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Optimization of electric bus vehicle scheduling and charging strategies under Time-of-Use electricity price

TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2025年 196卷

作者： Lu, Zhaoyang Xing, Tianyi Li, Yanfeng Southwest Jiaotong Univ Sch Econ & Management Chengdu 610031 Peoples R China Serv Sci & Innovat Key Lab Sichuan Prov Chengdu 610031 Peoples R China

With the growing awareness of environmental protection and energy conservation, more and more cities choose to utilize electric buses (EBs) in their public transit systems. Due to the limitations of battery technology, many fully charged EBs are not enough to complete their daily tasks, which must be charged twice or more times per day. Besides, many cities encourage the offpeak electricity power consumption, and the charging cost of EBs during peak hours is often extremely high. From an economic viewpoint, it is thus one practical and urgent problem on how to decide the fleet size of EBs and organize their charging schedules for the bus companies. To solve this problem, this manuscript builds a mixed-integer programming (MIP) model via taking the scheduling and charging constraints of EBs into consideration. Also, one dynamic label setting-based branch and price (DLS-BP) algorithm is proposed accordingly, whose efficiency is further verified and compared with two heuristic algorithms via some numerical experiments.

关键词： Electric bus Charging price mixed-integer programming TOU Branch and price

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Electric bus charging station location selection problem with slow and fast charging

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APPLIED ENERGY 2025年 382卷

作者： Gkiotsalitis, Konstantinos Rizopoulos, Dimitrios Merakou, Marilena Iliopoulou, Christina Liu, Tao Cats, Oded Natl Tech Univ Athens Sch Civil Engn Dept Transportat Planning & Engn 9 Iroon Polytech StrZografou Campus Athens 15780 Greece Univ Patras Dept Civil Engn Rion 26504 Greece Southwest Jiaotong Univ Natl Engn Lab Integrated Transportat Big Data Appl Chengdu 611756 Peoples R China Southwest Jiaotong Univ Sch Transportat & Logist Natl United Engn Lab Integrated & Intelligent Tran Chengdu 611756 Peoples R China Delft Univ Technol Fac Civil Engn & Geosci Bldg 23Stevinweg 1 NL-2628 CN Delft Netherlands

To facilitate the shift from conventional to electric buses, the required charging infrastructure must be deployed. This study models the charging station location selection problem for fixed-line public transport services consisting of electric buses. The model considers the deadheading time of electric buses between the final stop of their trip and the locations of the potential charging stations with the objective of minimizing vehicle running costs. The problem is solved at a strategic level;therefore, several parameters of day-to-day operations, such as deadheading distances, are included as aggregate data considering their average values. In addition, it considers different charger types (slow and fast), which are subject to a day-ahead scheduling of the charging sessions of the buses. The developed model is a mixed-integer nonlinear program, which is reformulated as a mixed-integer linear program and can be solved efficiently for large networks with more than 1940 bus trips and 336 charging installation options. The model is applied in the Athens metropolitan area, demonstrating its potential as a decision support tool for selecting charging station locations and charger types in large public transport networks.

关键词： Electric buses Charging station location selection Minimum deadheading Charging time slots mixed-integer programming

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Optimizing Electric Cold-Chain Vehicle Scheduling for Sustainable Urban Logistics: A Novel Framework Balancing Freshness and Vehicle Charging

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ENERGIES 2025年第7期18卷 1705-1705页

作者： Gan, Zhenkun Dong, Peiwu Fu, Zhengtang Ju, Yanbing Shen, Yajun Beijing Inst Technol Sch Econ Beijing 100081 Peoples R China Tsinghua Univ Sch Environm Beijing 100084 Peoples R China Beijing Inst Technol Sch Management Beijing 100081 Peoples R China

