Risk Quantification Models

The risk quantification models presented in the remaining sections of this chapter are based on the dissertations of the author s doctoral students (Yang, 2006 Bilsel, 2009) and the resulting publications of their doctoral work (Yang and Ravindran, 2007 Bilsel and Ravindran, 2011,2012). 

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The risk quantification models discussed in this chapter will take a broader view of supply chain risk and model it as a function of occurrence, impact, detectability, and recovery. Methods to quantify each risk component will be developed. We will begin with the development of a basic risk quantification model as a function of impact and occurrence. Separate mathematical models will then be developed for risk detectability and risk recovery time. All the models will be integrated and illustrated with a case study on risk adjusted multi-criteria supplier selection model at the end of the chapter. 

Bilsel, R. U. 2009. Disruption and operational risk quantification models for outsourcing operations. PhD dissertation. University Park, PA Pennsylvania State University. 

We devote an entire chapter to managing risks in the supply chain, emphasizing risk quantification models and risk mitigation strategies, and presenting important problems that extend beyond the traditional treatment of supply chain management. 

Bilsel, R. Ufuk. Disruption and Operational Risk Quantification Models for Outsourcing Operations. PhD dissertation, Pennsylvania State University, 2009. 

My wish is that, on the basis of the thinking that might come from reading this book, the reader will be able to forge appropriate tools for the appreciation of risk situations with which he is confronted. There are, in this book, several places where the reader is invited to work out for himself his quantification model and it happens each time that the model is narrowly based on a particular work situation. This is the case with the invitation to the reader to adapt the Dow Chemical method of analysis, developed for industrial chemical installations, to ordinary work situations. 

RIVM 2008 WORM Metamorphosis Consortium. The Quantification of Occupational Risk. The development of a risk assessment model and software. RIVM Report 620801001/2007 The Hague. 

VaR models were first developed for the financial industry in the early 1990s. They are considered as a standard measure for market risk and used extensively in portfolio risk management. From the financial point of view, VaR measures the maximum possible loss in the market value of a given portfolio. Considering the characteristics of VaR type risks caused by rare events, the concept of VaR can be applied to risk quantification in supply chain management also. 

There are several ways to include detectability of disruption risks in supply chain risk models. One way is to directly use the values in the MFPT matrix, the ntij values, and create an objective function to minimize the number of transitions between suppliers and the buyer. Otherwise, the MFPT values may not be suitable to use directly in risk quantification since values in the MFPT matrix are in transitions and need to be transformed to actual time units (e.g., hours, days, or weeks) for proper use in disruption quantification. This transformation to time units is supply chain specific, since the speed with which the information spreads through the nodes depends on the information technology systems implemented at each node and the availability and strength of connection among the nodes. For instance, if a buyer has implemented an ERP system that allows communication with all tiers of his supply chain, he would have much better connectivity to any supplier and the transition times would be much shorter than buyers that do not have a similar visibility. We call the time it takes any disruption news to reach from node i to j as the disruption delay between nodes i and j and denote it as Aij. 

Mathematical Models for Supply Chain Risk Quantification and Management... 

Part 4 consists of five chapters that provide quantification of the health risks of lead exposure in segments of human populations at significant risk of adverse health effects from such exposures. They sequentially present and quantify risk expressions using a reasonable and generally acceptable model of human health risk assessment for those contaminants such as environmental lead that have already been emitted into the human environment. Such a risk assessment model proceeds through merging and quantitative integration of the previous parts of this book and attempts to answer the question of how much of a threat to human health lead exposures pose. 

III Probability of frequency Uncertainty quantification Model seen to describe true risk Expert judgment is truth-approaching Uncertainty is quantified Judgment aiming at truth Risk is a property of the world. Based on hard evidence and judgment Uncertainty related to impredsion of underlying true risk... 

This chapter is organized as follows. Section 10.2 presents an overview of the recent literature on disruption risk research and multi-objective supply chain management models. An analytic disruption risk quantification framework is presented in Section 10.3. A multi-objective mathematical model for supplier selection under disruption risk is formulated in Section 10.4. Solution methods and a numerical example are discussed in Section 10.5 and Section 10.6, respectively. Concluding comments and future directions are provided in Section 10.7. 

This chapter presents a disruption risk quantification method and a multiobjective supplier selection model to generate mitigation plans against disruption risks. The proposed risk quantification method considers risk as a function of two components—impact and occurrence. Impact is modeled using GEVD distributions, and occurrence is assumed to be Poisson-distributed. The disruption risk quantification method calculates the estimated value of the loss due to disruptive events at a supplier, which is then used in a multi-objective optimization model. The model minimizes cost, lead time, and risk and then maximizes quality and determines the optimal supplier and order allocation for multiple products. The model is solved using four different GP solution techniques—preemptive, non-preemptive, min-max, and fuzzy GP Optimal solutions are displayed using the VPA, and the performance of the solution techniques is discussed. We observe that, for the data set we have tested, preemptive GP, non-preemptive GP, and min-max GP achieve three out of four objectives. 

In addition, the chapter will provide an overview of htunan reliability quantification techniques, and the relationship between these techniques and qualitative modeling. The chapter will also describe how human reliability is integrated into chemical process quantitative risk assessment (CPQRA). Both qualitative and quantitative techniques will be integrated within a framework called SPEAR (System for Predictive Error Analysis and Reduction). 

This chapter has provided an overview of a recommended framework for the assessment of human error in chemical process risk assessments. The main emphasis has been on the importance of a systematic approach to the qualitative modeling of human error. This leads to the identification and possible reduction of the human sources of risk. This process is of considerable value in its own right, and does not necessarily have to be accompanied by the quantification of error probabilities. 

In view of the considerable uncertainties in the extrapolation of results over several orders of magnitude, specification of risks in terms of predicted incidence or numbers of excess cancers per unit of the population implies a degree of precision that is considered misleading by some. Larsen (2006), e.g., noted that the model most often used in low-dose extrapolation is a linear extrapolation from the observable range, and the apparent precision of the calculations does not reflect the uncertainty in the risk estimate the results are therefore open to misinterpretation because the numerical estimates may be regarded as quantification of the actual risk. 

Apostolakis GE. 1994. A commentary on model uncertainty. In Mosleh A, Sin N, Smidts C, Lui C, editors. Proceedings of Workshop I in Advanced Topics in Risk and Reliabihty Analysis, Model Uncertainty Its Characterization and Quantification. 

In addition to the somewhat empirical and difficult development of NIR applications, thorough documentation must be produced. NIR methods have to comply with the current good manufacturing practice (cGMP) requirements used in the pharmaceutical industry. Various regulatory aspects have to be carefully considered. For example, NIR applications in classification, identification, or quantification require extensive model development and validation, a study of the risk impact of possible errors, a definition of model variables and measurement parameters, and... 

The critical use of extrapolation methods implies consideration of the issue of validation. It has been remarked that validation of an extrapolation method should be considered in view of the target of an assessment, so that 1 approach can be sufficient for 1 target (e.g., setting quality criteria) but not for others (precise quantification of risk at contaminated sites). Higher tier methods can be used to address the degree of validity of lower tier methods, especially in the case of the higher tier physical models of reality. 

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