An Integrated Scheduling Model for Airport Apron-Bus Drivers Under Stochastic Demand

Airport apron buses, which shuttle passengers between terminal gates and remotely parked aircraft, are vital for efficient ground operations. However, flight delays and disruptions make demand for apron-bus services uncertain and time-varying, creating substantial challenges for planning driver capacity and work schedules. To tackle this challenge, we develop an Integrated Stochastic-Flexible Planning Model (ISFPM), formulated as a mixed-integer linear program (MILP), that simultaneously optimizes workforce sizing, duty scheduling, and roster assignment for apron-bus drivers. The objective is to minimize the sum of labor costs and the expected penalty for understaffing. This penalty is evaluated under the assumption that driver demand in each period follows a Poisson-binomial distribution, which is derived from probabilistic models of flight delays. For computational efficiency, we reformulate the expected penalty term using continuity-corrected normal approximations based on the cumulative distribution function (CDF). Furthermore, we incorporate practical workforce flexibility features, including hourly-granularity duty start times and heterogeneous workday patterns across roster groups. The computational study is based on Beijing Capital International Airport and accompanied by deidentified replication materials. Across 100 materialized baseline scenarios, the ISFPM uses 148 drivers instead of the 175-driver deterministic fixed-shift benchmark, reducing average management cost by 21.9% and passenger waiting time by 85.6%. Across 18 representative-day scenarios with correlated and severe disruptions, it reduces mean management cost by 15.8% and passenger waiting time by 53.6%. The disruption-scenario analysis also indicates that deterministic flexible staffing attains the lowest waiting time at a higher cost, while common apron travel-time shocks reduce the service advantage of the ISFPM.