In a circular economy, the use of recycled resources in production is a key performance indicator for management. Yet, academic studies are still unable to inform managers on appropriate recycling and pricing policies. We develop an optimal control model integrating a firm's recycling rate, which can use both virgin and recycled resources in the production process. Our model accounts for recycling influence both at the supply- and demand-sides. The positive effect of a firm's use of recycled resources diminishes over time but may increase through investments. Using general formulations for demand and cost, we analytically examine joint dynamic pricing and recycling investment policies in order to determine their optimal interplay over time. We provide numerical experiments to assess the existence of a steady-state and to calculate sensitivity analyses with respect to various model parameters. The analysis shows how to dynamically adapt jointly optimized controls to reach sustainability in the production process. Our results pave the way to sounder sustainable practices for firms operating within a circular economy.

在循环经济中，在生产中使用回收资源是管理的关键绩效指标。然而，学术研究仍无法告知管理者适当的回收和定价政策。我们开发了一个整合公司回收率的最优控制模型，该模型可以在生产过程中同时使用原始资源和回收资源。我们的模型考虑了回收在供应方和需求方的影响。随着时间的流逝，企业使用可再生资源的积极影响逐渐减弱，但通过投资可能会增加。使用需求和成本的一般公式，我们分析性地研究联合动态定价和回收投资政策，以确定它们在一段时间内的最佳相互作用。我们提供了数值实验，以评估稳态的存在并针对各种模型参数计算灵敏度分析。分析显示了如何动态调整联合优化的控件以实现生产过程中的可持续性。我们的结果为在循环经济中运营的公司完善合理的可持续做法铺平了道路。