Exploring the interplay of costs and flow time in server allocation for flow lines with parallel non-identical machines

The Server Allocation Problem is a significant challenge in manufacturing systems involving deciding the number and version of machines for each stage. This optimization problem is of utmost importance when there is a trade-off between minimizing investment costs and flow time while achieving target performance, such as a minimum throughput. Manufacturing systems often employ hybrid flow lines, with non-identical machines at each stage. This paper analyzes the trade-off between minimizing costs and flow time when allocating servers in hybrid flow lines by proposing a bi-criteria approach that uses an efficient pattern-based problem representation and a Variable Neighborhood Search solution algorithm. The objectives are to minimize total cost and flow time while ensuring a target throughput. A metric for comparing obtained solutions is proposed, providing insights for practical implementation. A comprehensive numerical analysis is conducted, to validate the proposed approach and demonstrate its applicability in real-world manufacturing settings.