A tight approximation algorithm for problem P2→ D|v=1,c=1|C_max

This paper focuses on the scheduling problem on two parallel machines with delivery coordination. In particular, given a set of n jobs, we aim to find a schedule with a minimal makespan such that all jobs are first executed on two parallel machines then delivered at the destination with a transporter. This problem is known to be NP-hard Chang and Lee (Eur J Oper Res 158(2):470–487, 2004), cannot be solved with an approximation ratio strictly less than 3/2 unless P=NP. We close the gap by proposing a polynomial time algorithm whose approximation ratio is 3/2+ε with ε >0 , improve the previous best ratio 14/9 + ϵ .