Cold-chain logistics, characterized by high energy consumption and significant emissions, pose a critical challenge for the green transformation of global transportation. Electric cold-chain vehicles have emerged as a promising solution to reduce carbon emissions in urban logistics. However, their scheduling is highly complex due to the need to balance freshness and charging requirements, presenting operational challenges for cold-chain companies. To address this issue, this paper proposes an optimization model and algorithm for the efficient scheduling of these innovative electric cold-chain vehicles. First, we define the unique features of these vehicles and establishes an operational framework tailored to cold-chain logistics. Subsequently, we develop a mixed-integer programming model to optimize freshness preservation. Additionally, we design a state-of-the-art algorithm based on an improved genetic algorithm to solve the scheduling model effectively. Numerical experiments conducted using operational data from Shanghai, China, validate the proposed method and algorithm. This study provides valuable insights and tools to support the green transformation of urban cold-chain logistics and contributes to the reduction of urban carbon emissions.

关键词： electric cold-chain vehicles carbon reduction charging constraints freshness loss mixed-integer programming green transformation

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A multi-level rescheduling approach for a dynamic remote operations scheduling problem

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2025年第8期63卷 2711-2740页

作者： Castelletti, Annalisa Moreschini, Lorenzo Corvaglia, Marzia Mansini, Renata Univ Brescia Via Branze 38 I-25123 Brescia Italy Antares Vis Ltd Brescia Italy

In this paper, we tackle a dynamic scheduling problem faced by a large international company. The problem involves assigning installation projects arriving over time to specialised technicians who execute them remotely. Each project consists of several tasks having processing times, release dates, and execution deadlines. The company needs to assign projects to technicians and schedule tasks complying with technicians' skills, precedence constraints between tasks, and tasks requiring multiple technicians simultaneously. The problem is dynamic as new projects and tasks become available over time, requiring their allocation to technicians. We formulate the offline problem as a mixed integer linear program that minimises the makespan, and we address the dynamic version solving restricted problems within a rolling horizon framework. The approach systematically implements different levels of schedule adjustment to incorporate new information. To study scalability, we validate our algorithm by using both real-world and synthetic simulations demonstrating its efficiency and effectiveness. Additionally, we provide interesting managerial insights for the company.

关键词： Periodic predictive-reactive rescheduling rolling horizon mixed-integer programming makespan in parallel and identical machines machine eligibility schedule generation schemes

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Fast Task Scheduling With Model Predictive Control Integrating a Priority-Based Heuristic

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IEEE ACCESS 2025年 13卷 14499-14515页

作者： Liberati, Francesco Donsante, Manuel Cirino, Chiara Maria Francesca Tortorelli, Andrea Sapienza Univ Rome Dipartimento Ingn Informat Automat & Gestionale An I-00185 Rome Italy eCampus Univ Dipartimento Sci Teor & Applicate DiSTA I-22060 Novedrate Italy

This paper presents a scalable Model Predictive Control (MPC) algorithm for task scheduling and real time re-scheduling. The use case motivating the work is given by the problem of managing the integration activities involved in the final assembly of the Vega rocket at the European space center in Kourou, French Guiana. There are two main objectives. The algorithm shall suggest to the planning operators an optimized scheduling of the activities, i.e., one which minimizes the total completion time (the makespan), while satisfying all the applicable constraints. In addition, the algorithm shall provide in real time an update of the planning, in case some unforeseen events require a re-scheduling of the activities. While a standard application of mixed-integer optimization would not be feasible in practice due to the combinatorial complexity of the problem, the scalable MPC algorithm proposed in this paper retains all the flexibility and modelling power of optimization-based techniques, and is almost as fast as the state of the art scheduling heuristics, which in real scenarios can provide a sub-optimal solution in few seconds, or less. Extensive simulations on randomly generated realistic scenarios are carried out to validate the proposed approach. On average, the proposed MPC algorithm decreased by nearly 2% the makespan, compared to a state of the art scheduling heuristic, while having a comparable solving time, in the order of milliseconds, and while retaining (contrary to heuristics) all the flexibility and modelling power of the optimization based approaches (which took several hours to run on the test scenarios).

