Any real world system must have at least one constraint to limit the system from achieving its objective. How to make good use of constraints is of vital importance to increase the efficiency of the system. In this paper, an approximate algorithm consisting of two stages of approaches is proposed for solving the real world problems. The first stage of approach called Basic Approach (BA) is proposed for searching a suboptimal solution with non-relaxing resources. The second stage of approach called Buffer Management Approach (BMA) is proposed for improving the solution obtained from BA and excluding the situations of violating restrictions by relaxing resources. According to the complicacy, diversity and limited resources of real world problems, an idea of relaxing resources is embedded in the second stage of approach. The methods of Drum-Buffer-Rope (DBR) scheduling and buffer management are used in the approaches for excluding the constraints in the process and increasing the efficiency of the system. The proposed algorithm is applied to solving the Loading Allocation and Scheduling Problems (LASP) in real world. By combining the two stages of approaches, the proposed algorithm is considered to be effective and adaptive for solving a real world problem with complicated restrictions.