Incorporating stochastic optional pickup demand in routing operations with divisible services for hub-and-spoke e-commerce returns management systems

Nowadays, e-commerce is associated with many returns due to emotional consumption, information asymmetry, factory defects, or, more generally, customer dissatisfaction. However, little attention has been paid to reverse logistics in the e-commerce industry, although it has been proven crucial to improving the perceived quality of service and profit revenue. Depending on the nature of the goods, one successful option is to design combined forward-and-reverse logistics systems, where the collection of returns is ensured along with the traditional distribution of products, together with hub-and-spoke networks in which both distribution and collection demand from many spokes are aggregated into a few hubs. In this context, we study a variant of the vehicle routing problem with divisible deliveries and pickups, in which each hub may be associated with a mandatory delivery demand and a mandatory return pickup demand, and it may be visited more than once within the same or different routes. To address realistic scenarios, and given the large fluctuation of demand within the aggregating hubs, we also assume that an uncertain optional pickup quantity may arise and formulate the problem through two-stage Stochastic Programming, proposing and modeling ad-hoc recourse actions. Moreover, an integer L-shaped method enhanced with ad-hoc valid inequalities is developed for solving the resulting problem. Managerial insights on the underlying tactical and operational policies are inferred from extensive computational experiments on a case study and on realistic artificial instances.