A Mixed-Integer Programming Model for Assembly Line Balancing: Using Rework Station for Standard Tasks and Optimizing Station Position

In an assembly line, if a product does not meet some pre-defined specifications (i.e., if it is defective), it is generally sent to a rework station where necessary correction (rework) operations are performed. On the other hand, the number of products sent to the rework station for rework operations depends on the rework (defect) rate of the assembly line. If the defect rate is relatively low, the rework station can be used to perform standard tasks in addition to rework operations. Using the rework station for this purpose might decrease the cycle time of the assembly line. Although rework stations are generally positioned at the end of an assembly line, it might be advantageous to change its position if it is also used for performing standard tasks. In this study, a nonlinear-mixed-integer programming model is proposed to minimize the cycle time of an assembly line by dynamically positioning the rework station which is also used to perform standard tasks in addition to rework operations. The nonlinear structure of the proposed model is linearized using some variable transformations. The position of the rework station affects the number of potential tasks assigned to this station depending on the precedence relationships of the tasks. In this study, the position of the rework station is optimized using the proposed model. Another factor that affects the number of potential tasks assigned to the rework station is defect rate of the assembly line. The proposed model is tested for different defect rates using some sample problems from the literature. The problems are solved to optimality and the results are analyzed