We consider a single-stage multi-product production system. In such a system, a single machine is used to process multiple types of products. The demands and processing rates for a part are likely to differ across types. Setup activities are necessary when switches of part types are made. These setup activities require time and incur cost that depend on the specific part type. As a consequence of these differences, production scheduling will have great impact on the total amount of work in process (WIP) inventory and the average production cost. Optimal dynamic schedules and performance bounds for such a system under the stochastic setting are extremely difficult to obtain, even for very simple cases.; We analyze such a system with a fluid model. Under the fluid assumption, the demands and processing rates of products are assumed to be deterministic and continuous. The setup times are assumed to be deterministic as well. We develop a mathematical program to model this fluid system and use it to derive a lower bound and scheduling heuristics for such a fluid system. We then show that the fluid bound is a valid lower bound for the stochastic system operated under a static-type policy. The heuristics are then used as scheduling methods for the stochastic system. A simulation study is conducted to study the performance of the bound and scheduling heuristics. In addition, we extend the fluid bound to multi-stage systems under a specific assumption on the service discipline.
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