Optimal use of downward substitution in a manufacturing operation subject to uncertainty

We study the optimal use of downward substitution for a capacitated manufacturing firm subject to supply uncertainty. The firm may substitute units of a higher-quality component in place of the lower-quality component to mitigate the negative consequences arising from the disruption of a lower-quality component supplier. We use first-order optimality conditions to study the optimal use of downward substitution in a single-period setting and stochastic programming techniques to extend our analysis to a multi-period setting. We explicitly characterize the optimal use of downward substitution for the single-period setting. Interestingly, we identify two distinct applications of the tactic, one that increases the supply of the lower-quality product following a disruption and another that rations limited production capacity when no disruption occurs. We conduct a numerical study that investigates the use and profit impact of these two forms of downward substitution for varying problem parameters and length of the planning horizon. Our results show that both applications of downward substitution are widely applicable and investigates the impact of various factors including cost relationships, demand uncertainty, demand correlation, and the available production capacity on the usage of downward substitution and the marginal profit improvements it offers.