Mixed bus fleet scheduling under range and refueling constraints

Document Type

Journal Article

Publication Date


Subject Area

place - asia, place - urban, mode - bus, economics - operating costs, economics - subsidy, infrastructure - fleet management, infrastructure - vehicle, infrastructure - maintainance, operations - scheduling, technology - emissions, planning - methods


Bus scheduling, Mixed fleet, Electric bus, Driving range, Refueling/charging


This paper develops a formulation for the multiple depot (MD) vehicle scheduling problem with multiple vehicle types (MVT), including electric buses (EBs), under range and refueling constraints. A novel approach is developed to generate the feasible time-space-energy (TSE) network for bus flow and time-space (TS) network for passenger flow, where the range and refueling issues can be precisely addressed. We then introduce the external cost associated with emissions, and investigate the minimum total system cost to operators and passengers by scheduling the bus fleet and locating the refueling stations. The problem is formulated as an integer linear program (ILP) to find the global optimal solution. For computational efficiency, we develop a simplified formulation based on the TS bus flow network to handle larger-scale problems for approximate solutions. We apply the methods to bus services in Hong Kong to analyze the bus fleet size needed, operational cost, passenger cost, and emissions generated by buses with multiple energy sources. Through the formulation, we study the implications of government subsidy for EBs, bus scheduling in Low Emission Zone (LEZ), and safe driving ratio design for bus refueling.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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