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The public transport market in most global cities is dominated by diesel buses, which can have significant adverse impacts on the environment and human health. To reach carbon neutrality, many public transport operators are attempting to replace their existing bus fleets with electric buses (EBs). This paper develops a generic bus replacement model to help public transit (PT) operators progressively renew their existing bus fleets so as to reach particular electrification goals within a given planning horizon. Unlike existing studies, our model more comprehensively considers the external costs, which include external climate costs, external health costs and used battery recycling costs/profits. Furthermore, by incorporating different incentives, variants on the model can be adopted to investigate how different government incentives can affect the replacement behaviors of PT operators. Finally, our proposed approach is applied to real-world data from a bus operator in Singapore which is aiming to achieve a 100% cleaner energy bus fleet within 20 years. The experiments indicate that an EB subsidy can effectively accelerate the electrification process, and a 25% EB subsidy could achieve full electrification eight years earlier than if no EB subsidy were applied. Moreover, we explore how the diesel tax and diesel bus (DB) tax affect EB replacement. Our experiments suggest a 10% diesel tax rate can achieve good results but imposing a DB tax will not encourage PT operators to purchase EBs earlier. • A novel model for the bus fleet replacement problem is proposed. • Various external costs that borne by the society and environment are considered. • Our approach evaluates different policy incentives. • Our real case study provides managerial insights for PT operators and policymakers. [ABSTRACT FROM AUTHOR]