This talk presents the Inventory-Routing Problem, namely the combination of two well-known logistics problems: inventory management and vehicle routing. This problem has received great attention lately with several heuristic and exact algorithms that have been proposed in the past 10 years. We first introduce the business environment where this problem arises, and we then present two practical applications and their respective solutions. First, we show how one can optimize the distribution and inventory management of cash to a new class of recirculation ATM machines. This problem yields a rich pickup and delivery IRP. It is solved by a hybrid method that first simplifies its difficulty by making several heuristic decisions. The remaining subproblems are still NP-hard and are solved exactly by branch-and-cut. The second application arises in the collection of several types of olive oil a fleet of heterogeneous using multi-compartment trucks. This problem is solved exactly by a branch-and-cut algorithm.

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