Managing the Risk of Uncertain Threshold Responses: Comparison of Robust, Optimum, and Precautionary Approaches

Many commentators have suggested the need for new decision analysis approaches to better manage systems with deeply uncertain, poorly characterized risks. Most notably, policy challenges such as abrupt climate change involve potential nonlinear or threshold responses where both the triggering level and subsequent system response are poorly understood. This study uses a simple computer simulation model to compare several alternative frameworks for decision making under uncertainty -- optimal expected utility, the precautionary principle, and three different approaches to robust decision making -- for addressing the challenge of adding pollution to a lake without triggering unwanted and potentially irreversible eutrophication. The three robust decision approaches -- trading some optimal performance for less sensitivity to assumptions, satisficing over a wide range of futures, and keeping options open -- are found to identify similar strategies as the most robust choice. This study also suggests that these robust decision approaches offer a quantitative, decision analytic framework that captures the spirit of the precautionary principle while addressing some of its shortcomings. Finally, this study finds that robust strategies may be preferable to optimum strategies when the uncertainty is sufficiently deep and the set of alternative policy options is sufficiently rich.     

Scenario Discovery with Multiple Criteria: An Evaluation of the Robust Decision‐Making Framework for Climate Change Adaptation

There is increasing concern over deep uncertainty in the risk analysis field as probabilistic models of uncertainty cannot always be confidently determined or agreed upon for many of our most pressing contemporary risk challenges. This is particularly true in the climate change adaptation field, and has prompted the development of a number of frameworks aiming to characterize system vulnerabilities and identify robust alternatives. One such methodology is robust decision making (RDM), which uses simulation models to assess how strategies perform over many plausible conditions and then identifies and characterizes those where the strategy fails in a process termed scenario discovery. While many of the problems to which RDM has been applied are characterized by multiple objectives, research to date has provided little insight into how treatment of multiple criteria impacts the failure scenarios identified. In this research, we compare different methods for incorporating multiple objectives into the scenario discovery process to evaluate how they impact the resulting failure scenarios. We use the Lake Tana basin in Ethiopia as a case study, where climatic and environmental uncertainties could impact multiple planned water infrastructure projects, and find that failure scenarios may vary depending on the method used to aggregate multiple criteria. Common methods used to convert multiple attributes into a single utility score can obscure connections between failure scenarios and system performance, limiting the information provided to support decision making. Applying scenario discovery over each performance metric separately provides more nuanced information regarding the relative sensitivity of the objectives to different uncertain parameters, leading to clearer insights on measures that could be taken to improve system robustness and areas where additional research might prove useful.     

Impact of Uncertainty Parameter Distribution on Robust Decision Making Outcomes for Climate Change Adaptation under Deep Uncertainty

Deep uncertainty in future climatic and economic conditions complicates developing infrastructure designed to last several generations, such as water reservoirs. In response, analysts have developed multiple robust decision frameworks to help identify investments and policies that can withstand a wide range of future states. Although these frameworks are adept at supporting decisions where uncertainty cannot be represented probabilistically, analysts necessarily choose probabilistic bounds and distributions for uncertain variables to support exploratory modeling. The implications of these assumptions on the analytical outcomes of robust decision frameworks are rarely evaluated, and little guidance exists in terms of how to select uncertain variable distributions. Here, we evaluate the impact of these choices by following the robust decision-making procedure, using four different assumptions about the probabilistic distribution of exogenous uncertainties in future climatic and economic states. We take a water reservoir system in Ethiopia as our case study, and sample climatic parameters from uniform, normal, extended uniform, and extended normal distributions; we similarly sample two economic parameters. We compute regret and satisficing robustness decision criteria for two performance measures, agricultural water demand coverage and net present value, and perform scenario discovery on the most robust reservoir alternative. We find lower robustness scores resulting from extended parameter distributions and demonstrate that parameter distributions can impact vulnerabilities identified through scenario discovery. Our results suggest that exploratory modeling within robust decision frameworks should sample from extended, uniform parameters distributions.     

