The design of logistic trains fleet oriented distributed and scalability-robust control policies that ensure deadlock-free operations is of crucial importance for efficient material handling systems. This study considers a multi-item assembly system where in-plant transport operations are organized in milk-run loops. A solution to a milk-run routing and scheduling problem subject to fuzzy pickup and delivery time constraints is developed. This type of problem can be treated in terms of a fuzzy constraint satisfaction problem, therefore, the main objective is to provide a reference model analytical formulas of which enable one to obtain solutions that do not require time-consuming computer simulations. Two versions of the model were parameterized assuming independent implementation of convex and ordered fuzzy numbers. The accuracy of both models was experimentally verified according to the results of multiple simulations. Results from this study provide an approach to avoid time consuming computer simulation-based calculations of logistic trains fleet schedules avoiding congestions while concurrently maintaining throughput at maximal achievable level.