A matheuristic for solving inventory sharing problems

In this paper, we addressed a two-level supply chain in which a company manufactures products and sells them through its point of sale network. The problem of concern is a multi-product, multi-vehicle inventory sharing routing problem. We formulated it as a mixed-integer linear programming problem. We also designed a two-phase matheuristic that integrates mathematical modelling strengthened with relevant derived valid inequalities and hybridisation of sophisticated metaheuristics: Genetic Algorithm and Simulated Annealing. We tested 660 best known instances designed for the single and multi-vehicle inventory routing problem, and the results showed that the matheuristic outperformed the best known algorithms regarding computational times and enhanced 156 solutions for large instances. Extra experiments were conducted on a set of data specially designed for the multi-product multi-vehicle inventory sharing routing problem. Computational results highlighted the benefits of sharing inventory on the overall supply chain. Finally, a sensitivity analysis was conducted, which revealed the extent to which inventory sharing among different points of sale can be cost-effective by the savings it brings to reduce lost sales and inventory holding.