Farmers’ Risk‐Based Decision Making Under Pervasive Uncertainty: Cognitive Thresholds and Hazy Hedging

Researchers in judgment and decision making have long debunked the idea that we are economically rational optimizers. However, problematic assumptions of rationality remain common in studies of agricultural economics and climate change adaptation, especially those that involve quantitative models. Recent movement toward more complex agent‐based modeling provides an opportunity to reconsider the empirical basis for farmer decision making. Here, we reconceptualize farmer decision making from the ground up, using an in situ mental models approach to analyze weather and climate risk management. We assess how large‐scale commercial grain farmers in South Africa (n = 90) coordinate decisions about weather, climate variability, and climate change with those around other environmental, agronomic, economic, political, and personal risks that they manage every day. Contrary to common simplifying assumptions, we show that these farmers tend to satisfice rather than optimize as they face intractable and multifaceted uncertainty; they make imperfect use of limited information; they are differently averse to different risks; they make decisions on multiple time horizons; they are cautious in responding to changing conditions; and their diverse risk perceptions contribute to important differences in individual behaviors. We find that they use two important nonoptimizing strategies, which we call cognitive thresholds and hazy hedging, to make practical decisions under pervasive uncertainty. These strategies, evident in farmers' simultaneous use of conservation agriculture and livestock to manage weather risks, are the messy in situ performance of naturalistic decision‐making techniques. These results may inform continued research on such behavioral tendencies in narrower lab‐ and modeling‐based studies.     

Using Expert Judgments to Explore Robust Alternatives for Forest Management under Climate Change

We develop and apply a judgment‐based approach to selecting robust alternatives, which are defined here as reasonably likely to achieve objectives, over a range of uncertainties. The intent is to develop an approach that is more practical in terms of data and analysis requirements than current approaches, informed by the literature and experience with probability elicitation and judgmental forecasting. The context involves decisions about managing forest lands that have been severely affected by mountain pine beetles in British Columbia, a pest infestation that is climate‐exacerbated. A forest management decision was developed as the basis for the context, objectives, and alternatives for land management actions, to frame and condition the judgments. A wide range of climate forecasts, taken to represent the 10–90% levels on cumulative distributions for future climate, were developed to condition judgments. An elicitation instrument was developed, tested, and revised to serve as the basis for eliciting probabilistic three‐point distributions regarding the performance of selected alternatives, over a set of relevant objectives, in the short and long term. The elicitations were conducted in a workshop comprising 14 regional forest management specialists. We employed the concept of stochastic dominance to help identify robust alternatives. We used extensive sensitivity analysis to explore the patterns in the judgments, and also considered the preferred alternatives for each individual expert. The results show that two alternatives that are more flexible than the current policies are judged more likely to perform better than the current alternatives on average in terms of stochastic dominance. The results suggest judgmental approaches to robust decision making deserve greater attention and testing.     

Robustness of Risk Maps and Survey Networks to Knowledge Gaps About a New Invasive Pest

In pest risk assessment it is frequently necessary to make management decisions regarding emerging threats under severe uncertainty. Although risk maps provide useful decision support for invasive alien species, they rarely address knowledge gaps associated with the underlying risk model or how they may change the risk estimates. Failure to recognize uncertainty leads to risk‐ignorant decisions and miscalculation of expected impacts as well as the costs required to minimize these impacts. Here we use the information gap concept to evaluate the robustness of risk maps to uncertainties in key assumptions about an invading organism. We generate risk maps with a spatial model of invasion that simulates potential entries of an invasive pest via international marine shipments, their spread through a landscape, and establishment on a susceptible host. In particular, we focus on the question of how much uncertainty in risk model assumptions can be tolerated before the risk map loses its value. We outline this approach with an example of a forest pest recently detected in North America, Sirex noctilio Fabricius. The results provide a spatial representation of the robustness of predictions of S. noctilio invasion risk to uncertainty and show major geographic hotspots where the consideration of uncertainty in model parameters may change management decisions about a new invasive pest. We then illustrate how the dependency between the extent of uncertainties and the degree of robustness of a risk map can be used to select a surveillance network design that is most robust to knowledge gaps about the pest.     

Why Risk Analysis is Difficult,and Some Thoughts on How to Proceed

Risk analysis is challenged in three ways by uncertainty. Our understanding of the world and its uncertainties is evolving; indeterminism is an inherent part of the open universe in which we live; and learning from experience involves untestable assumptions. We discuss several concepts of robustness as tools for responding to these epistemological challenges. The use of models is justified, even though they are known to err. A concept of robustness is illustrated in choosing between a conventional technology and an innovative, promising, but more uncertain technology. We explain that nonprobabilistic robust decisions are sometimes good probabilistic bets. Info‐gap and worst‐case concepts of robustness are compared. Finally, we examine the exploitation of favorable but uncertain opportunities and its relation to robust decision making.     

