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 replenishmentpolicies are applied. We first propose a mathematical formulation and solve it byimplementing a branch-and-cut algorithm. Then, we carry out a worst-case analy-sis to show the cost increase we have in the worst case by using unsplit deliveriesinstead of split deliveries, both for the OU and the maximum-level replenishmentpolicies. Extensive computational results on benchmark instances allow us to eval-uate the benefit of introducing split deliveries. Finally, a sensitivity analysis oncustomer demands, initial inventory levels, maximum inventory levels and distanceto the depot allows us to understand the instance features that make split deliverieseffective in IRPs.