Single Vehicle’s Package Delivery Strategy with Online Traffic Congestion of Certain Delay Time

Abstract

Urban package delivery by single vehicle can be modeled as online Steiner travelling salesman problem. This paper investigates the scenario that delay time of traffic congestion is certain and of real-time information to delivery vehicle, the vehicle can obtain specific delay time of traffic congestion just upon reaching an end vertex of the corresponding edge. Given a graph G = (V, E) and a subset D in V, the goal is to design a minimum-weight closed tour that departs from the depot s in D and returns to s after visiting each destination node in D at least once. When delivery vehicle encounters at most k times of traffic congestion, we first show $min\left\{ {k + 1,\rho_{\Sigma } + 1} \right\}$ is a lower bound on competitive ratio for the problem, where $\rho_{\Sigma }$ is the ratio compared sum of delay time of all congested edges with cost of optimal route. We further present an online algorithm for the problem with its competitive ratio proved to be very close to the lower bound.