The Inventory Routing Problem Under Uncertainty

We study an uncertain inventory routing problem with a finite horizon. The supplier acts as a central planner who determines the replenishment quantities and also, the delivery times and routes to all retailers. We allow ambiguity in the probability distribution of each retailer’s uncertain demand. Adopting a service-level viewpoint, we minimize the risk of uncertain inventory levels violating a prespecified acceptable range. We quantify that risk using a novel decision criterion, the service violation index, that accounts for how often and how severely the inventory requirement is violated. The solutions proposed here are adaptive in that they vary with the realization of uncertain demand. We provide algorithms to solve the problem exactly and then, demonstrate the superiority of our solutions by comparing them with several benchmarks.

Funding: D.Z. Long is supported by the National Natural Science Foundation of China [Grants 71971187, 72231002]. J. Qi is supported by the Hong Kong Research Grants Council [Grants 16213417, 16209918]. L. Zhang is supported by the National Natural Science Foundation of China [Grants 72171156, 72231002].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2407.