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

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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.