The inventory routing problem (IRP) is of central importance to the successful execution of a vendor-managed inventory strategy. Retailer demand is characterized by uncertainty. Consequently, the IRP decision-maker is required to set a cost target for the inventory routing solution in advance to mitigate the risk of potential budget breaches. To this end, we propose a robust budget target-oriented optimization framework to optimize IRP with demand uncertainty. Based on the Lagrangian duality theory, we convert the proposed robust IRP model into a non-linear deterministic model. A binary search algorithm is developed to solve the ultimately reconstructed model. Empirical findings demonstrate that the inventory routing scheme derived from the proposed model achieves favorable performance in terms of out-of-sample cost, stock-out rate, and target violation rate. 

Inventory routing,uncertainty,target-oriented optimization,Robust optimization