larger capacity level, while higher volatility rates result in larger values for both trigger demand and capacity level. Compared to capacity expansion decisions under geometric Brownian motion (GBM) demand modeling, which tends to overestimate future demand growth, our approach better captures long-term saturation effects and provides more realistic results. This methodology can be effectively applied to other capacity expansion planning and investment decision problems in transportation.