The leading position in contributing to the economics of many countries is hold occupied by the garments factory and it has great opportunity to enhance its area .In Bangladesh, the garment factory is the top of the organization, which takes the vital role in the economic sector. As the number of jobs and machines increase, the flow shop scheduling problems in the industry approaches to difficulty. Consider a regular flow shop cell with several bottleneck stages. If such were the case, the industry owners would provide more resources to these bottleneck stages. In this case it is so much important to eliminate the bottleneck in production section and improve the total productivity of the industry. This paper deals with the Branch and Bound technique for solving M machines and N jobs in flow-shop scheduling problem. Here the optimal sequence of jobs is obtained through minimizing the total elapsed time by a lower Bounding (LB) method based on the Branch and Bound algorithm. The working of the algorithm has been illustrated by numerical example and also a C++ code was used to generate an algorithm for finding the optimal solution. The input parameters are process time and operation sequence for each job in the machines provided. This research ensures the makespan optimal values of the schedules comparing with the Tabu search method.
