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.

The paper presents a method of automated modelling and performance evaluation of concurrent production flows carried out in Flexible Manufacturing Systems. The method allows for quick assessment of various variants of such systems, considering their structure and the organization of production flow of possible ways of their implementation. Its essence is the conditions imposed on the designed model, limiting the space of possible variants of the production flow only to deadlock-free variants. The practical usefulness of the model implemented in the proposed method illustrates the example, which describes the simultaneous assessment of alternative variants of the flexible machining module's structure and the planned multi-assortment production. The ability of the method to focus on feasible solutions offers attractive perspectives for guiding the Digital Twin-like scenario in situations caused by the need to change the production flow.

The paper presents a method of automated modelling and performance evaluation of concurrent production flows carried out in robotic assembly systems. The method allows for quick assessment of various variants of such systems, considering their structure and the organization of production flow of possible ways of their implementation is carried out. The reference model follows the Petri net theory formalism framework. Its essence is the conditions imposed on the designed model, limiting the space of possible variants of the production flow only to deadlock-free variants. The practical usefulness of the model implemented in the proposed method illustrates the example describing the simultaneous assessment of alternative variants of the assembly system's structure and the planned multi-assortment production. Finally, its capacity to focus on feasible solutions offers attractive perspectives for guiding the Digital Twin like scenario in situations caused by the need to change the production flow.