Technology Category
Planning, Routing, and Scheduling: Mixed Discrete/Continuous PlanningConstraint Satisfaction and Optimization: Mixed Discrete/Continuous OptimizationSearch and Optimization: Mixed Discrete/Continuous Search
An exact approach for the multi-depot electric vehicle scheduling problem
🤖 AI Summary
This paper addresses the multi-depot electric bus scheduling problem, formulating a multi-objective optimization model that minimizes fleet size, number of charging events, and total energy consumption to support the transition from diesel to zero-emission public transport. Methodologically, it introduces a novel graph-based modeling approach without explicit time-indexed variables and proposes scalable mixed-integer linear programming (MILP) formulations: a 3-index model and a 2-index model enhanced with branch-and-cut techniques, both enabling Pareto-front quantification for objective trade-offs. Contributions include the first integrated treatment of partial charging, lexicographic optimization, and multi-depot constraints. Computational experiments on an 80-trip benchmark instance demonstrate that the 3-index model efficiently solves instances with fewer depots, while branch-and-cut substantially expands the solvable problem scale in multi-depot settings. The framework delivers quantifiable decision support for fleet sizing and charging infrastructure planning.
Technology Category
Application Category
📝 Abstract
The"avoid - shift - improve"framework and the European Clean Vehicles Directive set the path for improving the efficiency and ultimately decarbonizing the transport sector. While electric buses have already been adopted in several cities, regional bus lines may pose additional challenges due to the potentially longer distances they have to travel. In this work, we model and solve the electric bus scheduling problem, lexicographically minimizing the size of the bus fleet, the number of charging stops, and the total energy consumed, to provide decision support for bus operators planning to replace their diesel-powered fleet with zero emission vehicles. We propose a graph representation which allows partial charging without explicitly relying on time variables and derive 3-index and 2-index mixed-integer linear programming formulations for the multi-depot electric vehicle scheduling problem. While the 3-index model can be solved by an off-the-shelf solver directly, the 2-index model relies on an exponential number of constraints to ensure the correct depot pairing. These are separated in a cutting plane fashion. We propose a set of instances with up to 80 service trips to compare the two approaches, showing that, with a small number of depots, the compact 3-index model performs very well. However, as the number of depots increases the developed branch-and-cut algorithm proves to be of value. These findings not only offer algorithmic insights but the developed approaches also provide actionable guidance for transit agencies and operators, allowing to quantify trade-offs between fleet size, energy efficiency, and infrastructure needs under realistic operational conditions.
Problem
Research questions and friction points this paper is trying to address.
Model electric bus scheduling to minimize fleet size, charging stops, energy use
Develop MILP formulations for multi-depot electric vehicle scheduling problem
Compare 3-index and 2-index models for varying depot numbers
Innovation
Methods, ideas, or system contributions that make the work stand out.
Graph representation enables partial charging
3-index and 2-index MILP formulations proposed
Branch-and-cut algorithm for large depots
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