Supplemental Appendix to “Disruption Risk and Optimal Sourcing in Multi-tier Supply Networks”

In this section we numerically extend the analytical insights regarding heterogeneous unreliable Tier 2 suppliers derived in the main text to a more general case in which Tier 2 suppliers may di↵er in both procurement cost and disruption risk, which we denote cj and j , j = 1, 2. As in the main text, we assume that 1  2, but the cost parameters may be ordered in any way. Our chief goal is to confirm the following four key results. (1) Holding all else equal, a diamond shaped supply chain results in less reliance on manufacturer mitigation and more reliance on supplier mitigation than a V shaped supply chain. (2) Tier 1 suppliers are less likely to select a V shaped supply chain as the manufacturer’s unit revenues increase, while the manufacturer always prefers a V shaped supply chain. (3) A preference conflict between the manufacturer and Tier 1 suppliers over the supply chain configuration is more likely for more severe disruptions and more heterogeneous Tier 2 suppliers. (4) Penalty contracts can eliminate the perverse incentives for Tier 1 suppliers to select a diamond shaped supply chain. It is clearly the case that (1) and (4) hold even under cost heterogeneity. To show (1), we must consider the limit as cost and risk become equal between the Tier 2 suppliers, as in the main text, so that comparisons between the supply chain configurations are truly made “all else being equal.” Because we have already made this comparison in the paper for the case of c1 = c2 and 1 = 2, there is no additional analysis necessary. In addition, (4) is also clearly true even with heterogeneous costs, as the manufacturer can still extract all surplus from Tier 1 suppliers using appropriate penalties, thereby making Tier 1 suppliers indi↵erent between the supply chain configurations. Thus, in our numerical analysis we must only show that (2) and (3) continue to qualitatively hold under cost and risk heterogeneity. To accomplish this, we numerically calculate the manufacturer’s optimal strategy in the diamond and V shaped supply chains, as well as the equilibrium to the supply chain configuration game, for