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.