A special case of transfer lines balancing by graph approach

A balancing problem for paced production lines with workstations in series and blocks of parallel operations at the workstations is considered. Operations of each workstation are partitioned into blocks. All operations of the same block are performed simultaneously by one spindle head. All blocks of the same workstation are also executed simultaneously. The relations of the necessity of executing some operations at the same workstation, the possibility of combining the blocks at the same workstation as well as precedence constraints are given. The operation time of the workstation is the maximal value among operation times of its blocks. The line cycle time is the maximal workstation time. The problem is to choose blocks from a given set and allocate them to workstations in such a way that (i) all the operations are assigned, (ii) the above constraints are satisfied, (iii) a given cycle time is not exceeded, and (iv) the line cost is minimal. A method for solving the problem is based on its transformation to a constrained shortest path problem.