Online Traveling Salesman Problem With Per-Unit-Time Penalty

Abstract

Considering that the time of arriving at the request’s position is very important for emergency vehicle and emergency vehicle can’t reject any request, we introduce a more realistic penalty form into online traveling salesman problem(OL-TSP). When a new request arrives, if the salesman can’t serve the request immediately, per-unit-time penalty will be generated. The goal is to minimize server’s costs(travel makespan plus the penalties). We show that neither deterministic nor randomized online algorithms can achieve constant competitive ratio for OL-TSP with per-unit-time penalty on general metric space. While on truncated line segment, we present the lower bound, give the algorithm, and analyze the competitive ratio.