灾后不确定需求下应急医疗移动医院鲁棒选址问题研究

我国灾害医学救援主要采用"现场救治"模式，应急医疗移动医院的选址是否合理直接影响救援效率，但各受灾点伤员数量的不确定性增加了决策的困难。本文引入多面体不确定集合刻画伤员数量的不确定性，同时考虑伤员分类及移动医院分型，构建一个以伤员总生存概率最大化为目标的鲁棒选址模型。利用鲁棒优化理论，将模型转化为等价的混合整数规划问题，通过GAMS软件编程并调用CPLEX求解器求解。最后，以四川芦山地震应急医疗救援为例，验证模型和求解方法的可行性和鲁棒性。结果表明，扰动比例和不确定水平对移动医院的选址和伤员的分配方案有显著影响，决策者可根据自己对不确定性风险的偏好程度选择最佳的扰动比例和不确定水平组合，以获得最优的选址分配方案。     

有限需求信息下基于回购契约的供应链鲁棒协调策略

研究了仅知需求均值和区间信息条件下,基于最小最大后悔值准则的供应链回购契约协调问题。针对未知需求具体分布形式的两级供应链系统,在回购契约框架下,建立了以鲁棒决策和最优决策下的供应链及其成员绩效之差为目标函数的供应链协调模型。在仅知需求区间和均值信息条件下,采用鲁棒优化方法求解了最小最大后悔值准则下的集成供应链鲁棒订货策略和分散供应链鲁棒契约协调策略及其绩效偏差。分析了不同服务水平和契约参数条件下,由于信息缺失而未能实现最优运作的供应链及其成员绩效损失情况。最后,进行了数值计算,验证了通过鲁棒优化方法得到的供应链回购契约协调策略的鲁棒性和有效性。结果表明,基于回购契约的供应链鲁棒协调策略能够有效抑制需求不确定性对系统及其成员运作绩效的影响,同仅知需求区间信息相比,额外获得需求均值信息能够有效改进供应链运作绩效。     

Risk Communication,Public Engagement,and Climate Change: A Role for Emotions

This article discusses the potential role that emotions might play in enticing a lifestyle that diminishes climate change. Climate change is an important challenge for society. There is a growing consensus that climate change is due to our behavior, but few people are willing to significantly adapt their lifestyle. Empirical studies show that people lack a sense of urgency: they experience climate change as a problem that affects people in distant places and in a far future. Several scholars have claimed that emotions might be a necessary tool in communication about climate change. This article sketches a theoretical framework that supports this hypothesis, drawing on insights from the ethics of risk and the philosophy of emotions. It has been shown by various scholars that emotions are important determinants in risk perception. However, emotions are generally considered to be irrational states and are hence excluded from communication and political decision making about risky technologies and climate change, or they are used instrumentally to create support for a position. However, the literature on the ethics of risk shows that the dominant, technocratic approach to risk misses the normative‐ethical dimension that is inherent to decisions about acceptable risk. Emotion research shows that emotions are necessary for practical and moral decision making. These insights can be applied to communication about climate change. Emotions are necessary for understanding the moral impact of the risks of climate change, and they also paradigmatically provide for motivation. Emotions might be the missing link in effective communication about climate change.     

MODEL UNCERTAINTY

We study decision problems in which consequences of the various alternative actions depend on states determined by a generative mechanism representing some natural or social phenomenon. Model uncertainty arises because decision makers may not know this mechanism. Two types of uncertainty result, a state uncertainty within models and a model uncertainty across them. We discuss some two‐stage static decision criteria proposed in the literature that address state uncertainty in the first stage and model uncertainty in the second (by considering subjective probabilities over models). We consider two approaches to the Ellsberg‐type phenomena characteristic of such decision problems: a Bayesian approach based on the distinction between subjective attitudes toward the two kinds of uncertainty; and a non‐Bayesian approach that permits multiple subjective probabilities. Several applications are used to illustrate concepts as they are introduced.     

Facility Location: A Robust Optimization Approach

In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi‐period fixed‐charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi‐dimensional box, and demand within a multi‐dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.     

Robust allocation of a defensive budget considering an attacker's private information

Attackers' private information is one of the main issues in defensive resource allocation games in homeland security. The outcome of a defense resource allocation decision critically depends on the accuracy of estimations about the attacker's attributes. However, terrorists' goals may be unknown to the defender, necessitating robust decisions by the defender. This article develops a robust-optimization game-theoretical model for identifying optimal defense resource allocation strategies for a rational defender facing a strategic attacker while the attacker's valuation of targets, being the most critical attribute of the attacker, is unknown but belongs to bounded distribution-free intervals. To our best knowledge, no previous research has applied robust optimization in homeland security resource allocation when uncertainty is defined in bounded distribution-free intervals. The key features of our model include (1) modeling uncertainty in attackers' attributes, where uncertainty is characterized by bounded intervals; (2) finding the robust-optimization equilibrium for the defender using concepts dealing with budget of uncertainty and price of robustness; and (3) applying the proposed model to real data.     

