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We considered the online scheduling problem of simple linear deteriorating job families on m parallel batch machines to minimize the makespan, where the batch capacity is unbounded. In this paper, simple linear deteriorating jobs mean that the actual processing timep jof jobJ jis assumed to be a linear function of its starting times j    , i.e.,p j  =  α j   s j, whereα j  &gt; 0is the deterioration rate. Job families mean that one job must belong to some job family, and jobs of different families cannot be processed in the same batch. Whenm = 1    , we provide the best possible online algorithm with the competitive ratio of( 1 +  α max  )  f    , where f is the number of job families andα maxis the maximum deterioration rate of all jobs. Whenm ≥ 1andm = f    , we provide the best possible online algorithm with the competitive ratio of1 +  α max.

Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families