SINGLE BOTTLENECK SYSTEMS WITH PROPORTIONAL EXPECTED YIELDS AND RIGIDDEMAND

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 y ield (number of good units) at each stage is proportional to the lot s ize and only good items may proceed from one stage to another. We reve al several general features of the optimal policy and discuss some spe cific yields in detail. In particular it is shown that if units are pr ocessed one-by-one on the non-BNs, the optimal lotsizing problem can b e reduced to the problem of optimally lotsizing a single-stage 'equiva lent machine'. Then, if the BN has Binomial yield, the 'equivalent mac hine' itself has Binomial yields. Also, examples are given which demon strate the non-intuitive structure of the optimal policy.