A production system with random yield and equipment deterioration: Single period

We consider the problem of determining production quantities for a single-product production system with random yield and equipment deterioration. Units are processed on a single machine with renewal but no catastrophic failure. At the beginning of each period, we observe the equipment condition and the net inventory level and make two decisions: whether or not to repair the machine and how many units to produce. If we choose to repair, the machine instantaneously returns to good-as-new condition. Items are produced instantaneously and used to fill the demand at the beginning of each period. Unsatisfied demand is backlogged. We assume that the yield (output) follows a binomial distribution, where the probability of generating a good output from one unit of input is a function of the cumulative units produced since last renewal.