An ordered-fuzzy-numbers-driven approach to the milk-run routing and scheduling problem

Internal logistics systems aim at supplying the right materials at the right locations at the right time. This fact creates the need for the design of logistic-train-fleet-oriented, distributed and scalability-robust control policies ensuring deadlock-free operations. This paper presents a solution to a milk-run vehicle routing and scheduling problem subject to fuzzy pick-up and delivery transportation time constraints. Since this type of problem can be treated as a fuzzy constraint satisfaction problem, an elegant solution can be determined using both computer simulation and analytical ordered-fuzzy-number-driven calculations. In contrast to standard fuzzy numbers, the support of a fuzzy number obtained by algebraic operations performed on the ordered fuzzy numbers domain does not expand. The possibility of carrying out algebraic operations is limited to selected domains of the computability of these supports. The proposed sufficient conditions implying the calculability of arithmetic operations guarantee interpretability of the results obtained. Consequently, they confirm the competitiveness of the analytical approach in relation to time-consuming computer-simulation-based calculations of logistic train fleet schedules. Finally, it is demonstrated on the basis of the results obtained in the study that the proposed approach constitutes an effective solution to the problem discussed. In this context, the proposed paper is a continuation of the authors' recent research presented at the International Conference on Computational Science 2020.