The Line Traveling Salesman and Repairman Problem with Collaboration

TL;DR

This paper explores extensions of the Line Traveling Salesman and Repairman Problems where both server and clients can move and collaborate, analyzing problem complexity across various scenarios and constraints.

Contribution

It introduces and analyzes new problem variants with client-server collaboration, mapping their complexity and identifying easy and hard subproblems.

Findings

Identified problem variants with different processing times and time windows.

Mapped the complexity landscape of collaborative line routing problems.

Built upon prior literature to analyze problem structures.

Abstract

In this work, we consider extensions of both the Line Traveling Salesman and Line Traveling Repairman Problem, in which a single server must service a set of clients located along a line segment under the assumption that not only the server, but also the clients can move along the line and seek to collaborate with the server to speed up service times. We analyze the structure of different problem versions and identify hard and easy subproblems by building up on prior results from the literature. Specifically, we investigate problem versions with zero or general processing times, clients that are either slower or faster than the server, as well as different time window restrictions. Collectively, these results map out the complexity landscape of the Line Traveling Salesman and Repairman Problem with collaboration.