Algorithms for Capacitated Vehicle Routing

Abstract

Given $n$ identical objects (pegs), placed at arbitrary initial locations, we consider the problem of transporting them efficiently to $n$ target locations (slots) with a vehicle that can carry at most $k$ pegs at a time. This problem is referred to as $k$-delivery TSP, and it is a generalization of the Traveling Salesman Problem. We give a 5-approximation algorithm for the problem of minimizing the total distance traveled by the vehicle. There are two kinds of transportations possible --- one that could drop pegs at intermediate locations and pick them up later in the route for delivery (preemptive) and one that transports pegs to their targets directly (non-preemptive). In the former case, by exploiting the freedom to drop, one may be able to find a shorter delivery route. We construct a non-preemptive tour that is within a factor 5 of the optimal preemptive tour. In addition we show that the ratio of the distances traveled by an optimal non-preemptive tour versus a preemptive tour is bounded by 4. (Also cross-referenced as UMIACS-TR-97-79)