Multiproduct Systems with Both Setup Times and Costs: Fluid Bounds and Schedules

This paper considers a multi-product, 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 static, but is only an approximation when scheduling is dynamic. Heavy-traffic analysis yields a refined bound that includes second-moment terms. The fluid bound suggests both dynamic and static scheduling heuristics, which are tested via a simulation study.