The Distributionally Robust Cyclic Inventory Routing Problem

TL;DR

This paper introduces a distributionally robust cyclic inventory routing model that accounts for demand uncertainty, providing a deterministic reformulation and an efficient solution framework validated on real-world data.

Contribution

It develops a novel distributionally robust optimization approach with a tractable reformulation and a nested branch-and-price algorithm for the cyclic inventory routing problem.

Findings

The worst-case expected inventory cost is achieved by a multi-point distribution.

The distributionally robust chance constraint can be reformulated into a deterministic form.

The proposed method is effective and efficient on real-world data.

Abstract

We study the cyclic inventory routing problem that involves joint decisions on vehicle routing and inventory replenishment on an infinite, cyclic horizon. It considers a single warehouse and a set of geographically dispersed retailers. We model retailer demand as random variables with uncertain distributions belonging to a moment-based ambiguity set. We develop a distributionally robust optimization formulation that minimizes the worst-case expected cost over the ambiguity set, while ensuring service reliability through a distributionally robust chance constraint. Our main results are that we prove that the worst-case expected inventory cost is attained under a multi-point distribution, which can be identified a posteriori via linear programming, and that the distributionally robust chance constraint can be reformulated into near-equivalent deterministic forms. This yields a deterministic reformulation of the original problem. To solve it, we design a nested branch-and-price framework, in which the first level partitions retailers into clusters, and the second level concerns routing and replenishment decisions within each cluster. Computational experiments on both synthetic instances and real-world data from SAIC Volkswagen Automobile Co., Ltd. demonstrate the effectiveness and efficiency of the proposed approach.