关键词： Task scheduling assembly lines makespan reduction makespan reduction model predictive control model predictive control global optimization global optimization mixed-integer programming mixed-integer programming scheduling heuristic scheduling heuristic greatest rank positional weight greatest rank positional weight greatest rank positional weight

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mixed-integer linearity in nonlinear optimization: a trust region approach

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OPTIMIZATION LETTERS 2025年 1-22页

作者： De Marchi, Alberto Univ Bundeswehr Munich Inst Appl Math & Sci Comp Dept Aerosp Engn Werner Heisenberg Weg 39 D-85577 Neubiberg Germany

Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential mixed-integer linearization with trust region safeguard, computing feasible iterates via calls to a generic mixed-integer linear solver. Convergence to critical, possibly suboptimal, feasible points is established for arbitrary starting points. Finally, we present numerical applications in nonsmooth optimal control and optimal network design and operation.

关键词： mixed-integer programming Nonlinear programming Successive linearization schemes Trust region methods

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Partially adaptive multistage stochastic programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第1期321卷 192-207页

作者： Kayacik, Sezen Ece Basciftci, Beste Schrotenboer, Albert H. Ursavas, Evrim Univ Groningen Fac Econ & Business Dept Operat Groningen Netherlands Univ Iowa Tippie Coll Business Dept Business Analyt Iowa City IA 52242 USA Eindhoven Univ Technol Sch Ind Engn Operat Planning Accounting & Control Grp Eindhoven Netherlands

Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, organizations are not able to be fully flexible, as decisions cannot be revised too frequently in practice. Consequently, decision commitment becomes crucial to ensure that initially made decisions remain unchanged for a certain period of time. This paper introduces partially adaptive multistage stochastic programming, a new optimization paradigm that strikes an optimal balance between decision flexibility and commitment by determining the best stages to revise decisions depending on the allowed level of flexibility. We introduce a novel mathematical formulation and theoretical properties eliminating certain constraint sets. Furthermore, we develop a decomposition method that effectively handles mixed-integer partially adaptive multistage programs by adapting the integer L-shaped method and Benders decomposition. Computational experiments on stochastic lot-sizing and generation expansion planning problems show substantial advantages attained through optimal selections of revision times when flexibility is limited, while demonstrating computational efficiency attained by employing the proposed properties and solution methodology. By adhering to these optimal revision times, organizations can achieve performance levels comparable to fully flexible settings.

关键词： Stochastic programming Multistage stochastic optimization mixed-integer programming Lot-sizing Generation expansion planning

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A HYBRID METAHEURISTIC METHOD TO OPTIMIZE THE TOTAL WEIGHTED TARDINESS AND DELIVERY COST FOR AN INTEGRATED PRODUCTION AND DISTRIBUTION SCHEDULING MODEL IN SUPPLY CHAIN MANAGEMENT

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2025年第3期21卷 2396-2415页

作者： Zhao, Lin Peng, Zhihao Pirozmand, Poria Dalian Neusoft Univ Informat Sch Comp & Software Dalian Peoples R China Zhejiang Yuexiu Univ EIT Data Sci & Commun Coll Shaoxing Peoples R China Zhejiang Yuexiu Univ New Zealand Res Ctr Shaoxing Peoples R China Holmes Inst Fac Higher Educ Sydney NSW Australia

