Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families

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 time pj of job Jj is assumed to be a linear function of its starting time sj, i.e., pj = a jsj, where aj > 0 is 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. When m = 1, we provide the best possible online algorithm with the competitive ratio of ( 1 + amax) f, where f is the number of job families and amax is the maximum deterioration rate of all jobs. When m 1 and m = f, we provide the best possible online algorithm with the competitive ratio of 1 + alpha(max).