Risk, risk aversion and the optimal time to produce

Abstract

This paper studies the order-fulfillment process of a supplier producing a customized capital good. When they decide at what time to begin production, suppliers in these industries typically face the following dilemma. On the one hand, their customers expect them to be responsive and the time that they are prepared to wait for the product is much shorter than the time needed to produce and deliver it. On the other hand, it is risky for the suppliers to start production before the customers confirm their orders due to inventory holding costs and the possibility of order cancellation. We offer a model to help understand this dilemma and investigate the comparative statics effects of lead time, lead time uncertainty and the risk aversion of the supplier. Relative to existing work, our model has two novel components: demand distribution updating and the supplier's risk attitude. Previous empirical studies reveal that the supplier is very conservative when commencing the order fulfillment. The studies attribute this to high holding and cancellation costs relative to the delay cost. Our model provides two alternative explanations. First, other than costs, when the supplier starts to produce depends also on how the distribution of the demand arrival time is updated as time progresses. Second, although the effect of increasing risk aversion of the supplier on the optimal time to produce is ambiguous, we show that it plays a major role in the decision and thus it alone may have caused the supplier to be conservative.

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