A matheuristic for the two-echelon inventory-routing problem

Effective coordination of operational decisions in today's global supply chains has grown increasingly important. This paper considers a two-echelon inventory-routing problem under a vendor-managed inventory system, where suppliers are responsible for fulfilling the demands of geographically scattered customers through a set of intermediate facilities over a finite planning horizon. The problem involves determining the routing and delivery decisions to minimize the total routing and inventory costs. We introduce an effective two-phase matheuristic approach that combines tabu search and mathematical programming models. Computational experiments show that our approach achieves excellent results regarding solution quality and computational time. For small instances, the matheuristic finds 99 optimal solutions out of 165 known optimal solutions and achieves an average gap of (−2.32%) over 235 instances with a known best upper bound only, improving 159 known best upper bounds. Our approach also solves larger instances within a reasonable computational time and provides upper bounds for all 400 large-sized instances for the first time in the literature. Through a comprehensive series of experiments, we provide insights into the efficacy of different components of the proposed solution method.