Modelling and comparison of stability metrics for a re-optimisation approach of the Inventory Routing Problem under demand uncertainty

The inventory routing problem (IRP) is an optimisation problem that integrates transportation and inventory management decisions. When subjected to unexpected events such as demand changes, the a posteriori approach consists in re-optimising including the data related to this event; the challenge is to ensure that the obtained solution does not deviate too much from the original one, lest that creates important organisational issues. Therefore, a stability metric is needed when re-optimising IRP models. This article proposes a panel of stability metrics adapted from the scheduling, routing and inventory management literature to fit the requirements of the IRP and proposes mathematical formulations for the most relevant ones. A framework of comparison is proposed to validate and compare these metrics over a benchmark of 3000 instances generated from the literature. A strong correlation between the metrics is observed. Moreover, the results show that ensuring the stability of the re-optimised solutions has little impact on the initial objective, the total cost.