Modelling transfer line design problem via a set partitioning problem

The design of a transfer line is considered. This line is used for a repetitive execution of a given set of operations to produce identical items. The line is composed of a sequence of workstations equipped with processing modules (blocks). Each block performs specific operations. The machined items move along the workstations in the same direction. There is the same cost associated with each workstation and different costs associated with diverse blocks. The problem is to determine the number of workstations, select a set of blocks and assign the selected blocks to the workstations so that, for each item, each operation is performed exactly once with total line cost to be minimized. The specificity of the problem is that all operations of the same workstation are performed in parallel. There are inclusion, exclusion, and precedence relations that restrict the assignment of blocks and operations to the same workstation and constrain the processing order of the operations on the transfer line. We suggest a reduction of this transfer line design problem to a simple set partitioning problem. This reduction is based on the concept of a locally feasible workstation.