Production Systems with Rigid Demands, Random Yields, and Inspections

When production yield is random and demand needs to be satisfied in full, several production runs may need to be attempted until the number of usable products is sufficient. The tradeoff is then between using small lots possibly incurring setup cost many times and large lots which may result in costly overproduction. We generalize this problem to include inspection costs and show how to compute the optimal lot size and the expected number of inspections. Four useful models with binomial, discrete uniform, all-or-nothing, and interrupted geometric yields are examined in detail. Numerical results are presented to obtain insights into the lotsizing in production systems with random yields.