Approximation algorithms for the capacitated traveling salesman problem with pickups and deliveries

Abstract

We consider the Capacitated Traveling Salesman Problem with Pickups and Deliveries (CTSPPD). This problem is characterized by a set of n pickup points and a set of n delivery points. A single product is available at the pickup points which must be brought to the delivery points. A vehicle of limited capacity is available to perform this task. The problem is to determine the tour the vehicle should follow so that the total distance traveled is minimized, each load at a pickup point is picked up, each delivery point receives its shipment and the vehicle capacity is not violated. We present two polynomial-time approximation algorithms for this problem and analyze their worst-case bounds.

Balancing the stations of a self service “bike hire” system

“…They call this problem "the C-delivery TSP". They give an 9.5-approximation algorithm, which we adapt in Section 5 (this ratio has been improved in [1,5]). Nevertheless, their algorithm is polynomial in the capacity C of the truck and in the total number N of items.…”

“…If there is a capacity u ∈ Z E + on the edges, we can speak of a capacited perfect b-matching m, which requires in addition to Equation (1) that m e ≤ u e for each edge e.…”

The multi-commodity one-to-one pickup-and-delivery traveling salesman problem

“…The quantities q k are randomly generated integers in [1,5]. Different capacities Q are considered also.…”

“…See Chalasani and Motwani [12], Anily and Bramel [1] and Hernández and Salazar [22,23] for articles on the case where all the objects are identical (i.e., only one commodity is moved by the vehicle from many sources to many destinations). We also keep the assumption that each object is associated with exactly one source and exactly one destination, thus the term one-to-one in the name of the problem.…”

An Algorithm for the One Commodity Pickup and Delivery Traveling Salesman Problem with Restricted Depot

“…We briefly introduce them below. The Q-delivery TSP (Chalasani and Motwani 1999) or the capacitated TSP with pickups and deliveries (CTSPPD) (Anily and Bramel 1999) is actually a special case of the 1-PDTSP with all pickups and deliveries being 1. There exists approximation algorithms for the CTSPPD.…”