Optimal Deliveries in a Vendor Managed Inventory Service

In a VMI service, a central production center (i.e. the vendor) can control the inventory of each retailer according to the optimization of the costs due both to the overfilling/stock-out of the inventories and to the travels required for the deliveries. In this work, an original mathematical programming approach has been formulated and implemented in order to show that under specific but common conditions (the most important of which are: capacity of the retailer warehouse higher than the demand and than the vehicle capacity, a maximum of two drops for travel, unsatisfied demand lost and not backlogged), a true direct delivery VMI service may not be the best solution. Results are shown on a fictional network as well as on a real logistics system represented by a central depot and by a network of petrol service stations, giving evidence to some peculiar aspects of the VMI service which can be useful on their own to enhance the decision making strategies of a logistic company.