Collaborative Optimization of Vehicle and Crew Scheduling for a Mixed Fleet with Electric and Conventional Buses

Abstract

Replacing conventional buses with electric buses is in line with the concept of sustainable development. However, electric buses have the disadvantages of short driving range and high purchase price. Many cities must implement a semi-electrification strategy for bus routes. In this paper, a bi-level, multi-objective programming model is established for the collaborative scheduling problem of vehicles and drivers on a bus route served by the mixed bus fleet. The upper-layer model minimizes the operation cost and economic cost of carbon emission to optimize the vehicle and charging scheme; while the lower-layer model tries to optimize the crew-scheduling scheme with the objective of minimizing driver wages and maximizing the degree of bus-driver specificity, considering the impact of drivers’ labor restrictions. Then, the improved multi-objective particle swarm algorithm based on an ε-constraint processing mechanism is used to solve the problem. Finally, an actual bus route is taken as an example to verify the effectiveness of the model. The results show that the established model can reduce the impact of unbalanced vehicle scheduling in mixed fleets on crew scheduling, ensure the degree of driver–bus specificity to standardize operation, and save the operation cost and driver wage.

E-Bus Scheduling

“…Time-based constraints regarding the E-VSP include no time overlap between events (e.g. charging and service trips) assigned to one vehicle (Rogge et al, 2018;Olsen et al, 2020); charging done only within a pre-defined time window (Rogge et al, 2018); travel time feasibility (Wang et al, 2022); and route time feasibility (Perumal et al, 2022).…”

“…Battery capacity and e-bus driving range constraints are battery capacity limitations (Olsen et al, 2020;Josephine et al, 2015); State of Charge (SOC) check to determine whether or not a bus has sufficient remaining energy to complete a trip and the successive deadhead trip (Olsen et al, 2020;Chao et al, 2013;Rogge et al, 2018;C. Tang et al, 2023;Wang et al, 2022) taking into account a safe driving ratio variable (Li et al, 2019); unit distance energy consumption of a trip in relation with running speed and stop density (C. Tang et al, 2023); driving range and maximum distance without recharging (Wang et al, 2022;Perumal et al, 2021;Josephine et al, 2015) on all service arcs (Li et al, 2019); battery renewal constraints (Perumal et al, 2021); minimum SOC energy level threshold when traveling from one stop to another (Perumal et al, 2022); minimum vehicle battery capacity level (Josephine et al, 2015).…”

“…Charging process constraints include recharging can only happen at charging stations (Olsen et al, 2020); buses leave the depot after full charging (Rogge et al, 2018;(Tang et al, 2019); flow constraints of charging infrastructure network (Rogge et al, 2018); at any point the capacity of each refuelling station must be satisfied (Li et al, 2019); buses should not be charged between two trips (C. Tang et al, 2023); re-charging time and needs (Perumal et al, 2021;Wang et al, 2022;Josephine et al, 2015;Perumal et al, 2022); minimum recharging duration (Perumal et al, 2021); the energy provided from the charging station does not exceed the maximum battery capacity (Perumal et al, 2022); a vehicle can only be charged at defined stop points (Josephine et al, 2015); minimum proportion of chargers of each type with respect to the number of electric buses in the fleet (Perumal et al, 2022).…”

“…Crew scheduling and crew requirements constraints involve early, day and late work modes with time shift (Wang et al, 2022); work intensity constraints (Wang et al, 2022); (local) labour regulations (Wang et al, 2022;Perumal et al, 2021); daily driving trips (Wang et al, 2022); driver wages (Wang et al, 2022); maximum duration of a duty without break (Perumal et al, 2021); minimum break duration (breaks often allowed only at certain bus stops) (S.S.G. Perumal et al, 2021); maximum number of driver vehicle changes (Perumal et al, 2021); continuous attendance of vehicles, during idle time (Perumal et al, 2021); every trip is covered by exactly one block and one duty respectively (Perumal et al, 2021); duties are selected to cover deadheads (Perumal et al, 2021).…”

“…Furthermore, monetary constraints, externality constraints and other types of constraints should be taken into account: operation costs (Wang et al, 2022); Time of Use (TOU) power price policy and electricity prices (Wang et al, 2022); carbon emission constraints (Wang et al, 2022); total (vehicles plus chargers) procurement cost not exceeding allocated budget (Perumal et al, 2021;Perumal et al, 2022); a bus cannot be operated after a certain age and has to be salvaged (Perumal et al, 2022), and the End of Life (EOL) of an ebus battery is conventionally defined as a remaining capacity of 80% to prevent operational complications (Rogge et al, 2018); and, the total power consumption during each time period cannot exceed the contracted capacity (Perumal et al, 2022).…”