Control limits for multi-stage manufacturing processes with binomial yield (single and multiple production runs)

The problem of ordering a single or a series of production runs to meet a single make-to-order demand, where the various stages in the production process have binomial yields, is addressed. Use of additional procurement of part-finished products or reworking defective material previously made to supplement yields at any stage is considered. The costs of this and manufacture, disposal of surplus or shortages are assumed to be proportional to the numbers involved. It is shown that when a single production run is considered, the optimal policy is defined by two critical numbers (control limits) at each stage. The treatment of ordering a series of production runs follows from and builds on the single run analytical result by developing an approximation in which the problem is decomposed into a series of single runs. Set-up costs may or may not be incurred.