Manufacturing under uncertainty: offsetting the inability to instantaneously adjust production with dynamic pricing

In many manufacturing systems the production rate cannot be instantaneously adjusted in response to inventory updates. This article addresses such a system under price-dependent stochastic demand. The objective of the system is to choose a time-invariant production rate and time-dependent product price that maximize the expected profit. This manufacturing system is compared to a benchmark system where both production rate and product price are adjustable. It is shown that the expected inventory level does not necessarily increase when the manufacturer can handle stock spikes only by leveling the demand with the product price. Although the inability to adjust production rate under a high level of uncertainty is difficult to offset with dynamic pricing, the non-linear components of the production and inventory costs can make a difference. For example, by reducing the non-linear component of the production cost and increasing price volatility, the manufacturer may close the profit gap between the two systems from 25% to only 5%.