Abstract
We are given an undirected complete graph G=(V,E) and a set Q of n transfer requests. Each transfer request i∈Q is characterized by a starting vertex s_i∈V, a destination t_i∈V, a handling time h_i, and the number q_i of staff members to be dispatched for serving the transfer request. A symmetric travel time w(u,v)=w(v,u) is associated with each edge e=(u,v)∈E, and the edge-weight function w satisfies the triangle inequality. Every vehicle is initially situated at a specified home location v_0∈V, and returns to the home after serving at most b transfer requests. We refer to integer b as the serving capacity of the vehicles. The tour time of a vehicle must not exceed a given upper limit l_<max>. For each vehicle, the maximum of the number q_i of staff members among the assigned transfer requests are dispatched. The objective is to minimize the total number of dispatched staff members for serving all n transfer requests. In this paper, we show that the vehicle scheduling problem can be solved in polynomial time if the serving capacity is two.
