The present paper deals with the optimal management of a batch arrival, bulk service queueing system with random set-up time under Bernoulli vacation schedule and \(N\)-policy. If the number of customers in the system at a service completion is less than some integer \(r\), then the server idles and waits for the queue to grow up to some other integer \(N\), greater or equal to \(r\). If, on the other hand, it is larger than \(r\), then the server starts processing a group of \(r\) requests. The model is analysed by the method of embedded Markov chain and semi-regenerative techniques. All the key elements to build an appropriate queueing model are derived, and steady-state measures, such as mean system size, mean busy period length, etc. The perspective model of this system consists in searching for optimal values for the threshold levels \(r, N\), that minimize the expected linear cost per unit of time of the systems. Illustrative examples are presented to see the behaviour of the system.