Evaluation of an existing bus network using a transit network optimisation model: a case study of the Hiroshima City Bus network

Abstract

This study evaluates an existing bus network from the perspectives of passengers, operators, and overall system efficiency using the output of a previously developed transportation network optimisation model. This model is formulated as a bi-level optimisation problem with a transit assignment model as the lower problem. The upper problem is also formulated as bi-level optimisation problem to minimise costs for both passengers and operators, making it possible to evaluate the effects of reducing operator cost against passenger cost. A case study based on demand data for Hiroshima City confirms that the current bus network is close to the Pareto front, if the total costs to both passengers and operators are adopted as objective functions. However, the sensitivity analysis with regard to the OD pattern fluctuation indicates that passenger and operator costs in the current network are not always close to the Pareto front. Finally, the results suggests that, regardless of OD pattern fluctuation, reducing operator costs will increase passenger cost and increase inequity in service levels among passengers.

Appendix: Gini coefficient

The Gini coefficient is a value that is often used to measure income inequity; it has also been used in operations research (Shimamoto et al. 2005). The Gini coefficient is defined as twice the area between the Lorentz curve and a 45° line in the population-share and income-share plane. By definition, the Gini coefficient has a value between 0 and 1, where 0 corresponds to perfect equity and 1 to perfect inequity. The Gini coefficient regarding the total cost among OD pairs can be formulated as:

$$ Gini^{m} = {\frac{1}{{2 \cdot Q^{2} \cdot \overline{CR}^{m} }}}\sum\limits_{i = 1}^{I} {\sum\limits_{j = 1}^{I} {Q_{i} Q_{j} \left| {CR_{i}^{m} - CR_{j}^{m} } \right|\,} } $$

(A1)

where

$$ CR_{i}^{m} = {{g_{i}^{0} } \mathord{\left/ {\vphantom {{g_{i}^{0} } {g_{i}^{m} }}} \right. \kern-\nulldelimiterspace} {g_{i}^{m} }} $$

$$ \overline{CR}^{m} = \sum\limits_{i = 1}^{I} {{{CR_{i}^{m} } \mathord{\left/ {\vphantom {{CR_{i}^{m} } I}} \right. \kern-\nulldelimiterspace} I}} $$

where Gini ^m is the Gini coefficient at solution m; I is the set of OD pair; Q _i is the passenger demand of OD pair i; g ⁰ _i is the generalise cost of OD pair i at current network; g ^m _i is the generalise cost of OD pair i at solution m.