A novel two-phase approach for the bi-objective simultaneous delivery and pickup problem with fuzzy pickup demands

This paper is dedicated to providing a solution framework for the bi-objective vehicle routing problem with simultaneous delivery and pickup which aims to minimize the comprehensive cost as well as maximize the recycling revenue in each round of dispatching. Considering that the real weights of goods to be recycled from the customers are fixed but cannot be precisely given while making one-time routing scheme in the daily operations, the pickup demands are considered as fuzzy numbers, and accordingly a fuzzy chance-constraint programming model for obtaining a prior route solution from the perspective of risk is presented. Afterwards, by demonstrating the continuity and monotonicity of the objective functions, a two-phase approach based on the operational law of the inverse credibility distribution is introduced to solve the model, including translating it into an equivalent nonlinear programming model and resorting to the existing algorithms for obtaining optimal solutions afterwards. Subsequently, in order to validate the performance of the proposed approach and in consideration of the inherent complexity of the vehicle routing problem, a two-phase-based genetic algorithm and the conventional fuzzy simulation-based genetic algorithm are designed and compared by a clothes delivery and pickup problem. The computational results demonstrate that the proposed solution framework is competitive in effectiveness and efficiency, and the parameter analyses provide some suggestions for guidance.