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.

中文翻译：

---

生产和质量决策

质量在运营管理中起着核心作用，因为质量是组织客户关注其决策的一个相关问题。在短期生产模型中，我们可以假设质量是恒定的。然后，我们将生产率和质量水平的最优选择作为带有参数的最优控制问题。从Kamien和Schwartz的生产计划模型开始，我们将质量作为决策变量。在解决方案中，我们观察到最佳质量水平和生产率彼此独立。接下来，当市场清算价格取决于质量和数量时，我们假设订购的数量不是外生的，而是通过优化确定的，则修改模型。我们得到了一个更有趣的解决方案，其中最佳生产和最佳质量是相互依赖的，以一种不直接的方式。我们使用参数的最优过程的必要和充分条件来表征和讨论针对这些问题的最优解决方案。这再次表明，解决此类问题的充分条件过于严格，而引入更有效的充分条件仍然是一个悬而未决的问题。