Risk Preferences Of Decision Makers Research Articles

Numerical Methods to Calculate Fuzzy Boundaries for Brownfield Redevelopment Negotiations

A numerical method is proposed to represent the likelihood of contamination of a brownfield using fuzzy boundaries, and then to estimate the parameters in a fuzzy real options model for brownfield evaluation from different decision maker perspectives. These different values can be used to facilitate negotiations on redevelopment projects. Linguistic quantifiers and ordered weighted averaging (OWA) techniques are utilized to determine the pollution likelihood at sample locations based on multiple environmental indicators. Risk preferences of decision makers are expressed as different “orness” levels of OWA operators, which affect likelihood estimates. When the fuzzy boundary of a brownfield is generated by interpolation of sample points, the parameters of fuzzy real options, drift rate and volatility, can be calculated as fuzzy numbers. Hence, this proposed method can act as an intermediate between decision makers and the fuzzy real options models, making this model much easier to apply. A potential negotiation support system (NSS) implementing these numerical methods is discussed in the context of negotiating brownfield redevelopment projects. A public–private-partnership will be enhanced through information sharing, scenario generation, and conflict analysis provided by the NSS, encouraging more efficient brownfield redevelopment and leading to greater regional sustainability.

Two-stage credibility-constrained programming with Hurwicz criterion (TCP-CH) for planning water resources management

In water-resources management problems, uncertainties exist in a number of impact factors and water-allocation processes, which can bring about enormous difficulties and challenges in generating desired decision alternatives under such complexities. In this study, a two-stage credibility-constrained programming with Hurwicz criterion (TCP-CH) approach is developed for water resources management and planning under uncertainty. TCP-CH can tackle uncertainties presented as probability distributions and fuzzy sets that exist in left- and right-hand sides of constraints and in objective function; it can also permit in-depth analyses of various policy scenarios based on confidence degrees that are associated with different levels of economic penalties when the promised targets are violated. The TCP-CH method is applied to a real case of planning water resources in Kaidu-qongque River basin, which is one of the aridest regions of China. Support-vector-regression (SVR) technique is introduced into TCP-CH for predicting the water demand in the future, which takes advantage of uncertainty reflection and dynamic analysis. Results of water allocation, water shortage, system benefit, and economic penalty are obtained. The results discover that water deficit has brought negative effects on regional economic development, particularly for agricultural production activities. Moreover, tradeoffs between economic benefit and system-failure risk are also examined under different risk preferences of decision makers (i.e., optimistic and pessimistic criteria), which support generating an increased robustness in risk control for water resources allocation under uncertainties. These findings can facilitate the local decision makers in adjusting the current water-allocation pattern based on risk preference option (Hurwicz criterion) to satisfy the increasing water demand.

Minimizing the Cost of Keeping Options Open for Conservation in a Changing Climate

Policy documents advocate that managers should keep their options open while planning to protect coastal ecosystems from climate-change impacts. However, the actual costs and benefits of maintaining flexibility remain largely unexplored, and alternative approaches for decision making under uncertainty may lead to better joint outcomes for conservation and other societal goals. For example, keeping options open for coastal ecosystems incurs opportunity costs for developers. We devised a decision framework that integrates these costs and benefits with probabilistic forecasts for the extent of sea-level rise to find a balance between coastal ecosystem protection and moderate coastal development. Here, we suggest that instead of keeping their options open managers should incorporate uncertain sea-level rise predictions into a decision-making framework that evaluates the benefits and costs of conservation and development. In our example, based on plausible scenarios for sea-level rise and assuming a risk-neutral decision maker, we found that substantial development could be accommodated with negligible loss of environmental assets. Characterization of the Pareto efficiency of conservation and development outcomes provides valuable insight into the intensity of trade-offs between development and conservation. However, additional work is required to improve understanding of the consequences of alternative spatial plans and the value judgments and risk preferences of decision makers and stakeholders.

