The multi-product inventory-routing problem with pickups and deliveries: Mitigating fluctuating demand via rolling horizon heuristics

In this paper, we explore the value of considering simultaneous pickups and deliveries in multi-product inventory-routing problems both with deterministic and uncertain demand. We propose a multi-commodity, develop an exact branch-and-cut algorithm with patching heuristics to efficiently tackle this problem, and provide insightful analyses based on optimal plans. The simplicity of the proposed approach is an important aspect, as it facilitates its usage in practice, opposed to complicated stochastic or probabilistic methods. The computational experiments suggest that in the deterministic demand setting, pickups are mainly used to balance initial inventories, achieving an average total cost reduction of 1.1%, while transshipping 2.4% of total demand. Under uncertain demand, pickups are used extensively, achieving cost savings of up to 6.5% in specific settings. Overall, our sensitivity analysis shows that high inventory costs and high degrees of demand uncertainty drive the usage of pickups, which, counter-intuitively, are not desirable in every case.