Although the impact of layout on the productivity of manufacturing systems is well recognized, a quantification of this impact is an issue that is often ignored or crudely approximated in practice. When evaluating competing layouts for a manufacturing system, the trade-off between their relative benefits and their relative costs underlines the need for a reasonably accurate comparison of the productivity offered by these potential layouts. In this paper, we argue for this approach by comparing the productivity of two well-known layouts in robotic-cell manufacturing: circular and linear.
We consider the problem of optimizing throughput in single-gripper, bufferless robotic cells that produce identical parts under the free-pickup criterion and the additive-travel-time metric. For cells with a circular layout, we show that the problem of finding an optimal 1-unit cycle is NP-hard. Our main algorithmic result is a polynomial-time 5/3-approximation algorithm for this problem. We then demonstrate that our algorithm provides near-optimal solutions by compiling its performance on an extensive test bed of practically-relevant instances. Finally, we use the algorithm to assess the increase in throughput for cells with a circular layout over those with a linear layout. We show that a circular layout offers a significant improvement in productivity and demonstrate the robustness of this improvement by examining the sensitivity with respect to changes in the design parameters of the robotic cell. Thus, our work provides operations managers with a tool to trade off the resulting increase in revenue with the additional cost of acquiring and maintaining a robot that can exploit a circular layout.