Balancing reconfigurable machining lines by means of set partitioning model

We consider the problem of construction of an optimal reconfigurable machining line as a sequence of workstations performing specific sets of operations. The line is required to satisfy the given precedence order on operations, inclusion, exclusion and accessibility constraints. The cycle times of workstations are computed taking into account the processing and setup times of operations and must not exceed the given bound. For solving the problem, we propose a reduction of this machining line design problem to a set partitioning type problem. This approach implies generating all possible workstations and finding optimal sequence of operations in each workstation. To do this, a dynamic programming algorithm is developed. Several preprocessing procedures are suggested for reducing the number of workstations. For solving the obtained set partitioning type problem, a constraint generation algorithm based on mixed integer programming model is proposed.