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Optimal investment timing and scale when demand follows a product life cycle

Typically product demand follows a product lifecycle (PLC). This means that after a product is introduced, demand for this product first starts to grow, which after some time is followed by a decline in demand. Moreover, in most cases demand is stochastic. This paper combines these two characteristics by employing a geometric Brownian motion process with a first increasing and afterwards decreasing trend. Our aim of the paper is to investigate the optimal investment decision of a firm in production capacity. The investment decision involves deciding about the timing and the size of the investment. We make a distinction between firms being a ``product-lifecycle leader'' and a ``product-lifecycle follower''. For a PLC-leader the growth stage starts at the moment this firm invests. In case of a PLC-follower, the firm enters an existing product lifecycle, implying that the decline can already start before this firm even has invested.

One of the interesting results is that a PLC-leader waits for a higher demand level before it invests with the same amount when the expected length of the growth interval is shorter. For the PLC-follower it holds that it may be optimal to invest earlier because of this probability that the decline could already start before the firm invests. In such a case the expected future demand is lower, which makes it optimal that the firm attracts less capacity. This makes the investment cheaper and then the firm does not need to wait for a high demand level to make the investment profitable.