Fairness in optimizing bus-crew scheduling process

PLoS One. 2017 Nov 30;12(11):e0187623. doi: 10.1371/journal.pone.0187623. eCollection 2017.


This work proposes a model considering fairness in the problem of crew scheduling for bus drivers (CSP-BD) using a hybrid ant-colony optimization (HACO) algorithm to solve it. The main contributions of this work are the following: (a) a valid approach for cases with a special cost structure and constraints considering the fairness of working time and idle time; (b) an improved algorithm incorporating Gamma heuristic function and selecting rules. The relationships of each cost are examined with ten bus lines collected from the Beijing Public Transport Holdings (Group) Co., Ltd., one of the largest bus transit companies in the world. It shows that unfair cost is indirectly related to common cost, fixed cost and extra cost and also the unfair cost approaches to common and fixed cost when its coefficient is twice of common cost coefficient. Furthermore, the longest time for the tested bus line with 1108 pieces, 74 blocks is less than 30 minutes. The results indicate that the HACO-based algorithm can be a feasible and efficient optimization technique for CSP-BD, especially with large scale problems.

MeSH terms

  • Algorithms
  • Beijing
  • Humans
  • Models, Theoretical
  • Social Justice*
  • Transportation* / economics

Grant support

This study was supported by National Natural Science Foundation of China (no. 71131001-2, no. 71471014) WG, JHM; National Natural Science Foundation of China (under grant no. 71621001) WG, JHM; The Fundamental Research Funds for the Central Universities, CYS. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.