Matheuristic search techniques for the consistent inventory routing problem with time windows and split deliveries

This article introduces a new variant of the inventory routing problem related to real-world businesses. Specifically, in the beverage industry, business customers such as restaurants and bars, demand consistent delivery times, have different opening times and delivery time windows, and occasionally, due to special events, exhibit demands that exceed single-vehicle capacity leading to the need of splitting demands between several vehicles. We present two variants of a mathematical formulation that include all the characteristics of this inventory routing problem. In the first, we apply the maximum level policy, whereas in the second variant, we apply an order-up-to-level policy. As a solution technique, we propose a matheuristic based on an adaptive large neighborhood search algorithm for which we developed several destroy and repair operators specifically designed to address the special problem features. Extensive computational tests based on artificial and real-world instances affirm the efficiency of the solution approach. Furthermore, we analyze the solution quality, the impact of the characteristics and policies applied, and the practicability for the real world.