Decisions on production and quality

Quality plays a central role in Operations Management as it is a relevant issue on which the customers of an organization focus their judgment. In a short-term production model, we can assume that quality is constant. Then, we treat the optimal choices of production rate and quality level as an optimal control problem with a parameter. Starting from a production planning model by Kamien and Schwartz, we introduce quality as a decision variable. In the solution, we observe that the optimal quality level and production rate are independent of each other. Next, we modify the model assuming that the ordered quantity is not exogenous, but is determined through optimization, when the market-clearing price depends on both quality and quantity. We get a more interesting solution in which optimal production and optimal quality are interdependent, in a way that is not straightforward. We characterize and discuss the optimal solutions to these problems using the necessary and sufficient conditions for optimal processes with parameters. This shows once again that the sufficient conditions for this kind of problem are too restrictive and introducing a more effective kind of sufficient conditions is still an open question.