A PageRank-like measure for evaluating process flexibility

Uncertainty has always been a threat to system performance in both manufacturing and service industries. Although cost-budgeting may limit available resources, a more flexible structure can still improve the system’s ability to deal with uncertainty. In this study, we develop a new measure to help find a more flexible structure without extensive simulation. We create a PageRank-analogous score whereby we can calculate the Flexibility Gap (FG) index to predict the better of two alternative structures with topological information only. We theoretically analyze how the FG index recognizes flexible sparse structures such as expander graphs with high expansion ratios. Numerical experiments show that the FG index is effective in ranking the flexibility performance of different structures in terms of average waiting time and expected lost sales. Moreover, we extend the FG index with minimal modification to accommodate the case of imperfect flexibility (i.e., flexible suppliers with shrinking capacities) and demonstrate that the generalized FG index is still a good predictor of expected lost sales. Our approach provides a novel view to explain flexibility. That is, sparse structures with higher graph expansion ratios disperse the demand fluctuation more “rapidly” among resources to cushion the shock of uncertainty.