Option methods for incorporating risk into linear capacity planning models

Manufacturing and service operations decisions depend critically on capacity and resource limits. These limits directly affect the risk inherent in those decisions. While risk consideration is well developed in finance through efficient market theory and the capital asset pricing model, operations management models do not generally adopt these principles. One reason for this apparent inconsistency may be that analysis of an operational model does not reveal the level of risk until the model is solved. Using results from option pricing theory, we show that this inconsistency can be avoided in a wide range of planning models. By assuming the availability of market hedges, we show that risk can be incorporated into planning models by adjusting capacity and resource levels. The result resolves some possible inconsistencies between finance and operations and provides a financial basis for many planning problems. We illustrate the proposed approach using a capacity-planning example.