Batch List on-line Scheduling

We consider a batch online scheduling problem of minimizing the makespan on identical parallel machines. As a batch arrives, jobs in the batch are classified into groups and the jobs in the same group may start at different time but must finish at the same time. By compositing the batch schedule and online schedule, we derived two batch online algorithms with competitive ratios m/(1+gepsiv) and (m(-1+epsiv)(-1+epsiv
^m+mk

_min
)(-1+xi
^2m+mk

_max
))/((-1+epsiv
^m
)(-1+epsiv
^1+g+m+mk

_min
)(-1+xi
^m+mk

_max
)) respectively, under different conditions