The Interaction Between Quality Control and Production

A real options model of resource extraction is considered where management controls both the extraction rates as well as the quality of extracted material earmarked for processing into final product. The minimum quality of material acceptable for processing is called the cutoff grade. If the cutoff is too high, much of the extracted material will go to waste exacting an opportunity cost. If the cutoff is too low, then input capacity constraints will be fully utilized, but with poor revenues at output. The optimal strategy should attain a balance between these considerations. A form of opportunity cost associated with extracting the marginal unit of resource seems to play a crucial role in finding the optimal strategic balance. This opportunity cost has a structure resembling a call option on the commodity. A model is developed in the presence of input and output processing stage constraints, and the set of candidate optimal policies is identified. Simulations are used to expound on the nature of the optimal policies and the important role played by the opportunity cost.