On problem of optimal design of transfer lines with parallel and sequential operations

A problem of optimal design for a class of automatic production systems is considered. The investigated systems are transfer lines without buffers and with parallel and sequential operations at each workstation. Manufacturing operations for a workstation are partitioned into blocks. All operations of the same block are performed simultaneously, and different blocks are executed sequentially. The relations of necessity and possibility of combining operations in one block and in one workstation as well as precedence constraints are given. Operation time of a block depends of assigned operations, while the operation time of a workstation is the sum of operation times of its blocks. The problem is to minimize the weighted total number of workstations and blocks, providing a given cycle time and satisfying the above constraints. The proposed method is based on reducing the initial problem to the shortest constraint path problem.