An improved model and exact algorithm using local branching for the inventory-routing problem with time windows

The Inventory-Routing Problem (IRP) deals with the joint optimisation of inventory and the associated routing decisions. The IRP with time windows (IRPTW) considers time windows for the deliveries to the customers. Due to its importance and several real-world applications, in this paper, we develop an intricate solution algorithm for this problem. A combination of tools ranging from established groups of valid inequalities, pre-processing techniques, local search procedures, and a local branching algorithm is utilised to solve the IRPTW efficiently. We compare the performance of our algorithm on a benchmark set of instances and show how our solution algorithm provides promising results against a competing algorithm from the literature. Moreover, the results of our study provide an overview of the performance of several already proposed techniques and their integration in the literature.