Algorithms and implementation of a set partitioning approach for modular machining line design

Abstract : A transfer line design problem is considered. Transfer lines are sequences of workstations equipped with processing modules called blocks each of which performs specific operations. These lines are used for mass production of one type of product and thus execute repetitively a given set of operations. The machine parts move along the stations in the same direction. An identical cost is associated with each station and differing costs are associated with the blocks. The problem is to determine the number of stations, select a set of blocks and assign selected blocks to the stations so that operations of the selected blocks constitute the original set of operations and the total cost is minimized. A distinct feature of the problem is that operations at the same station are performed in parallel. Plus, there are inclusion, exclusion and precedence relations that restrict the assignment of the blocks and operations to the same station as well as the processing order of the operations on the transfer line. We implement a novel set partitioning formulation of this design problem with pre-processing procedures and heuristics. The presented approach has the best performance among the existing methods in terms of solution time and quality.