Pickup and delivery for moving objects on broken lines

Authors:
Yuichi Asahiro;Eiji Miyano;Shinichi Shimoirisa
Affiliations:
Department of Social Information Systems, Kyushu Sangyo University, Fukuoka, Japan;Department of Systems Innovation and Informatics, Kyushu Institute of Technology, Fukuoka, Japan;Products Development Center, Toshiba Tec Corporation, Japan
Venue:
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Year:
2005

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Abstract

We consider the following variant of the Vehicle Routing Problem that we call the Pickup and Delivery for Moving Objects (PDMO) problem, motivated by robot navigation: The input to the problem consists of n products, each of which moves on a predefined path with a fixed constant speed, and a robot arm of capacity one. In each round, the robot arm grasps and delivers one product to its original position. The goal of the problem is to find a collection of tours such that the robot arm grasps and delivers as many products as possible. In this paper we prove the following results: (i) If the products move on broken lines with at least one bend, then the PDMO is MAXSNP-hard, and (ii) it can be approximated with ratio two. However, (iii) if we impose the “straight line without bend” restriction on the motion of every product, then the PDMO becomes tractable.