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We address a vendor-managed inventory-routing problem where a supplier (vendor) receives a given amount of a single product each period and distributes it to multiple retailers over a finite time horizon using a capacitated vehicle. Each retailer faces external dynamic demand and is controlled by a deterministic order-up-to level policy requiring that the supplier raise the retailer's inventory level to a predetermined maximum in each replenishment. The problem is deciding on when and in what sequence to visit the retailers such that systemwide inventory holding and routing costs are minimized. We propose a branch-and-cut algorithm and a heuristic based on an a priori tour using a strong formulation. To the best of our knowledge, this study is the first to consider a strong formulation for the inventory replenishment part of inventory-routing problems. Computational results reveal that the new branch-and-cut algorithm and heuristic perform better than those noted in the literature.

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We consider the combined hubbing and routing problem in postal delivery systems and develop an iterative two-stage solution procedure for the problem. In the first stage, hub locations are determined and postal offices are multiply allocated to the hubs. The second stage gives the routes in hub regions that alter the distances between points used in the hub-location problem. The procedure then iterates between two stages by updating the distances used in hubbing in order to produce a route-compatible hub configuration. Computational experience is reported for the test problems taken from the literature. For a case study Turkish postal delivery system data are utilized. As the case study is applied on a road network, a final stage, seeking improvements based on special structures in the routed network, is appended to the two-stage solution procedure.