Inventory routing under stochastic supply and demand

It is well known that the integrated optimization of multiple and inter-related decisions in a supply chain can bring important benefits to companies. In this spirit, the inventory routing problem focuses on jointly optimizing inventory replenishment and vehicle routing decisions in a distribution context. In practice, the presence of uncertainty often further complicates the problem. We address a stochastic inventory routing problem under the consideration that both the product supply and the customer demands are uncertain. We propose a two-stage stochastic programming formulation, where routing decisions are made in the first stage, while delivery quantities, inventory levels and specific recourse actions are determined in the second stage. In this context, we analyze different recourse mechanisms such as lost sales, backlogging and an additional source for the product in a capacity reservation contract setting. We provide managerial insights from the results of computational experiments using instances based on a benchmark test set. In particular, we study the response mechanisms of the optimal solutions for different levels of uncertainty and cost configurations. Furthermore, we observe that supply and demand uncertainty have different effects on the value of taking the uncertainty into account. We also study the effect of incorporating a service level. Finally, we propose a heuristic solution method which is based on the progressive hedging algorithm and provides high-quality solutions within reasonable running times for problems with a large number of scenarios.