The inventory routing problem with split deliveries

We study the benefit of introducing split deliveries in the inventory routing problem (IRP), both when the order-up-to level (OU) and the maximum level replenishment policies are applied. We first propose a mathematical formulation and solve it by implementing a branch-and-cut algorithm. Then, we carry out a worst-case analysis to show the cost increase we have in the worst case by using unsplit deliveries instead of split deliveries, both for the OU and the maximum-level replenishment policies. Extensive computational results on benchmark instances allow us to evaluate the benefit of introducing split deliveries. Finally, a sensitivity analysis on customer demands, initial inventory levels, maximum inventory levels and distance to the depot allows us to understand the instance features that make split deliveries effective in IRPs.