Approximation algorithms for the twin robot scheduling problem

Abstract

We consider the $$\mathscr {NP}$$-hard twin robot scheduling problem, which was introduced by Erdogan et al. (Naval Res Logist (NRL) 61(2):119–130, 2014). Here, two moving robots positioned at the opposite ends of a rail have to perform automated storage and retrieval jobs at given positions along the gantry rail with a non-crossing constraint. The objective is to minimize the makespan. We extend the original problem by considering pickup and delivery times and present exact and approximation algorithms with a performance ratio of $$\approx \,1.1716$$ for large instances. Further, we compare the presented algorithms in a comprehensive numerical study.