Logistic planning and control of reworking perishable production defectives

We consider a production line that is dedicated to a single product. Produced lots may be non-defective, reworkable defective, or non-reworkable defective. The production line switches between production and rework. After producing a fixed number (N) of lots, all reworkable defective lots are reworked. Reworkable defectives are perishable, i.e., worsen while held in stock. We assume that the rework time and the rework cost increase linear with the time that a lot is held in stock. Therefore, N should not be too large. On the other hand, N should not be too small either, since there are set-up times and costs associated with switching between production and rework. For a given N, we derive an explicit expression for the average profit (sales revenue minus costs). Using that expression, the optimal value for N can be determined numerically.