A Redesigned Benders Decomposition Approach for Large-Scale In-Transit Freight Consolidation Operations

TL;DR

This paper introduces a redesigned Benders decomposition method for large-scale in-transit freight consolidation, significantly improving computational efficiency for complex multi-product, multi-period logistics problems.

Contribution

It develops a novel mixed-integer programming formulation and applies an enhanced Benders decomposition to handle large-scale freight consolidation problems efficiently.

Findings

Benders decomposition reduces problem size without losing optimality.

The approach scales to problems with over 27 million variables.

Significant performance improvements in solving large logistics problems.

Abstract

The growth in online shopping and third party logistics has caused a revival of interest in finding optimal solutions to the large scale in-transit freight consolidation problem. Given the shipment date, size, origin, destination, and due dates of multiple shipments distributed over space and time, the problem requires determining when to consolidate some of these shipments into one shipment at an intermediate consolidation point so as to minimize shipping costs while satisfying the due date constraints. In this paper, we develop a mixed-integer programming formulation for a multi-period freight consolidation problem that involves multiple products, suppliers, and potential consolidation points. Benders decomposition is then used to replace a large number of integer freight-consolidation variables by a small number of continuous variables that reduces the size of the problem without impacting optimality. Our results show that Benders decomposition provides a significant scale-up in the performance of the solver. We demonstrate our approach using a large-scale case with more than 27.5 million variables and 9.2 million constraints.