Optimizing Vehicle Scheduling Based on Variable Timetable by Benders-and-Price Approach

Abstract

In practice, vehicle scheduling is planned on a variable timetable so that the departure times of trips can be shifted in tolerable ranges, rather than on a fixed timetable, to decrease the required fleet size. This paper investigates the vehicle scheduling problem on a variable timetable with the constraint that each vehicle can perform limited trips. Since the connection-based model is difficult to solve by optimization software for a medium-scale or large-scale instance, a designed path-based model is developed. A Benders-and-Price algorithm by combining the Benders decomposition and column generation is proposed to solve the LP-relaxation of the path-based model, and a bespoke Branch-and-Price is used to obtain the integer solution. Numerical experiments indicate that a variable timetable approach can reduce the required fleet size with a tolerable timetable deviation in comparison with a fixed timetable approach. Moreover, the proposed algorithm is greatly superior to GUROBI in terms of computational efficiency and guarantees the quality of the solution.

Optimizing Train Formation Problem With Car Flow Routing and Train Routing by Benders-and-Price Approach

“…A. This approach has been applied to other integrated problems in transportation, such as aircraft routing and crew scheduling problem [20], and vehicle scheduling based on a variable timetable problem [21]. For more literature about this approach, we refer the reader to Mercier et al [22], Restrepo et al [23], and Lee and Han [24].…”

Vehicle scheduling for on-demand vehicle fleets in macroscopic travel demand models

“…Standard models and solution approaches for vehicle scheduling in public transport are summarized in Bunte and Kliewer (2009). Recent vehicle scheduling approaches usually incorporate problem specific aspects such as variable timetables (Desfontaines and Desaulniers 2018;Lan et al 2019) or limited range of electric vehicles and recharging strategies (Wen et al 2016;Rogge et al 2018). To be able to find good schedules for realistic instances, elaborate solution methods are proposed.…”

“…To be able to find good schedules for realistic instances, elaborate solution methods are proposed. For example, Desfontaines and Desaulniers (2018) rely on column generation, and Lan et al (2019) combine Benders decomposition with a branch-and-price approach. With these methods, instances with up to 2100 vehicle trips could be solved within less than 1 h to optimality or close to optimality.…”