Optimal control, pricing and empirical analysis of production and inventory systems

建议的研究计划涉及联合定价，库存和生产控制的生产/库存系统。 首先，我们考虑一个具有价格敏感需求的生产-库存系统。企业通过控制定价和生产率来优化无限时间范围内的预期贴现利润。除了建立最优的生产政策，我们专注于最优生产率和最优价格如何变化，并与其他模型参数，特别是生产的变化和需求的变化相互作用。建议的第二部分是关于随机需求的分析和经验模型。大多数文献在联合定价和库存控制假设随机成分的需求函数采取一个加法或乘法的形式。不同的假设可能会导致不同的最优定价和库存/生产控制的特性。要应用这一研究机构的理论，关键是要了解实际的需求特征。我们建议检查实际的工业数据，并描述需求水平，需求变化和各种产品类型的价格之间的关系。建议的第三部分涉及一个适用于炼油工业的生产库存系统。本文研究了在给定原材料和制成品价格的条件下，通过控制采购、生产和销售速度，使企业的期望贴现效用最大化的问题。除了生产和库存成本外，还有一项与生产率调整相关的成本。然后，我们考虑一个经济与许多这样的企业，并得出合理的预期均衡价格，库存和生产过程。我们用实际的行业数据拟合模型。

The proposed program of research is concerned with joint pricing, inventory and production control in production/inventory systems.  First, we consider a production-inventory system with price-sensitive demand. The firm optimizes the expected discounted profit over an infinite horizon by controlling pricing and production rate. In addition to establish the optimality of the produce-up-to policy, we focus on how the optimal production rate and the optimal price vary and interact with other model parameters, particularly the production variability and the demand variability. The second part of the proposal is on analytical and empirical modelling of the random demand. Most literature in joint pricing and inventory control assumes the random component in demand function take either an addictive or a multiplicative form. Different assumptions may lead to different characteristics of optimal pricing and inventory/production control. To apply the theory from this body of research, it is crucial to understand the actual demand characteristics. We propose to examine actual industrial data and to characterize the relationship between demand level, demand variability and prices for various product types. The third part of the proposal is concerned with a production-inventory system with applications to the petroleum refining industry. We consider an individual firm who maximizes its expected discounted utility over an infinite horizon through controlling its procurement, production and sales rate under given raw materials and finished goods prices. In additon to the production and inventory costs, there is a cost associated with production rate adjustment. Then we consider an economy with many such firms and derive the rational expectations equilibrium price, inventory and production processes. We fit the model with actual industry data.