A Fluid Model of Dynamic Pricing and Inventory Management for Make-to-Stock Manufacturing Systems

In this paper, we introduce a fluid model of dynamic pricing and inventory management for make-to-stock manufacturing systems. Instead of considering a traditional model that is based on how price affects demand, we consider a model that relies on how price and level of inventory affect the time a unit of product remains in inventory. Our motivation is based on the observation that in inventory systems, a unit of product incurs a delay before being sold. This delay depends on the unit price of the product, prices of competitors, and the level of inventory of this product. Moreover, delay data is not hard to acquire and is internally controlled and monitored by the manufacturer. It is interesting to notice that this delay is similar to travel times incurred in a transportation network. The model of this paper includes joint pricing, production and inventory decisions in a competitive, capacitated multi-product dynamic environment. In particular, in this paper we (i) introduce a model for dynamic pricing and inventory control that uses delay rather then demand data and establish connections with traditional demand models, (ii) study analytical properties of this model, (iii) establish conditions under which the model has a solution and finally, (iv) establish an algorithm that solves efficiently a discretized version of the model