Orders and inventory commodities with price and demand uncertainty in complete markets

The purpose of this paper is to price an order (inventory control) policy when both the demand and the price are uncertain and markets are complete. Inventory management is assumed to be equivalent to an investment for future and risky prospects for which a risk premium is required. Optimization of this risk premium defines the optimal-order policy. A number of examples are solved and we show how a zero-inventory policy can be replicated by a portfolio of options and of course an optimal-order quantity. The approach developed in this paper underlies as well a common practice by certain firms who use materials that are traded in speculative financial markets. In these situations, managers combine their production-based activities with speculations regarding their potential demand and the associated price of materials. For demonstration purposes and to highlight the practicality of this approach an extensive application and numerical results are used. In particular, we consider a two-period problem with an exponential utility function and a mean exponential demand, which is a function of price.