An MIP Approach to the U-Line Balancing Problem with Proportional Worker Throughput

One of the major challenges faced by manufacturing companies is to remain competitive in dynamic environments, where fluctuations in customer demand and production rates require systems capable of adapting in a practical and economical way. A U-shaped production cell is considered one of the most flexible designs for adapting the workforce level to varying conditions. However, re-balancing efforts are time consuming and often require a new work allocation and line design. In this paper, a two-stage MIP model to determine the best cell design under varying workforce levels is proposed. The model seeks to maintain proportionality between throughput and the number of workers. Computational experiments considering various line configurations (up to 19 stations) and workloads (up to 79 tasks) are performed. The results show the proposed algorithm provides excellent results for all small and medium size problems addressed in this study, as well as for certain configurations of large problems. This approach can be used to generate lookup tables of line designs to help with quick reallocation of worker assignments on the shop floor and with minimal disruption.