Approach 1 Risk Model

In this section we demonstrate the capability of our formulation in dealing with variations in the objective function prices, based on historical data. We present the uncertainty in terms of three scenarios (i) the above average or optimistic scenario 

As the main focus of this chapter is on the risk-incorporated models of Risk Models II and III, the computational results for Risk Model I are not presented here. 

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Consideration of the expected value of profit alone as the objective function, which is characteristic of the classical stochastic linear programs introduced by Dantzig (1955) and Beale (1955), is obviously inappropriate for moderate and high-risk decisions under uncertainty since most decision makers are risk averse in facing important decisions. The expected value objective ignores both the risk attribute of the decision maker and the distribution of the objective values. Hence, variance of each of the random price coefficients can be adopted as a viable risk measure of the objective function, which is the second major component of the MV approach adopted in Risk Model I. 

The goal of Approach 3 is to append an operational risk term to the mean-risk model formulation in Approach 2 to account for the significance of both financial risk (as considered by Approach 1) and operational risk in decision-making. 

Konno and Yamazaki (1991) proposed a large-scale portfolio optimization model based on mean-absolute deviation (MAD). This serves as an alternative measure of risk to the standard Markowitz s MV approach, which models risk by the variance of the rate of return of a portfolio, leading to a nonlinear convex quadratic programming (QP) problem. Although both measures are almost equivalent from a mathematical point-of-view, they are substantially different computationally in a few perspectives, as highlighted by Konno and Wijayanayake (2002) and Konno and Koshizuka (2005). In practice, MAD is used due to its computationally-attractive linear property. 

Therefore, in this approach, we develop Risk Model III as a reformulation of Risk Model II by employing the mean-absolute deviation (MAD), in place of variance, as the measure of operational risk imposed by the recourse costs to handle the same three factors of uncertainty (prices, demands, and yields). To the best of our knowledge, this is the first such application of MAD, a widely-used metric in the area of system identification and process control, for risk management in refinery planning. 

Quantitative uncertainty analysis is not appropriate when in a worst-case approach, risk is found to be negligible when held evidence indicates obvious and severe effects when information is insufficient to adequately characterize the model equation, input probability density functions (PDFs), and the relationships between the PDFs or when it is more cost-effective to take action than to conduct more analyses. 

Conceptual models link anthropogenic activities with stressors and evaluate the relationships among exposure pathways, ecological effects, and ecological receptors. The models also may describe natural processes that influence these relationships. Conceptual models include a set of risk hypotheses that describe predicted relationships between stressor, exposure, and assessment end point response, along with the rationale for their selection. Risk hypotheses are hypotheses in the broad scientific sense they do not necessarily involve statistical testing of null and alternative hypotheses or any particular analytical approach. Risk hypotheses may predict the effects of a stressor, or they may postulate what stressors may have caused observed ecological effects. 

Tier 3 involves the use of both CA and R A models together (mixed-model approaches). This approach differs from the previous tiers by using detailed information on the modes of action for the different mixture components as well as full-curve-based modeling approaches. Mixed models are used in human as well as ecological assessment. An example of mixed-model approaches in ecological risk assessments is the approach proposed for assemblages (De Zwart and Posthuma 2005) a similar approach has been proposed by Ra et al. (2006) see Chapter 4 and Figure 4.2. 

Sherratt, T.N. and PC. Jepson. 1993. A metapopulation approach to modeling the long-term impact of pesticides on invertebrates. ]. Appl. Ecol. 30 696-705. Shugart, L.R. 1990. DNA damage as an indicator of pollutant induced genotoxic-ity. In Aquatic Toxicology and Risk Assessment, Vol. 13, ASTM STP-1096, W.G. Landis and W.H. van der Schalie, Eds. American Society for Testing and Materials, Philadelphia, PA, pp. 348-355. 

Yokley, K., Tran, H. T, Pekari, K., Rappaport, S., Riihimaki, V, Rodiman, N., Waidyanatha, S., and Schlosser, P. M. (2006). Physiologically-based pharmacokinetic modeling of benzene in humans A Bayesian approach. Risk Anal 26(4), 925-943. 

Figure 7.1. A causal graph for risk analysis. The model depicted in this figure can be formalized using a Bayesian network (Ricci et al. 2006) A probabilistic framework interprets the model described in this figure as a Bayesian belief network or causal graph model. Each variable with inward-pointing arrows is interpreted as a random variable with a conditional probability distribution that depends only on the values of the variables that point into it. The essence of this approach to modeling and evaluating uncertain risks is to sample successively from the (often conditional) distribution of each variable, given the values of its predecessors. Algorithms exist to identify and validate possible causal structures.

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