This paper addresses a problem of continuous batch scheduling arising in the heating-process of blooms in steel industry.Each heating furnace is modeled as continuous batch processing machine

which can handle more than one job simultaneously.The processing time of a batch depends on its size

the longest processing time of jobs in the batch and the capacity of the batching machine.In this paper we consider the problem for minimizing total completion time.The theoretic analysis of optimal solution properties are given

and the optimal policy of batching and the method of sequencing the batches are provided.A dynamic programming algorithm with a polynomial running time is represented based on the properties of batching and scheduling.