Fooled by Local Robustness

One would have expected the considerable public debate created by Nassim Taleb’s two best selling books on uncertainty, Fooled by Randomness and The Black Swan, to inspire greater caution to the fundamental difficulties posed by severe uncertainty. Yet, methodologies exhibiting an incautious approach to uncertainty have been proposed recently in a range of publications. So, the objective of this short note is to call attention to a prime example of an incautious approach to severe uncertainty that is manifested in the proposition to use the concept radius of stability as a measure of robustness against severe uncertainty. The central proposition of this approach, which is exemplified in info‐gap decision theory, is this: use a simple radius of stability model to analyze and manage a severe uncertainty that is characterized by a vast uncertainty space, a poor point estimate, and a likelihood‐free quantification of uncertainty. This short discussion serves then as a reminder that the generic radius of stability model is a model of local robustness. It is, therefore, utterly unsuitable for the treatment of severe uncertainty when the latter is characterized by a poor estimate of the parameter of interest, a vast uncertainty space, and a likelihood‐free quantification of uncertainty.     

Robust Contracts in Continuous Time

We study a continuous‐time contracting problem under hidden action, where the principal has ambiguous beliefs about the project cash flows. The principal designs a robust contract that maximizes his utility under the worst‐case scenario subject to the agent's incentive and participation constraints. Robustness generates endogenous belief heterogeneity and induces a tradeoff between incentives and ambiguity sharing so that the incentive constraint does not always bind. We implement the optimal contract by cash reserves, debt, and equity. In addition to receiving ordinary dividends when cash reserves reach a threshold, outside equity holders also receive special dividends or inject cash in the cash reserves to hedge against model uncertainty and smooth dividends. The equity premium and the credit yield spread generated by ambiguity aversion are state dependent and high for distressed firms with low cash reserves.     

On the Robust Single Machine Scheduling Problem

The single machine scheduling problem with sum of completion times criterion (SS) can be solved easily by the Shortest Processing Time (SPT) rule. In the case of significant uncertainty of the processing times, a robustness approach is appropriate. In this paper, we show that the robust version of the (SS) problem is NP-complete even for very restricted cases. We present an algorithm for finding optimal solutions for the robust (SS) problem using dynamic programming. We also provide two polynomial time heuristics and demonstrate their effectiveness.     

Impact of Number of Interactions,Different Interaction Patterns,and Human Inconsistencies on Some Hybrid Evolutionary Multiobjective Optimization Algorithms*

We investigate the impact of the number of human–computer interactions, different interaction patterns, and human inconsistencies in decision maker responses on the convergence of an interactive, evolutionary multiobjective algorithm recently developed by the authors. In our context “an interaction” means choosing the best and worst solutions among a sample of six solutions. By interaction patterns we refer to whether preference questioning is more front‐, center‐, rear‐, or edge‐loaded. As test problems we use two‐ to four‐objective knapsack problems, multicriteria scheduling problems, and multiobjective facility location problems. In the tests, two different preference functions are used to represent actual decision maker preferences, linear and Chebyshev. The results indicate that it is possible to obtain solutions that are very good or even nearly optimal with a reasonable number of interactions. The results also indicate that the algorithm is robust to minor inconsistencies in decision maker responses. There is also surprising robustness toward different patterns of interaction with the decision maker. The results are of interest to the evolutionary multiobjective (EMO) community actively developing hybrid interactive EMO approaches.     

稳健的动态资产组合模型研究

事件风险与参数的不确定性对金融决策有重大的影响,投资者担心股市上极端金融事件的出现,突然改变股票价格和波动率,造成较大的损失.通过引入风险规避的稳健投资者以及模型设定可能存在误差,投资者在最小化模型设定误差的前提下,制定风险资产收益跳跃情况下的动态资产组合战略,最大化投资者的效用.结果表明,当投资者是风险规避和不确定性规避者时,稳健的投资准则会显著降低他们对风险资产的需求.     

Addressing Climate Change as an Emerging Risk to Infrastructure Systems

The consequences that climate change could have on infrastructure systems are potentially severe but highly uncertain. This should make risk analysis a natural framework for climate adaptation in infrastructure systems. However, many aspects of climate change, such as weak background knowledge and societal controversy, make it an emerging risk where traditional approaches for risk assessment and management cannot be confidently employed. A number of research developments aimed at addressing these issues have emerged in recent years, such as the development of probabilistic climate projections, climate services, and robust decision frameworks. However, additional research is needed to improve the suitability of these methods for infrastructure planning. In this perspective, we outline some of the challenges in addressing climate change risks to infrastructure and summarize new developments aimed at meeting these challenges. We end by highlighting needs for future research, many of which could be well‐served by expertise within the risk analysis community.