A New Framework for Strategic Risk Analysis in a Global Pump Manufacturing Network

Abstract

This paper presents a new risk analysis framework applied to a global production network for pump manufacturing considering strategic decisions regarding alternative suppliers and markets. External and internal risk scenarios are defined and alternative network configurations are evaluated considering the constructed risk scenarios. Inoperability of individual nodes in the global production networks caused by identified risks are determined by taking into account propagation of risks due to the interdependencies between nodes. Fuzzy arithmetic is applied to track the level of uncertainty inherent in the model parameters and the outcomes. It is demonstrated how recommendations can be made with regard to the network configuration and handling of the uncertainty in the results.

Appendix: Fuzzy Dynamic Inoperability Input Output Model

A vector representation of the fuzzy dynamic inoperability input output model function is as follows:

$$\tilde{q}\left({t + 1} \right) = \widetilde{K}\widetilde{{A}^{ *}} \tilde{q}\left(t \right) + \widetilde{K}\widetilde{{c}^{ *}} \left(t \right) + \left({I - \widetilde{K}} \right)\tilde{q}(t)$$

(1)

where $\tilde{q}\left({t + 1} \right)$ is the vector of fuzzy inoperability of nodes at time period $t + 1,\widetilde{K}$ is the fuzzy diagonal matrix of resilience, $\widetilde{A^{ *} }$ is the fuzzy interdependency matrix and $\widetilde{{c}^{ *}} \left(t \right)$ is the fuzzy perturbation of nodes for the risk scenario under consideration at time period t. Resilience represents the speed that the node can recover from disruptions.

The expected loss of risk for all risk scenarios is calculated as follows:

$$\tilde{Q} = \widetilde{{x}^{T}} \mathop \sum \limits_{s = 1}^{S} \widetilde{{p}_{s}} \mathop \sum \limits_{t = 1}^{T} \widetilde{{q}_{s} \left(t \right)}$$

(2)

where $\tilde{Q}$ is the fuzzy loss of risk for the GPN configuration, $\widetilde{{x}^{T}}$ is the transposed vector of the fuzzy intended revenues of the nodes, S is the number of risk scenarios, $\widetilde{{p}_{s}}$ is the fuzzy likelihood of risk scenario s, T is the number of time periods in the time horizon and $\widetilde{{q}_{s}} (t)$ is the fuzzy inoperability vector of nodes in scenario s at time period t.

The FDDIM method have been described in more details in [15].