Date: 6 April 2023, Thursday
Place: Faculty of Business Administration,
‘Stochastic Capacity Investment in the Presence of Production Resource Uncertainty and Its Implications for Hedging’
Singapore Management University
Abstract: 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.
To counteract against the production resource uncertainty resulting from some of the aforementioned exposures, the firm can rely on hedging instruments at the time of capacity investment to engineer the availability of production resource in the production stage. For example, if the production resource is an operating budget that depends on a financially hedgable index such as asset price, the firm can sell a forward contract written on this index from a fixed price to engineer the operation budget’s distribution. If the production resource is a commodity component, the firm can sell a forward contract written on the commodity price to engineer the component’s availability in the production stage. We extend our basic model to consider the hedging decision in the capacity investment stage. In particular, we assume that the firm decides on the forward contract volume to sell which corresponds to deciding on the (proportional) allocation between a deterministic production resource and an uncertain production resource which has an expected value equaling the former. In other words, consistent with practice, hedging decision does not change the mean production resource but alters its variability. When the allocation is made fully to the uncertain resource (i.e., no hedging scenario), this corresponds to the case in our basic model. When the allocation is made fully to the deterministic resource (i.e., full hedging scenario), the firm does not face production resource uncertainty. When both resources receive some allocation (i.e., partial hedging scenario), the firm faces a reduced production resource uncertainty. We characterize the joint optimal capacity investment and hedging decisions of the firm. We identify correlation between demand and production resource uncertainty and the capacity investment cost as the key drivers of the optimal hedging portfolio. In particular, when the correlation is non-positive, the firm always fully hedges and production resource uncertainty is inconsequential for the firm. When the correlation is positive, full hedging is optimal only when capacity investment cost is sufficiently high. Otherwise, the firm chooses a partial hedging policy. Interestingly, the optimal partial hedge is chosen in such a way that there is no effect of production resource variability on the firm’s profitability or capacity investment decision. We also find that the firm may optimally choose not to hedge at all, specifically, when the correlation is sufficiently high and the capacity investment cost is sufficiently low. In contrast with the basic model, with optimal hedging the firm always benefits from a higher production resource variability. Paralleling the basic model, with optimal hedging the firm always benefits from a higher correlation. By making a comparison with the basic model, we characterize the value of hedging. As intuition suggests, we find that the value of hedging increases in production resource variability. Interestingly, we also find that value of hedging decreases in correlation.