Rebalancing static bike-sharing systems: A two-period two-commodity multi-depot mathematical model

S. Mohammad Arabzad, Hadi Shirouyehzad, Mahdi Bashiri, Reza Tavakkoli-Moghaddam, Esmaeil Najafi

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
23 Downloads (Pure)


In this paper, an Integer Linear Programming (ILP) has been developed for rebalancing the stations of a Periodic Bike Relocation Problem (PBRP) in multiple periods. The objective function of the mathematical model is reducing costs of implementing trucks, transportation between stations and holding bikes on trucks during rebalancing. The variables we are following them in this model are conducting the optimal route in several periods, using the most appropriate trucks for these routes, and determining the best program for loading/unloading bikes for stations. The distinguishing features of the proposed model are considering several bike types, several exclusive trucks and several time periods. Finally, a numerical example confirms the applicability of the proposed model.

Original languageEnglish
Pages (from-to)718-726
Number of pages9
Issue number3
Publication statusPublished - 1 Jul 2018
Externally publishedYes

Bibliographical note

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unre-stricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


  • Bike-sharing systems (BSS)
  • Mathematical modelling
  • Periodic bike relocation problem (PBRP)

ASJC Scopus subject areas

  • Automotive Engineering
  • Mechanical Engineering


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