 
Summary: Restricted Delivery Problems on a Network
Esther M. Arkin y , Refael Hassin z and Limor Klein x
December 17, 1996
Abstract
We consider a delivery problem on a network one is given a network in which nodes have
supplies or demands for certain products, and arcs have lengths satisfying the Triangle
Inequality. A vehicle of infinite capacity, travels through the network, carrying products to
their destinations, and is limited in that it can carry only a single type of product at a time.
The general problem asks for a shortest delivery route of all products from their origin to their
destination. Here we consider certain restrictions on the delivery paths allowed, and compare
the quality of the solution of the unrestricted problem to that of the restricted one. Both the
general and restricted problems are NPhard, and we discuss approximation algorithms. We
also give a constant factor approximation algorithm for the Clustered Traveling Salesman
Problem.
Keywords: Traveling salesman problem, approximation algorithm.
1 Introduction
In this paper we are concerned with a delivery problem on a network. We are given a network
(a directed or undirected graph) G = (N; E) in which arcs have lengths (travel distances).
We assume throughout that the lengths satisfy the triangle inequality. Every node in the
graph is characterized by the type and quantity of product that it demands, and the type