Partner Selection in a Virtual Enterprise: A Group Multiattribute Decision Model with Weighted Possibilistic Mean Values

This paper proposes an extended technique for order preference by similarity to ideal solution (TOPSIS) for partner selection in a virtual enterprise (VE). The imprecise and fuzzy information of the partner candidate and the risk preferences of decision makers are both considered in the group multiattribute decision-making model. The weighted possibilistic mean values are used to handle triangular fuzzy numbers in the fuzzy environment. A ranking procedure for partner candidates is developed to help decision makers with varying risk preferences select the most suitable partners. Numerical examples are presented to reflect the feasibility and efficiency of the proposed TOPSIS. Results show that the varying risk preferences of decision makers play a significant role in the partner selection process in VE under a fuzzy environment.

Evolutionary risk preference inference model using fuzzy support vector machine for road slope collapse prediction

Road slope collapse events are frequent occurrences in Taiwan, often exacerbated by earthquakes and/or heavy rainfall. Such collapses disrupt transportation, damage infrastructure and property, and may cause injuries and fatalities. While significant efforts are regularly invested in reducing road slope collapse risk, most focus exclusively on limiting the potential for slope failure. Collapse prediction efforts may result in inference errors that cause allocated road slope maintenance resources to be expended inefficiently, resulting in relatively higher collapse risk than should be achievable under ideal circumstances. Most maintenance programs rely on decision maker risk preferences, as his/her knowledge and experience can contribute to risk assessment decision making. The decision maker is capable of choosing an acceptable balance between two types of inference error, i.e., α and β errors. This preference may later be used as guidance to minimize inference error. This paper proposed the evolutionary risk preference fuzzy support vector machine inference model (ERP-FSIM) as a hybrid AI system able to make predictions regarding road slope collapse that takes decision maker risk preference into account. Validation results demonstrate ERP-FSIM viability, as level of average error both for the training set and validation set conform to the decision maker risk preference ratio and is significantly lower than the error tolerance of ±10%.

Risk Preference Based Support Vector Machine Inference Model for Slope Collapse Prediction

Abstract Slope collapse prediction inference errors may be divided into two types, namely 1) predicted collapse followed by actual non-collapse (i.e., α error) and 2) predicted non-collapse followed by actual collapse (i.e., β error). As limited time and information make it difficult to reduce the rate of prediction error, making predictions in a manner that considers decision maker risk preferences in order to consider the preferred α to β error ratio in road slope maintenance strategy formulation represents an important issue. This study proposes an innovative inference model, the Risk Preference based Support Vector Machine Inference Model (RP-SIM). RP-SIM infers the mapping relationship between input and output variables from historical cases using a Support Vector Machine (SVM), and then uses a fast messy genetic algorithm (fmGA) to conduct an optimal search based on α and β values set in accordance with actual decision maker risk preference.

A Stackelberg single-period supply chain inventory model with weighted possibilistic mean values under fuzzy environment

This paper considers a single-period product inventory control in a distributed supply chain, which is composed of one manufacturer and one retailer and operates in the environment of uncertain market demand. A Stackelberg model with fuzzy demand is first developed, with using a L– R fuzzy number with a general membership function to depict the fuzzy market demand, and through adopting the weighted possibilistic mean value method to rank the retailer and the manufacturer's fuzzy profits, the risk preference of decision maker is also taken into consideration in the model. A special case where the market demand is assumed to be a triangular fuzzy number is further considered, and Genetic Algorithm and Pattern Search Algorithm are adopted to obtain the optimal solutions of the Stackelberg model. At last, numerical examples are used to illustrate the proposed model and sensitivity analyses are provided to get managerial implications.

A C-OWA Operator-based Method for Aggregating Intuitionistic Fuzzy Information and Its Application to Decision Making under Uncertainty

Abstract An IFS is suitable way to deal with uncertainty, but operators on it are complex in computation even though they work well. This study presents a C-OWA operator-based method to make aggregation over intuitionistic fuzzy information more easy and convenient, and then applies it to complicated decision making under uncertainty. IFNs or IIFNs are transformed into intervals which are easy to be aggregated to real values according to the risk preference of decision makers by C-OWA operator. In this way an uncertain decision problem might be converted into a certain one which is much easier to solve. Experimental study examines the feasibility and validity of the presented method.

