VEHICLE SCHEDULING ON A TREE TO MINIMIZE MAXIMUM LATENESS

Abstract

In this paper we deal with a single-vehicle scheduling problem on a tree-shaped road network. Let T = (V, E) be a tree, where V is a set of n vertices and E is a set of edges. A task is located at each vertex v ∈ V, which is also denoted as v. Each task v has its due date d(v) and processing time p(v). The travel times w(u, v) and w(v, u) are associated with each edge (u, v) ∈ E. The vehicle starts from an initial vertex v_O ∈ V, visits all tasks v ∈ V for their processing (no preemption is allowed) and returns to v_O. The problem asks to find a routing schedule of the vehicle that minimizes the maximum lateness from the due dates of tasks. This problem is called TREE-VSP(L_<max>). We prove that TREE-VSP(L_<max>) is strongly NP-hard in general, but show that it can be solved in polynomial time if only depth-first routing is allowed for the vehicle.