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This study investigates minimizing the number of weighted tardy jobs on a single machine when jobs are delivered to either customers or next station in various size batches. In real world, this issue may happen within a supply chain in which delivering goods to customers entails costs. Under such circumstances, keeping completed jobs to deliver in batches may result in reducing delivery costs; nevertheless, it may add to the tardy jobs, which in turn leads to higher costs. In literature review, minimizing the number of weighted tardy jobs is known as NP-Hard problem, so the present issue aiming at minimizing the costs of delivering, in addition to the aforementioned objective function, remains an NP-Hard problem. In this study, the issue is assessed where the customers are numerous, and a mathematical model is presented. We also present a meta-heuristic method based on simulated annealing (SA) and the performance of the SA is examined versus exact solutions.