A TFN–ANP based approach to evaluate Virtual Research Center comprehensive performance

The performance evaluation of Virtual Research Center (VRC) is an intrinsically complex multi-dimensional process and it should be evaluated and compared in a multi-criteria analysis method. To solve the problems caused by the fuzzy decision making, quantifying the qualitative indexes and dealing with the interdependence and interaction of some indexes during the process of VRC performance evaluation, a comprehensive performance evaluation method based on triangular fuzzy number and analytic network process (TFN–ANP) is proposed. In the method, an index evaluation system is first established and the interactive relationships of the evaluation indexes are analyzed. Secondly, the index evaluation decision-making matrix is constructed and the indexes attribute values are fuzzed with triangular fuzzy numbers. Thirdly, the evaluative indexes weights are determined by analytic network process. Then the concrete solving process is derived and the fuzzy utility value weights are ranked by the priority method with decision maker risk preference. In the end, the four project teams of Yalong River VRC are taken as examples, then their comprehensive performances are evaluated by TFN–ANP model and the utility value priorities are ranked, which could provide decision supports for VRC to optimize operational performance. In addition, a comparison with the previous method is performed, and experimental results are encouraging, which fully demonstrates the effectiveness and superiority of the proposed approach.

Ranking Fuzzy Numbers Based on Ideal Solution

In this paper, we consider the factor of the decision maker's risk preference, and define the left and right deviation degree respectively. Besides, we propose a new formula of the fuzzy degree. Then we get the multiattribute matrix of fuzzy numbers. We rank fuzzy numbers with the help of an ideal solution. Some numerical examples are displayed to illustrate the validity and advantages of the proposed ranking method.

Non-proportional reinsurance with risk preferences

The article on hand presents two complementary decision principles and their application to the non-proportional reinsurance business. Thereby these decision principles use a convex combination of risk measures and therefore allow the modelling of risk preferences of decision makers. In this regard, the main objective is to prove the risk preferences for this decision principles as well as to put them in the context of the decision theory. In this connection, the expected utility theory and the dual utility theory are explored. Furthermore the aspect of coherent risk measures is analyzed. Moreover for the two reinsurance models the special case of a fair reinsurance deductible on the one hand and the special case of a CVaR-decision maker on the other hand is examined.

A Risk based Approach to Estimate Key Uncertainties

Decisions during the early stages of R&D are often made under substantial uncertainty. Evaluation of R&D alternatives under uncertainty generally does not provide a clear choice that is best under all possible scenarios. For optimal investment of R&D resources, it is important to identify the key uncertainty contributors from a decision maker's perspective. Global sensitivity analysis (GSA) is a tool that can be used to determine key uncertainties that contribute the most to the variance of the bottom-line objective. It is often the case, however, that GSA is not able to distinguish between the uncertainties. Motivated by this, we propose a new tool called conditional – global sensitivity analysis, which further considers the decision-maker's risk preference. The conditional sensitivity measures (cGSAup/cGSAdown) quantify the contributions of different individual uncertainty factors to the upper and lower halves of the distribution function of the objective function. It is argued that the use of cGSAup may appeal to a risk-aversive decision maker as it leads to a lower rate of false acceptance decisions at the expense of a higher rate of false rejection decisions, whereas the use cGSAdown does the opposite.

Constructing Uncertainty Sets for Robust Linear Optimization

In this paper, we propose a methodology for constructing uncertainty sets within the framework of robust optimization for linear optimization problems with uncertain parameters. Our approach relies on decision maker risk preferences. Specifically, we utilize the theory of coherent risk measures initiated by Artzner et al. (1999) [Artzner, P., F. Delbaen, J. Eber, D. Heath. 1999. Coherent measures of risk. Math. Finance 9 203–228.], and show that such risk measures, in conjunction with the support of the uncertain parameters, are equivalent to explicit uncertainty sets for robust optimization. We explore the structure of these sets in detail. In particular, we study a class of coherent risk measures, called distortion risk measures, which give rise to polyhedral uncertainty sets of a special structure that is tractable in the context of robust optimization. In the case of discrete distributions with rational probabilities, which is useful in practical settings when we are sampling from data, we show that the class of all distortion risk measures (and their corresponding polyhedral sets) are generated by a finite number of conditional value-at-risk (CVaR) measures. A subclass of the distortion risk measures corresponds to polyhedral uncertainty sets symmetric through the sample mean. We show that this subclass is also finitely generated and can be used to find inner approximations to arbitrary, polyhedral uncertainty sets.

