Strengthening Dual Bounds for Network Design with Unsplittable Flow
Published:Dec 31, 2025 18:12
•1 min read
•ArXiv
Analysis
This paper addresses the challenging problem of multicommodity capacitated network design (MCND) with unsplittable flow constraints, a relevant problem for e-commerce fulfillment networks. The authors focus on strengthening dual bounds to improve the solvability of the integer programming (IP) formulations used to solve this problem. They introduce new valid inequalities and solution approaches, demonstrating their effectiveness through computational experiments on both path-based and arc-based instances. The work is significant because it provides practical improvements for solving a complex optimization problem relevant to real-world logistics.
Key Takeaways
- •Addresses the MCND problem with unsplittable flow constraints, relevant to e-commerce fulfillment.
- •Focuses on strengthening dual bounds to improve IP solvability.
- •Introduces new valid inequalities and solution approaches.
- •Demonstrates significant IP gap reduction in computational experiments.
- •Provides practical improvements for solving a complex optimization problem.
Reference
“The best solution approach for a practical path-based model reduces the IP gap by an average of 26.5% and 22.5% for the two largest instance groups, compared to solving the reformulation alone.”