Integrated Optimization of Inventory Routing, Transshipments, and Backordering: A Fix-and-Optimize Matheuristic

This paper addresses a multi-product, multi-vehicle Inventory Routing Problem with Transshipments and Backordering (IRPTB), integrating replenishment, lateral inventory sharing, and backordering decisions within a unified framework. The problem is formulated as a mixed-integer linear program (MILP) and solved using a matheuristic based on the Fix-and-Optimize (F&O) paradigm, designed to balance solution quality and computational efficiency. Extensive computational experiments on benchmark instances under varying demand variability levels demonstrate that the proposed approach consistently delivers near-optimal solutions with substantial computational gains over the CPLEX solver. Across moderate, high, and extreme demand ranges, the matheuristic achieves average relative gaps below 2.2%, 1.5%, and 1.7%, respectively, while reducing computation times by factors ranging from 3× to 15×. The results further indicate strong robustness of the approach, with limited sensitivity to increasing demand variability. From a managerial perspective, the findings confirm that combining transshipments with backordering improves service levels by alleviating lost sales and reducing inventory imbalances across the network. Overall, the proposed F&O matheuristic offers an effective and scalable solution method for complex inventory routing problems under demand variability.