Single bottleneck systems with proportional expected yields and rigid demand

This study considers single bottleneck systems: multistage production systems where all setup costs except one are zero. The stage with non-zero setup cost is defined to be the bottleneck (BN). Production is in lots and demand needs to be satisfied in its entirety. The expected yield (number of good units) at each stage is proportional to the lot size and only good items may proceed from one stage to another. We reveal several general features of the optimal policy and discuss some specific yields in detail. In particular it is shown that if units are processed one-by-one on the non-BNs, the optimal lotsizing problem can be reduced to the problem of optimally lotsizing a single-stage ‘equivalent machine’. Then, if the BN has Binomial yield, the ‘equivalent machine’ itself has Binomial yields. Also, examples are given which demonstrate the non-intuitive structure of the optimal policy.