We investigate the problem of the online scheduling with non-delayed processing constraint and bounded delivery times on a single machine where jobs arrive over time. The non-delayed processing ( \(\text{ NDP }\) ) constraint means that the available jobs cannot be delayed for processing when a machine is idle. Each job’s information, such as processing time and delivery time, becomes known at its release time. Once the processing of a job is completed on the machine, we deliver it to the destination by a vehicle. The objective is to minimize the time by which all jobs have been delivered. In this paper, we assume that all jobs have bounded delivery times, i.e., \(\beta q_j\leqslant p_j\) for each job \(J_j\) , where \(p_j\) and \(q_j\) denote the processing time and delivery time of \(J_j\) , respectively, and \(\beta \) is a given non-negative real number. We present a best possible online algorithm with a competitive ratio of \(1+\frac{1}{\beta +2}\) .
