School accessibility evaluation under mixed-load school bus routing problem strategies

Abstract

Mixed-load school bus routing problem (SBRP) strategy helps to improve the efficiency of school bus systems. School accessibility is a student-oriented measurement indicator that visually demonstrates the influence of mixed-load SBRP strategies on student commuting efficiency. In order to improve the convenience of students commuting to school while greatly reducing the operational cost of school buses, this paper proposes two mixed-load SBRP strategies (strategy 1: mixed-load mode and strategy 2: single-load mode). The bi-level programming model is constructed to model the two mixed-load SBRP strategies. In the bi-level programming model, the upper-level is to maximize school accessibility, and the lower-level optimizes school bus routes with the goal of minimizing the total number of school buses. The entropy-based weight method is introduced for comprehensive evaluation of strategies. Case studies are presented based on school bus data in Dalian, China to measure the performance of the two strategies. In computational experiments, the effect of weighted commuting time on school accessibility is also investigated. The results indicate that the SBRP strategy of mixed load mode (strategy 1) is the most effective in terms of comprehensive assessment of operating costs and school accessibility. In addition, it is found that the weighted commuting time has expanded the horizontal differentiation of school accessibility.