Competitive analysis for the on-line Vehicle Routing Problem

The on-line Vehicle Routing Problem (VRP), motivated by the research concerning on-line Traveling Salesman Problem (TSP) and on-line transportation problem, is studied in this paper. Unlike the TSP, in which the salesman has no capacity limitation, the vehicle in on-line VRP has a limited capacity. In the on-line VRP, when the capacity of the vehicle cannot satisfy the customers' request, it must return to the depot to refill goods and then to serve them again. With this new feature, two different strategies, Greedy Strategy (GS) and Ignore Strategy (IS), are proposed to address the on-line VRP. It is proved that the tight competitive ratios of the two strategies are 5/2 and 3, respectively. Furthermore, the lower bound of competitive ratio for the on-line VRP is presented.