A Branch-and-Price Algorithm for the Two-Echelon Inventory-Routing Problem

TL;DR

This paper introduces a branch-and-price algorithm to efficiently solve the complex two-echelon inventory-routing problem, optimizing costs in a multi-level supply network with numerous instances tested.

Contribution

It develops a novel route-based formulation and a branch-and-price algorithm, achieving optimal solutions for many instances and providing insights into its computational performance.

Findings

Optimal solutions for 116 instances

Good upper bounds for 60 instances with less than 5% gap

The algorithm can solve 7 additional instances to optimality

Abstract

The two-echelon inventory-routing problem (2E-IRP) addresses the coordination of inventory management and freight transportation throughout a two-echelon supply network. The latter consists of geographically widespread customers whose demand over a discrete planning horizon can be met from either their local inventory or intermediate facilities' inventory. Intermediate facilities are located in the city outskirt and are supplied from distant suppliers. The 2E-IRP aims to minimize transportation costs and inventory costs while meeting customers' demand. A route-based formulation is proposed and a branch-and-price algorithm is developed for solving the 2E-IRP. A labeling algorithm is used to solve several pricing subproblems associated with each period and intermediate facility. We generate 400 instances and obtain optimal solutions for 116 instances, and good upper bounds for 60 instances with a gap of less than 5% (with an average of 2.8%). Variations of the algorithm could solve 7 more instances to optimality. We provide comprehensive analyses to evaluate the performance of our solution approach.