Resource allocation for an air-rail-integrated co-modality platform considering both demand and supply uncertainties

The co-modal mode, i.e., passenger-and-freight mixed transportation, has received increasing interest, given the rapid growth of parcel volume and its potential to save transportation costs. This paper examines an air-rail-integrated co-modal mode that utilizes the excess capacity of passenger trains and flights considering uncertainties in both supply and demand. On the supply side, uncertainty arises from travel time delays of passenger trains and flights. On the demand side, while historical data on cargo orders are available, such as volume distribution between each origin and destination pair, the daily cargo orders/demands remain uncertain and will be revealed in real-time. We aim to dynamically allocate these resources (excess capacity of trains and flights) to serve cargo orders while effectively accommodating uncertainties. To address this problem, a two-stage stochastic programming model is developed to minimize the total costs associated with cargo transportation, holding, transshipment, delays, and ad-hoc service options (when the co-modal mode is unavailable). The sample average approximation solution approach, embedded with an adaptive large neighborhood search algorithm, is employed to solve the problem. The above model and algorithm are implemented in a rolling horizon framework to make time-dependent resource allocation decisions. The test instances are generated based on rail and air transportation data in Hong Kong (with Hong Kong West Kowloon Station and Hong Kong International Airport). Numerical studies and sensitivity analysis are conducted to evaluate (i) the benefits of the air-rail-integrated co-modality, (ii) the effectiveness of the proposed solution algorithm, and (iii) the impact of demand/supply characteristics on the air-rail-integrated co-modality operation.