This paper presents a real-life scheduling problem of minimizing total weighted tardiness on identical parallel machines with eligibility constraints which is originated from the manufacturing plant of an industrial metal nuts company. Because the problem is NP-hard, a new electromagnetism-like mechanism algorithm is proposed to solve the problem. In the proposed algorithm, the particle is redesigned to represent jobs with valid assignment to machines. A distance measure between particles is proposed by the concept of a number-guessing game. Then, the new attraction and repulsion operators are developed to move a particle to the new particle. The computational results show that the proposed algorithm performs better than the current scheduling method of the metal nut plant and other existing algorithms.