Designing Zonal-Based Flexible Bus Services Under Stochastic Demand

Abstract

In this paper, we develop a zonal-based flexible bus services (ZBFBS) by considering both passenger demands’ spatial (origin-destination or OD) and volume stochastic variations. Service requests are grouped by zonal OD pairs and number of passengers per request, and aggregated into demand categories which follow certain probability distributions. A two-stage stochastic program is formulated to minimize the expected operating cost of ZBFBS, in which the zonal visit sequences of vehicles are determined in stage 1, whereas in stage 2, service requests are assigned to either regular routes determined in stage 1 or ad hoc services that incur additional costs. Demand volume reliability and detour time reliability are introduced to ensure quality of the services and separate the problem into two phases for efficient solutions. In phase 1, given the reliability requirements, we minimize the cost of operating the regular services. In phase 2, we optimize the passenger assignment to vehicles to minimize the expected ad hoc service cost. The reliabilities are then optimized by a gradient-based approach to minimize the sum of the regular service operating cost and expected ad hoc service cost. We conduct numerical studies on vehicle capacity, detour time limit and demand volume to demonstrate the potential of ZBFBS, and apply the model to Chengdu, China, based on real data to illustrate its applicability.

Trends in passenger transport optimisation

“…Some authors proposed exact solution methods, such as branch‐and‐cut (Guo et al., 2019; Wu et al., 2022b), branch‐and‐price (B&P) (Zhang et al., 2021) and branch‐and‐bound (Huang et al., 2020b), sometimes combined with Lagrangian relaxation (Tong et al., 2017). Non‐linear models are usually solved by employing linearization techniques (Huang et al., 2020c; Gong et al., 2021) and approximation techniques (Lee et al., 2021b; Sangveraphunsiri et al., 2022). As expected, given the complexity, as well as the flexible and time‐sensitive nature of the problems tackled, the large majority of the solution approaches are heuristics, such as local search (LS; Guo et al., 2020; Li et al., 2022a).…”

Vehicle routing for customized on-demand bus services

“…In that study, a branch-and-price based algorithm and a CG-based heuristic are implemented to solve small-scale and large-scale instances, respectively. To handle uncertain demand environments, Lee et al (2021a) propose and develop a zone-based flexible bus service that considers the uncertainties of passenger volume and origindestination requirements; they further propose a two-stage stochastic programing model and gradient-based solution method to minimize the costs of regular service operations and expected ad hoc services. The same research team further considers the elastic feature of demands in this flexible service (Lee et al 2021b).…”

Flexible Scheduling Model of Bus Services between Venues of the Beijing Winter Olympic Games

“…Constraints (7) to (9) indicate that the bus should satisfy all passenger demands; the bus is not allowed to return from the drop-of depot to the pickup depot after fnishing each pickup service. Constraints (10) to (13) ensure that the bus starts from the depot and must return to the depot. Constraint (14) implies that more than one bus can be sent to serve passengers if these demands exceed the bus capacity.…”

“…Myungseob et al [12] considered the stochastic variability in travel times and wait times of fexible buses and proposed probabilistic optimization models to integrate and coordinate bus transit services for one terminal and multiple local regions. Lee et al [13] considered passenger demands' spatial (origin-destination) and stochastic variation of volume and developed a zonal-based fexible bus service. Tas [14] also focused on the fexible time window constraint, in which vehicles should serve customers before and after the earliest and latest time window boundaries, respectively.…”