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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Veröffentlicht in:	Optimization and engineering Jg. 26; H. 3; S. 1781 - 1813
Hauptverfasser:	Ikonen, Teemu J., Heljanko, Keijo, Harjunkoski, Iiro
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Dordrecht Springer Nature B.V 01.09.2025
Schlagworte:	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
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Abstract	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.
AbstractList	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.
Author	Harjunkoski, Iiro Heljanko, Keijo Ikonen, Teemu J.
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SubjectTerms	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
Title	A generalized disjunctive programming model for the static bike sharing rebalancing problem with demand intervals
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