Market risk and process uncertainty in production operations

Abstract

By adopting a real options framework we develop a production control model that jointly incorporates process and market uncertainties. In this model, process uncertainty is defined by random fluctuations in the outputs' yield and market risk through demand uncertainty for the output. In our approach, production outputs represent commodities or items for which financial contracts do not trade. Outputs are also functionally linked to the level of input inventories. To extend the model's applicability to a wide range of production industries, inputs are modeled to reflect either renewable or partially renewable or non-renewable resources. Given this setting, techniques of stochastic control theory are employed to obtain value maximizing production policies in a constrained capacity environment. The rate of production is modeled as an adapted positive real-valued process and analogously evaluated as a sequence of complex real options. Since optimal adjustments to the rate of production also functionally depend on the outputs' yield, we optimally establish “trigger boundaries” justifying controlled variations to the rate of production over time. In this context, we provide closed form analytic results and demonstrate their robustness with respect to the stochastic (including mean reverting) processes considered. Using these results, we also demonstrate that the value (net of holding costs) accrued to the producer from having an inventory of the output is equivalent to the producer's reservation price to operationally curb its process yield. These generalizations extend the scope of model applicability and provide a basis for applying the real options methodology in the operations arena. The model is explored numerically using a stylized example that allows for both output and demand uncertainty and achieves greater realism by incorporating an element of smoothing into the sequence of production decisions. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006