In this paper, a new approach to respond rapidly changing market demands has been created for the line balancing problem(LBP) having an important role in textile and apparel industry. The material of fir study is the operation details that will be balanced the line in the sewing department. Some of the operations can flexibly be assigned to the operators; these are named as flexible operations. The others, non-flexibles, must be performed to the order. The integer mathematical programming is the method of the study. With the operation details of the product to be balanced the line, an integer model finding minimum idle time per operator in a production range have been developed using integer mathematical programming. Besides, because of the NP-hardness of the LBP, a new heuristic algorithm which responds immediately to market demands, has polynomial complexity, and finds the minimum number of operators has been designed. Using the algorithm designed, software has been programmed in C# to be used in the industry and the high-efficiency balancing results obtained by means of the software have been presented for a sample industrial model.