| Abstract: |
Nowadays, returns management has become an outstanding issue in the e-commerce market, since the underlying operations involve high additional costs and externalities. A well-consolidated strategy for managing e-commerce logistics integrates forward and reverse transportation systems, ensuring the collection of returns alongside traditional product distribution. This approach also employs hub-and-spoke networks to aggregate both distribution and collection demands from several customers into a few central hubs. Within this framework, we study a complex variant of the Vehicle Routing Problem with divisible deliveries and pickups in which each hub may have mandatory delivery and return pickup demands and can be visited multiple times within the same or different routes [1]. Due to the large fluctuation of demand within the aggregating hubs, we also assume that an uncertain optional pickup quantity may arise and that the pickup service for this demand is optional as well. The problem involves two main decisional stages, the day ahead and the operational day times, in which different aspects of the problem must be decided. For this reason, we propose a two-stage Stochastic Programming formulation including ad-hoc recourse actions, namely, the possibility for a vehicle to perform a detour to the depot (where it is possible to unload the already picked up demand) and the opportunity to pay for external spot-market transportation services. To tackle the complexity of solving this model using numerous scenarios, we have developed an exact method based on Integer L-shaped decomposition and ad-hoc valid inequalities. The obtained optimal solutions are used to create an economic analysis of the problem with the aim of providing important managerial insights [2]. Finally, to address very large instances, a Progressive Hedging-based matheuristic approach [3] is also proposed. This method exploits a scenario problem decomposition, an Augmented Lagrangian Relaxation framework, and various heuristic enhancements. Our approach overcomes state-of-the-art solvers in terms of solution quality and efficiency over a representative set of realistic instances and can be readily adapted to similar contexts.
1. Nagy, G., Wassan, N.A., Speranza, M.G., Archetti, C. (2015). The vehicle routing problem with divisible deliveries and pickups, Transportation Science 49 (2), 271–294.
2. Gobbi A., Manerba, D., Vocaturo, F. (forthcoming). Incorporating stochastic optional pickup demand in routing operations with divisible services for hub-and-spoke e-commerce returns management systems (under III round revision on an international journal).
3. Christiansen, J., Dandurand, B., Eberhard, A., Oliveira, F. (2023). A study of progressive hedging for stochastic integer programming, Computational Optimization and Applications 86, 989–1034. |