Production planning and scheduling is a long standing research area of great practical value, while industrial demand for production planning and scheduling systems is acute. Regretfully, most research results are seldom applied in industry because existing planning and scheduling methods can barely meet the requirements for practical applications. This paper identifies four major requirements, namely generality, solution quality, computation efficiency, and implementation difficulty, for practical production planning and scheduling methods. Based on these requirements, method, a multi-agent based beam search (MABBS), is developed. It seamlessly integrates the multi-agent system (MAS) method and beam search (BS) method into a generic multi-stage multi-level decision making (MSMLDM) model to systematically address all the four requirements within a unified framework. A script language, called EXASL, and an open software platform are developed to simplify the implementation of the MABBS method. For solving complex real-world problems, an MABBS-based prototype production planning, scheduling and execution system is developed. The feasibility and effectiveness of this study is demonstrated with the prototype system and computation experiments.