A metaheuristic for the rural school bus routing problem with bell adjustment

Abstract

This paper addresses the school bus routing problem with bell adjustments. This problem extends the traditional school bus routing problem by having the school working times as decision variables instead of input data. Adjusting schools working times (bell adjustment) increases managerial flexibility to lower transportation costs. On the other hand, this comes at the price of having to deal with more complex solution design and greater computational complexity, as underlaid by the scarce literature on the theme. Here we propose different bell adjustment strategies for a rural variant of the problem which has particular importance both economically and socially for developing countries that usually have schooling with multiple shifts and budget restrictions. The memetic algorithm combines an iterated local search with specialized neighborhood structures arranged in a variable neighborhood descent strategy and enriched with a diversification scheme that relies on an elite set to solve large scale real instances. Different bell adjustment strategies are richly explained, tested, and analyzed thoroughly. The results of statistical analysis show significant cost savings for both cases with or without multi-loading. The new strategy achieved up to 9% savings and 2.55% savings on the consolidated results. Instances with a lower number of vehicles and a higher number of schools presented higher savings.