Robust inventory routing problem under uncertain demand and risk-averse criterion

Inventory routing problem (IRP), which plays an important role in implementing vendor-managed-inventory strategy, is to determine the optimal timing and quantity of products to be delivered as well as the optimal vehicle delivery routes from the vendor to retailers. Retailers’ demand is usually uncertain and their distributions are ambiguous. We utilize limited historical demand data of retailers to construct a series of scenarios to characterize demand uncertainties. Moreover, we develop a framework to construct ambiguity sets and describe the ambiguities in demand distributions. To cater to the new feature of IRP as being exposed to downside risk and balance the mean and risk level of cost, we incorporate the worst-case mean-conditional value-at-risk (M-CVaR) criterion into the objective function and present a new distributionally robust IRP model. We transform the proposed model into a tractable formulation based on duality theory. A case study demonstrates the feasibility of the proposed method. The results indicate that our model can provide a robust delivery solution for immunizing against the influence of ambiguous demand distributions. In addition, an out-of-sample performance analysis shows that the delivery solution provided by our model can effectively reduce the product shortage rate.