We study the flow-shop problem nonpreemptively scheduling $n$ jobs 
on $m$ machines to maximize the number of just-in-time jobs. 
This network type algorithm is based on a binary tree structure. 
We define the superiority relation of a partial schedule, 
and propose an efficient rule that searches only partial schedules 
extensible to optimal schedules. We show that this algorithm 
finds an optimal schedule for this problem in a low polynomial time.