Online Batch Scheduling of Incompatible Job Families with Variable Lookahead Interval

We consider online parallel-batch scheduling of [Formula: see text] incompatible unit-length job families with variable lookahead interval to minimize the maximum completion time, where [Formula: see text] is the number of job families which is known in advance. Incompatible job family means that a batch only contains the jobs from the same job family. At any time [Formula: see text], an online algorithm can foresee the information of the jobs arriving in the time interval [Formula: see text], where [Formula: see text] is variable. When the batch capacity [Formula: see text] and [Formula: see text], we provide a best possible online algorithm with competitive ratio [Formula: see text] for [Formula: see text] and [Formula: see text], where [Formula: see text] is a positive root of [Formula: see text]. When the batch capacity [Formula: see text] and [Formula: see text], we give an online algorithm with competitive ratio [Formula: see text] for [Formula: see text] and [Formula: see text], and prove that it is the best possible for [Formula: see text] and [Formula: see text].