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• A mixed-integer non-linear and nonconvex programming (MINL&NCP) model, which captures the unique feature of the EBCS problem is developed. We further approximate it by two novel MILP models in a smart way. • Non-linear charging profile and battery degradation effect are considered. • Three tailored valid inequalities are proposed to enhance the solution efficiency. • Extensive numerical experiments are carried out to seek valuable managerial insights for the public transport operators. This study deals with a fundamental electric bus charging scheduling (EBCS) problem for a single public transport route by considering the nonlinear electric bus (EB) charging profile and battery degradation effect under the partial charging policy, which allows EBs to be charged any length of time and make good use of dwell times between consecutive trips. Given a group of trip tasks for an EB fleet and charger type, the problem is to minimize the total cost for a public transport operator of providing peak-hour bus services for a focal single public transport route by simultaneously determining the EB-to-trip assignment and EB charging schedule with charger type choice subject to the necessary EB operational constraints. We first build a mixed-integer nonlinear and nonconvex programming (MINL&NCP) model for the EBCS problem. To effectively solve the MINL&NCP model to global optimality, we subsequently develop two mixed-integer linear programming (MILP) models by means of linearization and approximation techniques. To accelerate the solution efficiency, we further create three families of valid inequalities depending on the unique features of the problem. A real case study based on the No.171 bus route in Singapore is conducted to demonstrate the performance of the developed models. Extensive numerical experiments are carried out to seek valuable managerial insights for public transport operators. [ABSTRACT FROM AUTHOR]

This paper investigates the electric bus charging facility planning (EB-CFP) problem for a bus transit company operating a heterogeneous electric bus (EB) fleet to provide public transportation services, taking into account uncertainties in both EB travel time and battery degradation. The goal of the EB-CFP problem is to determine the number and type of EB chargers that should be deployed at bus terminals and depots to meet daily EB charging demand while minimizing total cost. The problem is formulated as a two-stage stochastic programming model, with the first stage determining the EB charger deployment scheme and the second stage estimating the EB daily operational cost with respect to a predetermined EB trip timetable for a given EB charger deployment scheme. To effectively address the second stage problem, a multi-agent EB transit simulation system that mimics the daily EB operation process is developed. We then design two heuristic methods, the reinforcement learning (RL)-based method and the surrogate-based optimization (SBO), that use the developed multi-agent EB transit simulation system to solve the two-stage stochastic programming model for large-scale instances. Lastly, we run a series of experiments on a fictitious EB transit network and a real-world EB transit network in Singapore to evaluate the performance of the models and algorithms. In order to improve the performance of the EB transit system, some managerial insights are also provided to urban bus transit companies. • A two-stage stochastic model considering uncertainties is proposed. • A multi-agent simulation system is created to mimic the daily electric bus operations. • A reinforcement learning method and a surrogate-based optimization are proposed. • Experiments are performed to seek managerial insights for the operators. [ABSTRACT FROM AUTHOR]

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]

Caregivers of children in the child welfare system (CWS) often need more support in their parenting efforts. Some of these caregivers only need parenting related advices, whereas others may need more intensive training to prevent recurrence of maltreatment. Few parenting interventions can be delivered to both groups of caregivers with satisfying results. This study investigated the treatment change associated with Positive Parenting Programme (Triple P) on 83 caregivers who completed either the Level 4 version or the Level 5 (Pathways) version of the programme (mean age = 40.6 years). Repeated measure analysis showed significant improvement in common outcomes such as parenting practices, children's behaviour problems, parental satisfaction, and parents' psychological adjustment for both groups of caregivers. However, changes on Level 5 (Pathways) specific outcomes were not statistically significant. Further analysis suggested this lack of change may be due to the distinct profiles of dropouts in Level 5 Triple P. Study limitation and its implication for future research as well as programme development was also discussed. [ABSTRACT FROM AUTHOR]

• Investigate an integrated planning problem for electric-bus systems. • Incorporate muliple practical factors and requirements of electric-bus operations. • Develop robust optimization model to address energy consumption uncertainty. • Conduct empirical study in Singapore and provide managerial insights for operators. Public transit (PT) operators have been replacing existing bus fleets with electric buses (EBs) to achieve carbon neutrality. To ensure a cost-effective EB operation with driving range anxiety, fast en-route charging technology has been adopted to recharge EBs during the dwell time. This study aims to determine an integrated robust planning for EB systems, by simultaneously optimizing en-route charger deployment, charging schedule and EB battery configuration, with the goal to minimize the total cost. A deterministic optimization model was first formulated that incorporates multiple practical factors such as weight-related energy consumption and charging capacity. Then we move forward to build robust optimization models to consider the energy consumption uncertainty. The developed models are transformed into equivalent and tractable formulations, which can be solved efficiently by off-the-shelf solvers. Lastly, numerical experiments demonstrate that the proposed models can provide an optimal and robust EB system planning solution for PT operators. [ABSTRACT FROM AUTHOR]