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.

In this paper, we propose a novel priority-aware solution named bypass to handle high- and low-priority traffic in multi-layer networks. Our approach assumes diversification of elastic optical spectrum to ensure additional resources reserved for emergency situations. When congestion occurs, the solution dynamically provides new paths, allocating a hidden spectrum to offload traffic from the congested links in the IP layer. Resources for a bypass are selected based on traffic priority. High-priority traffic always gets the shortest bypasses in terms of physical distance, which minimizes delay. Bypasses for low-priority traffic can be established if the utilization of the spectrum along the path is below the assumed threshold. The software-defined networking controller ensures the global view of the network and cooperation between IP and elastic optical layers. Simulation results show that the solution successfully reduces the amount of rejected high-priority traffic when compared to regular bypasses and when no bypasses are used. Also, overall bandwidth blocking probability is lower when our priority-aware bypasses are used.