In this paper, we consider a bilevel adversarial scheduling problem on parallel machines. Given a set of jobs that the leader has to select some jobs within the leader’s budget. Then, the follower next schedules these jobs to minimize the makespan. The goal is to select the jobs so that the optimal (minimum) value of the makespan is maximum. We design a simple (2+ \(\varepsilon \) )-approximation algorithm and a polynomial time approximation scheme (PTAS) for this problem. We also propose a simple efficient polynomial time approximation scheme (EPTAS) for this problem when the number of machines is fixed.