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This paper investigates a new kind of single machine scheduling problem derived from the production scheduling of reheating furnaces in the iron and steel industry. In this problem, the single machine can simultaneously process multiple jobs. However, there is no batch and the jobs enter and leave the machine one by one and continuously. The objective is to minimize the total weighted tardiness of all jobs. We formulate this problem as a mixed integer linear programming (MILP) model and propose a simplified scatter search algorithm. The computational results on randomly generated instances show that the MILP model is correct and the proposed SSS algorithm outperforms CPLEX.