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.