Double-row facility layout with replicate machines and split flows

This paper presents a new variant of the double row layout problem (DRLP) that features types of capacitated machines. This variant dramatically improves the fidelity with which the DRLP represents the complex production alternatives in many production environments, especially in the microcomputer industry. The problem consists of placing different classes of machines, each with multiple replicates, on either side of a central aisle. This is a common type of layout problem observed in many production and service environments. This work extends the DRLP literature by utilizing machine replicates in the layout. Multiple replicates of the same machine allow the product flow to split into multiple branches, each representing a parallel flow line. Flow splitting can improve machine utilization and reduces the number of machines needed. We also introduce machine sharing, which lets different products use the same machine. This eliminates the need for dedicated assignments of products to machines, which is a common assumption in the current literature. The consideration of re-entrant product flow, whereby each product can visit the same machine multiple times, represents another unique aspect of this research. The problem is formulated as a nonlinear mixed integer program. Due to the computational complexity of this problem a hierarchical optimization approach is developed and evaluated on test problems of various sizes. Computational results show that the proposed method produces consistent and high quality solutions across problem sizes.