Abstract
• A mixed integral programming mathematical model was proposed. • A vehicle-coordinated strategy is designed to solve the service failure. • A hybrid algorithm with the artificial immune algorithm is presented to solve the problem. • Tolerant possibility degree impacts on the planned distance, additional distance and the total distance. • The total distance with the vehicle-coordinated strategy is U type. In this paper, a vehicle routing problem with interval demands is investigated based on the motivation of dispatching vehicles to deliver perishable products in practice. A nonlinear interval-based programming method is used to build a model for the vehicle routing problem with interval demands, which assumes that demands of customers are uncertain but fall in given intervals and actual demand of a customer becomes known only when the vehicle visited the customer. A vehicle-coordinated strategy was designed to solve the service failure problem. A hybrid algorithm based on the artificial immune system is also proposed to solve the model for vehicle routing problem with interval demands. The validity of methods and sensitivity analysis are illustrated by conducting some numerical examples. We find that the tolerant possibility degree of interval number has significant impacts on the distances. The planned distance strictly increased, while the additional distance strictly decreased and the total distance after coordinated transport has a U-typed relationship with the tolerant possibility degree of interval number.
Published Version
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