A generalized disjunctive programming model for the static bike sharing rebalancing problem with demand intervals

Solving a static bike sharing rebalancing problem requires finding the minimum-cost route for rebalancing vehicles, subject to meeting the demand at the bike sharing stations of the system. In this work, we study the variant of the problem where the demand is specified by intervals, which adds flexi...

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Bibliographic Details
Published in:Optimization and engineering Vol. 26; no. 3; pp. 1781 - 1813
Main Authors: Ikonen, Teemu J., Heljanko, Keijo, Harjunkoski, Iiro
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.09.2025
Subjects:
Algorithms
Bicycles
Clustering
Computing time
Customer services
Decomposition
Demand
Heuristic
Integer programming
Intervals
Linear programming
Mathematical programming
Mixed integer
Optimization
Traveling salesman problem
Vehicle routing
Vehicles
ISSN:1389-4420, 1573-2924
Online Access:Get full text
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Summary:Solving a static bike sharing rebalancing problem requires finding the minimum-cost route for rebalancing vehicles, subject to meeting the demand at the bike sharing stations of the system. In this work, we study the variant of the problem where the demand is specified by intervals, which adds flexibility to the routing of the rebalancing vehicles. We propose a generalized disjunctive programming (GDP) model to represent the problem and its reformulation into a mixed-integer linear programming (MILP) model. We use demand splitting to duplicate stations that require multiple visits. The model is designed for single-vehicle routing but can be used jointly with a clustering approach proposed in the literature for multi-vehicle routing. The model can solve to optimality 86.8% of benchmark instances with 70 stations within two hours of computing time. On test cases derived from real process data, the model is more than two orders of magnitude faster than the reference model in the literature.
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ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-024-09942-z