Supply Chain Management (SCM) is one of the issues that scholars have studied for many years, both theoretically and practically, and given the subject's breadth and variety, it has received a great deal of research and is still the focus of a great deal of study. An integrated production and distribution scheduling problem in a single customer mode for the "production for an ordering" system in a supply chain is a subproblem of SCM. In this problem, a manufacturer receives orders from a customer and processes them on a machine then sends them to the customer in batches. Sending batches of orders will reduce delivery costs but may increase the lateness of some orders. The goal is to sequence the processing of tasks and determine their classification for delivery so that the total weight of tasks and delivery costs are minimized. In this paper, two new linear programming models, including mixed-integer programming (MIP) and mixed-integer Nonlinear programming (MINP) models, as well as a new Heuristic Algorithm (HA), are proposed to solve this Np-hard problem. In order to evaluate the performance of these three methods, computational tests have been performed using the experimental design of 8340 different case studies to show their effectiveness and speed in solving production and distribution scheduling problems in SCM. The experimental results show the efficiency of the HA that could solve 45.13% of problems with a maximum solving time of 0.05917s which is much faster than MIP and MINLP.

关键词： Supply chain management distribution scheduling mixed-integer programming heuristic algorithm

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An exact method to solve the flex-route transit operational planning problem considering energy consumption

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2025年

作者： Li, Mingyang Tang, Jinjun Feng, Tao Cent South Univ Sch Traff & Transportat Engn Smart Transportat Key Lab Hunan Prov Changsha Peoples R China Southwest Jiaotong Univ Sch Transportat & Logist Natl United Engn Lab Integrated & Intelligent Tran Chengdu 610031 Peoples R China Hong Kong Polytech Univ Fac Business Dept Logist & Maritime Studies Hong Kong Peoples R China

In recent years, the flex-route transit (FRT) has become increasingly popular due to its convenience, especially in scenarios where transportation demands are sparse or dispersed. However, due to growing concerns about greenhouse gas emissions, reducing the energy consumption of vehicle travel has emerged as a critical issue. To this end, this paper aims to address the flex-route transit operational planning problem with energy consumption (FRTOPP-EC) through a mixed-integer programming (MIP) formulation. The objective is to minimize the energy consumption of all deployed vehicles by optimising their routes. Given the computationally intractable nature of FRTOPP-EC, we develop a branch-and-price (BAP) algorithm to solve it exactly. To tackle the pricing problem efficiently arising in the proposed algorithm, a tailored label correcting algorithm (LCA) is designed. Computational experiments are conducted using benchmark instances derived from a real-life system of FRT. The results indicate that our BAP algorithm outperforms the commercial solver (e.g. CPLEX) in terms of solution quality, the size of problems it can solve, and computational efficiency. Furthermore, comparative results with the commonly used heuristic insertion algorithm (HIA) underscore the superior effectiveness of our BAP algorithm. Finally, extension experiments are discussed to offer managerial insights for employers.

关键词： Flex-route transit operational planning energy consumption mixed-integer programming branch-and-price

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On the split closure of the periodic timetabling polytope

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MATHEMATICAL programming 2025年 1-43页

作者： Lindner, Niels Masing, Berenike Free Univ Berlin Berlin Germany Zuse Inst Berlin Berlin Germany

The Periodic Event Scheduling Problem (PESP) is the central mathematical tool for periodic timetable optimization in public transport. PESP can be formulated in several ways as a mixed-integer linear program with typically general integer variables. We investigate the split closure of these formulations and show that split inequalities are identical with the recently introduced flip inequalities. While split inequalities are a general mixed-integer programming technique, flip inequalities are defined in purely combinatorial terms, namely cycles and arc sets of the digraph underlying the PESP instance. It is known that flip inequalities can be separated in pseudo-polynomial time. We prove that this is best possible unless P=NP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {P}=\hbox {NP}$$\end{document}, but also observe that the complexity becomes linear-time if the cycle defining the flip inequality is fixed. Moreover, introducing mixed-integer-compatible maps, we compare the split closures of different formulations, and show that reformulation or binarization by subdivision do not lead to stronger split closures. Finally, we estimate computationally how much of the optimality gap of the instances of the benchmark library PESPlib can be closed exclusively by split cuts, and provide better dual bounds for five instances.

关键词： Periodic event scheduling problem Periodic timetabling Split closure mixed-integer programming

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