Scenario-based Stochastic Capacity Planning Model and Decision Risk Analysis

Abstract To study the capacity planning problem under uncertainty in which market demand and product price are stochastic, multi period capacity planning model based on scenario was investigated in this paper. Two models were proposed: one is a prearranged planning model in which the capacity investment plan do not change with the stochastic market demand, and the other is an adaptive planning model in which capacity investment plan could trace the evolution progress of the stochastic market demand. The computational study compared the decision results of both models, which reveals that the adaptive planning model could suggest better decision. Moreover, based on downside risk analysis, the investment risk of stochastic capacity planning has been investigated, and a prearranged capacity planning model considering the expected downside risk of the objective revenue was proposed. In the model, a constraint of expected downside risk is added to the initial stochastic model to reflect the decision-maker's risk preference. Whether to consider the risk or not will result in different decisions, which, in the computational study, were compared.

Multi-product pricing via robust optimisation

We propose an approach to model demand uncertainty in pricing problems with capacitated resources that builds upon: (i) range forecasts for various product lines and (ii) bounds on the amount of the resources that can be used by the random part of the cumulative demand. The bounds are adjusted to reflect the decision-maker's risk preferences. Although revenue management traditionally assumes that enough historical observations are available to estimate the underlying probability distributions accurately, the model of uncertainty presented in this work is particularly well suited to the level of information available in real-life settings, in particular in applications with long production lead times, short shelf life or brand new products. We derive robust counterparts to the deterministic pricing problem in the case of additive uncertainty, and analyse the impact of uncertainty and risk aversion on the decision-maker's strategy. In particular, when the price response function is linear or when uncertainty is small, we provide an explicit characterisation of the impact of the system parameters on the optimal strategy and establish the existence of a reference price for each product, which plays a key role in understanding how randomness affects the optimal prices.

Risk Preferences Estimation for Small Raspberry Producers in the Bío-Bío Region, Chile

A B S T R A C T Decisions are strongly influenced by risk and risk preferences of decision makers; however, in Chile there are few studies in the agricultural sector focused on this topic. The present paper analyzes the risk preferences of small producers of raspberries (Rubus idaeus L.) and the production function associated with their production system in the Bio-Bio Region of Chile. Under a mean-variance approach, the estimation procedure uses a flexible utility function to incorporate a variety of risk preference alternatives. Three different estimation procedures were used: Least Squares Estimation, Seemingly Unrelated Regression and Full Information Maximum Likelihood, which revealed the same conclusions. Results showed that small farmers are risk averse (γ = 0.104) and present increasing relative and absolute aversion to risk (θ = 0.099 < 1 and θ < γ, respectively). The hypotheses of risk neutrality (γ = 0) and constant absolute risk aversion (θ = 1) were rejected with 94% and 99% confidence, respectively. The chosen function of production is the Cobb Douglas type, because it presents a better adjustment, and the relevant factors are fertilizer quantity per hectare, the experience of the producer and the planted area. This function presents decreasing returns to scale, then β2 + β3 + β4 is equal to 0.18. The hypothesis of constant returns to scale is rejected with 99% confidence.

Optimal ordering quantities for multi-products with stochastic demand: Return-CVaR model

Multi-product-ordering problem with stochastic demand is often optimized by the expected cost reduction or the expected profit improvement, in most of previous works. Moreover, risk preference of decision maker is often ignored. Evidently, this approach is impracticable when the corresponding volatility is larger. Based on the outstanding characteristics of conditional value at risk (CVaR) as a risk measure, the paper proposes an optimal-order model for multi-product with CVaR constraints, also the model is finally formulated as a linear programming problem. The model is simulated for the case of a newsvendor to analyze to what degree it succeeds. The solution, in fact, is bound consistent fully with the decision maker's intuition on return-risk decision making. Finally, results of return-CVaR model and the classical model are compared and shows that return-CVaR model is more flexible than the classical model.

