We address an offline job scheduling problem where jobs can either be processed on a limited supply of energy-efficient machines, or offloaded to energy-inefficient machines (with an unlimited supply), and the goal is to minimize the total energy consumed in processing all tasks. This scheduling problem can be formulated as a problem of scheduling with rejection, where rejecting a job corresponds to process it on an energy-inefficient machine and has a cost directly proportional to the processing time of the job. To solve this scheduling problem, we introduce a novel 5/4(1+ε) approximation algorithm BEKP by associating it to a Multiple Subset Sum problem. Our algorithm is an improvement over the existing literature, which provides a (3/2 − 1/2m) approximation for scheduling with arbitrary rejection costs. We evaluate and discuss the effectiveness of our approach through a series of experiments, comparing it to existing algorithms.