Periodic Distributed Delivery Routes Planning Subject to Uncertainty of Travel Parameters

Abstract

In the Periodic Vehicle Routing Problem (PVRP), in which scheduling of the fleet of vehicles is based on constituting the timetable for the passage of individual vehicles along the planned routes, the imprecise nature of transport/service operation times implies the need to take into account the fact that the accumulating uncertainty of previously performed operations results in increased uncertainty of timely execution of subsequent operations. In the article, the authors pose the question as to the method of avoiding additional uncertainty introduced during aggregating uncertain operation execution deadlines. Due to the above fact, an algebraic model for calculating fuzzy schedules for individual vehicles, and for planning time buffers enabling the adjustment of the currently calculated fuzzy schedules is developed. The model uses Ordered Fuzzy Numbers (OFNs) to conduct the uncertainty of times. The advantage of using the OFNs formalism for algebraic operations is non-expanding of fuzzy number support. However, the possibility of carrying out algebraic operations is limited to selected domains of computability of these supports. Due to this fact a constraint satisfaction problem framework has been adapted. The conducted research demonstrated that the proposed approach allows to develop conditions following the calculability of arithmetic operations of OFNs and guarantee interpretability of results obtained.