Milk-run routing and scheduling subject to a trade-off between vehicle fleet size and storage capacity

The objective of the milk-run design problem considered in this paper is to minimize transportation and inventory costs by manipulating fleet size and the capacity of vehicles and storage areas. Just as in the case of an inventory routing problem, the goal is to find a periodic distribution policy with a plan on whom to serve, and how much to deliver by what fleet of tugger trains travelling regularly on which routes. This problem boils down to determining the trade-off between fleet size and storage capacity, i.e. the size of replenishment batches that can minimize fleet size and storage capacity. A solution obtained in the declarative model of the milk-run system under discussion allows to determine the routes for each tugger train and the associated delivery times. In this context, the main contribution of the present study is the identification of the relationship between takt time and the size of replenishment batches, which allows to determine the delivery time windows for milkrun delivery and, ultimately, the positioning of trade-off points. The results show that this relationship is non-linear