Principal Component Analysis was used to cull 450 possible supply chain configurations down to 50. Each configuration was then tested 30 times for every stress value from 0 to 100 in increments of 5, giving 630 measurements for each configuration.

Data gathered for each possible configuration was the steady state average delivery rate, or the average delivery rate for 5000 ticks, the heuristically determined time length for the delivery rate to stabilize. Averaging 30 average delivery rates gives the averaged delivery rate for a configuration at a given stress level. We can then plot these 21 values to construct a influence vs averaged delivery rate graph for each configuration.

• Unweighted Resilience Metric:

$A(f(x)) = \int_{0}^{100}f(x)dx \approx \sum_{k=1}^{21}\frac{f(x_{k-1})+f(x_k)}{2}*5$

• Weighted Resilience Metric:

$W(f(x)) = \sum_{k=1}^{21}\frac{f(x_{k-1})+f(x_k)}{2}*5 + 25 * \ln{(x_1)_0}$

• Continuous Frèchet Distance:

$F(A,B) = \inf_{\alpha,\beta} \max_{t\in[0,1]} \{d(A(\alpha(t)),B(\beta(t)))\}$*The discrete formula was too long to render but it's the same general idea

For each graph, we can then gather 2 metrics, the unweighted and weighted resilience scores. Unweighted describes raw resiliency, while weighted resilience measures the raw resiliency while accounting for overall system performance. For comparing graphs directly, we use a 3rd metric, Frèchet Distance, which describes the 'distance' between two graphs. These are given by the above equations.