This paper focuses on the multi-agent parallel machines scheduling problem with consumer agents and resource agents. Within the context, all the agents are self-interested aiming at maximising their profits, and have private information, precluding the use of the centralised scheduling approaches that require complete information of all the consumer agents. Therefore, an iterative combinatorial auction mechanism based on a decentralised decision procedure is proposed to generate a collaborative scheduling scheme without violating information privacy. The developed approach adopts flexible bidding strategies to reduce the conflict in resource allocation, and a hybrid auction termination condition is developed to ensure the convergence of the approach while guaranteeing sufficient competition among agents. Experimental results show the developed approach generates high-quality solutions with a small price of anarchy compared with centralised approaches and outperforms the state-of-the-art decentralised scheduling approach in improving social welfare, especially for problems with a large number of consumer agents.