Most studies on scheduling in dynamic job-shops assume that the holding cost of a job is given by the flowtime of the job and that the tardiness cost of a job is given by the tardiness of the job. In other words, unit holding and unit tardiness costs of a job are assumed. However, in reality, such an assumption need not hold, and it is quite possible that there are different costs for holding and tardiness for different jobs. In addition, most studies on job-shop scheduling assume that jobs are independent and that no assembly operations exist. The current study addresses the problem of scheduling in dynamic assembly job-shops (manufacturing multilevel jobs) with the consideration of different holding and tardiness costs for different jobs. An attempt is made to develop efficient dispatching rules by incorporating the relative costs of holding and tardiness of jobs in the form of scalar weights. The primary objective of scheduling considered here is the minimization of the total scheduling cost consisting of the sum of holding and tardiness costs. The performance of the scheduling rules in minimizing the individual components of total scheduling cost is also observed. The results of an extensive simulation study on the performance of different dispatching rules show that the proposed rules are effective in minimizing the means and maximums of the primary measure, and are quite robust with respect to different job structures and experimental settings.