The effect of machine availability on the worst-case performance of LPT

We consider the makespan minimization parallel machine scheduling problemwhere each machine may be unavailable for a known time interval. For this problem, we investigate how the worst-case behavior of the longest processing timefirst algorithm (LPT) is affected by the availability ofmachines. In particular, for givenmmachines, we analyze the cases where arbitrary number, , ranging from one tom− 1, machines are unavailable simultaneously. Then, we show that the makespan of the schedule generated by LPT is never more than the tight worst-case bound of 1 + 1 2 m/(m − ) times the optimum makespan. © 2004 Elsevier B.V. All rights reserved.