A Single Bottleneck System with Binomial Yields and Rigid Demand

This paper considers a "single bottleneck system": a multistage production system where all setups except one are zero. The stage with nonzero setup is defined to be the bottleneck; it may be thought of as the critical resource whose throughput largely determines the throughput of the entire system, as a envisioned by the OPT philosophy. Production is in lots with uncertain (binomial) yields and demand needs to be satisfied in full, thus possibly necessitating multiple production runs. We show how the optimal control problem can be reduced to that of optimal lotsizing a single stage.