Periodic distributed delivery routes planning subject to operation uncertainty of vehicles travelling in a convoy

Abstract

This paper considers a Problem of Periodic Routing of Vehicles Platoons (PRVPP), which is a novel extension of the Periodic Vehicle Routing Problem (PVRP). The PRVPP boils down to scheduling of the fleet of vehicles travelling in a convoy while constituting the timetable for the passage of individual vehicles along the planned routes. The imprecise nature of transport/service operation times means there is a 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. This raises the question as to the method required to avoid 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 reflect the uncertainty of times. The conducted research demonstrated that the proposed model allows us to develop conditions following the calculability of arithmetic operations of OFNs and guarantee the interpretability of the results obtained.