Optimization of Investments in Natural Gas Distribution Networks

This paper presents an optimization model and solution procedure for planning investments in gas distribution networks for residential customers. The situation can be considered a capital budgeting problem under uncertainty. There is uncertainty about whether a potential customer will convert to gas service if a distribution main is built, the revenue generated if the household does convert, and the cost of constructing the main. A fixed annual budget is allocated to a set of discrete, competing projects over time. The allocation is done by maximizing the expected net present value (NPV) given the decision-maker's risk preferences. The probability distribution of the NPV for each competing project is created from two statistical models. A binary probit model is used to estimate the probability of conversion for a potential customer. A random effects regression model is used to estimate the revenue generated should a particular potential customer switch to gas. A rollout value greedy heuristic was devised to solve the resulting optimization formulation. Two case studies based on data from a large gas company illustrate the analysis.

Detecting a Security Disturbance in Multi Commodity Stochastic Networks

Here is a multi-criteria approach to identify and evaluate network-flow monitoring strategies in a stochastic environment. We propose an analytical approach for assessing flow disturbance, based on limited sampling of arc-flow information in multi commodity, or multiple origin-destination (O---D), networks. A disturbance is defined here as abnormal network traffic beyond routine fluctuations. The network is characterized by arcs that are available with certain probabilities, suggesting a busy packet-switching/circuit-switching network, or simply network with failing components. Given the huge state space of such stochastic networks, our first objective is to bound the expected flow for computational efficiency. This is accomplished by extending available single-commodity-network results to the multi commodity case. The second objective is to determine the best placement of flow monitors to obtain the most accurate estimates of traffic flow, as represented by O---D pair traffic volumes in order to detect a disturbance. We followed a multi-criteria approach in defining and evaluating all possible monitor-placement strategies satisfying monitor availability. To assess a traffic pattern, O---D volumes are estimated using the l p -metric for p = 1, 2 and ?, representing a decision-maker's risk-preference structure. The final objective is to define a disturbance metric providing confident assessments on the occurrence of a flow disturbance. In this regard, we use linear-regression to generate confidence intervals around the expected flow for each O---D pair. This is supplemented by the Fisher Method of Randomization, a non-parametric test, for small networks. Unlike the Fisher-test results, it appears the linear-regression "disturbance metric" is very sensitive to detecting "disturbance." Preliminary results suggest that among the three l p metrics in O---D estimation, it appears that the best is the l 2-metric, which provides the appropriate sensitivity and accuracy. Counter to intuition, it is also observed that the "disturbance" estimation error generally decreases as the number of sampled arcs decreases.

Decision support for identifying spruce forest stand edges with high probability of wind damage

In multiple-purpose forestry, windstorms affect both the ecological and economic values that forest stands represent. Silvicultural treatments and forest planning can reduce the probability of wind damage. A tool for the identification of spruce stands with a high probability of wind damage, aimed at helping forestry practitioners target such measures, is presented. Initial assessments of the annual probability of wind damage of exposed stand edges were made for a landscape of about 1200 ha in southern Sweden, using the WINDA system of models. In the calculations, each edge was classified as having either a high or a low annual probability of wind damage. Decision tree methodology using easily accessible variables was employed for identifying the edges classified as having a high probability of wind damage. Since in a multiple-use situation, the risk preferences of decision makers differ, one decision tree was constructed for each of three threshold probabilities of wind damage: 5, 10, and 20%. This corresponds to disturbance intervals of 20, 10, and 5 years or less in each case. The decision trees were found to correctly classify 64–71% of the high-probability stand edges, the misclassification rate for the low-probability stand edges being 12–26%. Alternative cost-matrices were used to take account of user-preferences regarding misclassification rates in the model output. Among the most important predictor variables used in the decision trees were stem taper, gap size in front of the stand edge, and the direction of wind exposure. In an evaluation landscape located 250 km from the parameterization landscape, the decision trees were found to correctly classify 44–50% and 0–83% of the high-probability stand edges with and without use of cost-matrices, respectively. For the evaluation landscape, a statistically significant difference between classifications produced by the decision tree approach and a set of randomly classified stand edges was obtained just for four of the decision trees. This result was explained in terms of the high degree of complexity of the underlying processes, limitations in the parameterization data set, and differences between the landscapes involved. Decision trees of the type described can thus provide help in practical forestry within and nearby the landscape used for constructing the decision trees. In general, the presented methodology appears to be suitable for developing management decision support tools.