This research investigates the bounded batch online-scheduling issue, specifically focusing on incompatible job families assigned to unit flowshop machines. The main criterion is to reduce the makespan. Within a unit flowshop setting, each machine standardizes the processing time of a job to one unit. The concept of linear lookahead pertains to an online algorithm’s ability to anticipate job information within the time interval \((t, \lambda t +\beta ]\) at time t. The bound batch capacity, denoted by \(b < \infty\) , signifies a restriction on the number of jobs that can be contained within a batch. For two unit machines, we introduce the optimal online algorithm \(A^{b}\) . In instances where multiple unit machines are employed with parameters \(\lambda \ge 1\) , \(0 \le \beta < 1\) , and \(f \ge 2\) , we establish a competitive ratio bounded by at most \(1 + \max \left\{ {\frac{f}{{(2f - 1)(1 + \alpha )}},\frac{f}{{\lambda (2f - 1)\alpha + \beta + f}}} \right\}\) based on the online algorithm \(A_{f}^{b}\) . Specifically, we present an optimal online algorithm when \(\lambda =1\) and \(0 \le \beta \le \displaystyle \frac{3f + 1-\sqrt{9 f^{2}-2f +1}}{4}\) . Additionally, we extend our findings to the bounded batch scheduling problem incorporating a linear lookahead interval and \(f (=m)\) incompatible job families on multiple unit machines.
