Hybrid heuristic for the inventory location-routing problem with deterministic demand

The Inventory Location-Routing Problem with deterministic demand can be seen as an approach to both optimize a supply chain design and minimize its operational costs. This problem considers that vehicles might deliver products to more than one retailer per route and that inventory management decisions are included for a multi-depot, multi-retailer system with storage capacity over a discrete time planning horizon. The problem is to determine a set of candidate depots to open, the quantities to ship from suppliers to depots and from depots to retailers per period, and the sequence in which retailers are replenished by an homogeneous fleet of vehicles. A mixed-integer linear programming model is proposed to describe the problem and to provide bounds on the solutions. It is strengthened by two sets of valid inequalities with an analysis of their impact. Since the model is not able to solve the targeted instances exactly within a reasonable computation time, a hybrid method, embedding an exact approach within a heuristic scheme, is presented. Its performance is tested over three sets of instances for the inventory location routing, location-routing and inventory-routing problems. Results show important savings achieved when compared to a decomposed approach and the capability of the algorithm to solve the problem.