Modeling Disruption Risk in Supply Chain Risk Management

Introduction

Disruptions are among the most significant threats to supply chains. Although disruptive events such as earthquakes, fires, hurricanes and labor strikes (also called rare events or extreme events due to their infrequent nature) are rare, they have caused major damage to various companies in different business segments (see Griffy-Brown, 2003, for a survey). Despite its seriousness, supply chain literature is still short of research on risk quantification, especially for the quantification of disruption risks. The purpose of this paper is to fill this gap by proposing analytical models and methods of risk quantification as a basis for better risk management and mitigation. The methods make use of several techniques of probability and mathematical statistics, including Extreme Value Distributions and Markov chains, together with concepts from reliability engineering.

The major contributions of the paper are the analytical methods that can be used to quantify disruption risks and the identification of different components of disruption risks. To the best our knowledge, a complete framework to quantify disruption risk is not available in the literature and this paper aims at filling this gap.

The paper begins with a short discussion of disruptive events and a review of the current literature. A general risk function is introduced in the Disruptive Events and Risk Quantification Section. The risk function defines risk as a function of impact, and occurrence. Impact of a risk event is modeled using the Generalized Extreme Value Distributions. Occurrence of risk events is modeled as a Poisson random variable. Closed form expressions of the expected value and variance parameters of the combined risk function are derived. The Quantile Estimation Section provides several theoretical results for combining multiple risk functions under mild assumptions under a priori knowledge of the number of occurrences. Closed form expressions obtained in this section involve integration of complicated functions which was carried out using numerical techniques. The next section discusses the detectability aspect of the disruptive events. Detectability is modeled using the Mean Fist Passage Time concept of Markov chains. The section A Conceptual Model for Risk Recovery introduces our propostion for including disruption recovery time in risk analysis. The section that follows combines all the risk quantification models proposed in the paper and presents a comprehensive example for risk management. Conclusions Section summarizes the major contributions.