ECOMFIN webinar | Stochastic Capacity Investment in Presence of Production Resource Disruption

In practice, manufacturing firms face a number of uncertainties while choosing their capacity investment levels. Besides the uncertainty in product demand, capacity investment may also be subject to uncertainty in the availability of production resources (used together with the capacity invested) and these resources may become constraining in the production stage. The production resource can be a financial resource such as operating budget, and its shortage can be attributed to the worsened external financing conditions (e.g., 2008 financial crisis). The production resource can also be a physical resource such as a component and its shortage can be attributed to a variety of factors including health and safety issues in supplier’s premises (e.g., Covid 19 pandemic) and industry-wide shortage (e.g., shortage in semiconductor components in the automotive industry). Motivated by these observations, this paper studies a manufacturing firm’s capacity investment decision under demand and production resource uncertainties. To this end, we consider a firm who produces and sells a single product in a single selling season to maximize its expected profit. We formulate a two-stage stochastic model. In the first stage, the firm chooses the capacity investment level in the presence of demand and production resource uncertainties. In the second stage, after both uncertainties are realized, the firm then decides on the optimal production quantity constrained by the available capacity and production resource. We conduct sensitivity analyses to examine the impact of production resource variability and its correlation with demand. We find that the firm always benefits from a higher correlation. For the effect of production resource variability, we identify the critical roles played by the correlation and the capacity investment cost. In particular, we find that the firm benefits from a lower production resource variability when the capacity investment cost is sufficiently high or the correlation is sufficiently low. In other cases, the firm benefits from a lower production resource variability only when this variability is sufficiently high; otherwise a higher production resource variability increases profitability. These results have important managerial implications on how a local versus global supply chain disruption affects the firm where correlation is weak (or zero) for the former and it is large in absolute value for the latter.
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