Capacitated vehicle routing problem on line with unsplittable demands

In this paper we study the capacitated vehicle routing problem. An instance of capacitated vehicle routing problem consists of a set of vertices with demands in a metric space, a specified depot, and a capacity bound C . The objective is to find a set of tours originating at the depot that cover all the demands, such that the capacity of each tour does not exceed C and the sum of the tour lengths is minimized. For the case that the metric space is a line and the demands are unsplittable, we provide a 5/3 -approximation algorithm. An instance is given to show that the bound is tight.