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

拟议的研究方案涉及生产/库存系统中的联合定价、库存和生产控制。首先，我们考虑一个具有价格敏感需求的生产库存系统。企业通过控制价格和生产率，在无限范围内实现预期贴现利润的最优化。除了建立生产到政策的最优性之外，我们还关注最优生产率和最优价格如何变化以及与其他模型参数（特别是生产可变性和需求可变性）的相互作用。第二部分是对随机需求的分析和实证建模。大多数关于联合定价和库存控制的文献都假设需求函数中的随机成分要么呈成瘾形式，要么呈乘法形式。不同的假设可能导致最优定价和库存/生产控制的不同特征。为了应用这一研究的理论，了解实际需求特征是至关重要的。我们建议检查实际的工业数据，并描述需求水平、需求变异性和各种产品类型价格之间的关系。提案的第三部分是关于在石油炼制工业中应用的生产库存系统。我们考虑在给定的原材料和制成品价格下，通过控制其采购、生产和销售率，在无限范围内最大化其预期贴现效用的单个企业。除了生产和库存成本外，还有与生产率调整相关的成本。然后，我们考虑一个有许多这样的企业的经济体，并推导出理性预期、均衡价格、库存和生产过程。我们用实际的行业数据来拟合模型。

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.