Stochastic analysis of disruption in supply chain networks

Supply chain risk management is becoming an increasingly important research area. A significant source of supply chain risk that should be considered in the design and control of supply chains is disruptions and random supplies. Many real-world examples in which a single catastrophic event has significantly degraded the capabilities of several suppliers leading to considerable erosion of profits and goodwill for a company exist. It is therefore essential to consider stochastic dependence among disruptions in supply chain risk management. The dependence of disruptions may have either adverse or favorable impact on the cost and service level of the supply chain depending on the structure of the supply chain. In addition, the inventory control policies of the nodes can be changed as the dependence among the capacities of the nodes increases or decreases. This forms the central thesis of the research presented. We focus on modeling and analysis of supply chains with stochastically dependent disruptions and their impact on the design, control, and performance evaluation of supply chains.;We first consider an m-manufacturer, 1-retailer, newsvendor inventory system with stochastically dependent manufacturing capacities, caused by random disruptions that may simultaneously inflict damages to the capacities of the manufacturers. We develop the structural/analytical properties of key performance measures and optimal inventory policies for the multi-source and assembly inventory systems. We show that stochastic dependence in disruptions can have opposite effects on system performance in the multi-source and assembly systems. While risk diversification is preferred in the multi-source system, risk concentration is preferred in the assembly system. We then introduce a new method to numerically estimate the joint distribution of the disruptions. Estimating this dependence relation is a difficult undertaking since the estimate should be based on the manufacturers' spatial layout, possible causal relations, and field data. We propose to use a new methodology developed in recent years, vine copula, to construct the dependence relation of the disruption vector. The proposed method first receives required input from the user, including manufacturing location, historical data and other system parameters. Based on the user inputs, we create the vine and estimate the parameters of the vine copula by applying likelihood methods. To test the performance of our method we construct a comprehensive set of numerical examples and show that our method can predict the costs of the multi-source and assembly systems with the average error of 2.1% and 3.3%, respectively.;Finally, we extend our dependence analysis to m-manufacturer, 1-retailer, periodic-review inventory systems. Under this dynamic setting, we assume that the disruption of a manufacturer in each period depends on its disruption in the previous period and an external shock factor, where the shock factors across suppliers are stochastically dependent. This multivariate Markov chain model allows us to capture temporal and spatial effects of disruptions. Under backlogging scenario, we show that similar to the single-period results, positive dependence of supply disruptions has adverse effects on the performance of the multi-source system, but favorable effects on the performance of the assembly system. We then apply the vine copula method to numerically estimate the joint distribution of the disruption vector under the dynamic setting.