Multiproduct systems with both setup times and costs: fluid bounds and schedules

This paper considers a multiproduct, single-server production system where both setup times and costs are incurred whenever the server changes product. The system is make-to-order with a per unit backlogging cost. The objective is to minimize the long-run average cost per unit time. Using a fluid model, we provide a closed-form lower bound on system performance. This bound is also shown to provide a lower bound for stochastic systems when scheduling is local or static, but is only an approximation when scheduling is global or dynamic. The fluid bound suggests both local and global scheduling heuristics, which are tested for the stochastic system via a simulation study.