Two ways to handle dependent uncertainties in multi-criteria decision problems

We consider multi-criteria group decision-making problems, where the decision makers (DMs) want to identify their most preferred alternative(s) based on uncertain or inaccurate criteria measurements. In many real-life problems the uncertainties may be dependent. In this paper, we focus on multicriteria decision-making (MCDM) problems where the criteria and their uncertainties are computed using a stochastic simulation model. The model is based on decision variables and stochastic parameters with given distributions. The simulation model determines for the criteria a joint probability distribution, which quantifies the uncertainties and their dependencies. We present and compare two methods for treating the uncertainty and dependency information within the SMAA-2 multi-criteria decision aid method. The first method applies directly the discrete sample generated by the simulation model. The second method is based on using a multivariate Gaussian distribution. We demonstrate the methods using a decision support model for a retailer operating in the deregulated European electricity market.     

Expedient and Monotone Learning Rules

This paper considers learning rules for environments in which little prior and feedback information is available to the decision maker. Two properties of such learning rules are studied: absolute expediency and monotonicity. Both require that some aspect of the decision maker's performance improves from the current period to the next. The paper provides some necessary, and some sufficient conditions for these properties. It turns out that there is a large variety of learning rules that have the properties. However, all learning rules that have these properties are related to the replicator dynamics of evolutionary game theory. For the case in which there are only two actions, it is shown that one of the absolutely expedient learning rules dominates all others.     

Preference-Order Recursion for Finding Relevant Pure,Admissible and Optimal Statistical Decision Functions*

A preference-order recursion algorithm for obtaining a relevant subset of pure, admissible (non-dominated, efficient) decision functions which converges towards an optimal solution in statistical decision problems is proposed. The procedure permits a decision maker to interactively express strong binary preferences for partial decision functions at each stage of the recursion, from which an imprecise probability and/or utility function is imputed and used as one of several pruning mechanisms to obtain a reduced relevant subset of admissible decision functions or to converge on an optimal one. The computational and measurement burden is thereby mitigated significantly, for example, by not requiring explicit or full probability and utility information from the decision maker. The algorithm is applicable to both linear and nonlinear utility functions. The results of behavioral and computational experimentation show that the approach is viable, efficient, and robust.     

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.     

基于实物期权的新技术投资决策实证研究

本文基于对我国高新技术企业的实际调研,从实物期权视角检验不同类型不确定性对企业新技术投资决策的影响。研究结果表明,市场与政策不确定性对投资的延迟作用与技术不确定性对投资的促进作用得到不同程度验证,而竞争强度与投资不可逆程度对不确定性与投资关系的调节作用则不完全符合实物期权的理论预期。论文结果揭示了我国高新技术企业进行投资决策的一般规律,可为企业应用实物期权方法提供参考。     

CONSTRAINED DECISION CRITERIA1

The choice of a suitable decision criterion is a difficult decision for many decision makers. In general, each criterion selects a different optimal act, each having its own appealing features. This paper proposes an approach allowing the decision maker to incorporate multiple criteria into an easily solved mathematical programming model whose solution is the optimal act. Optimality is defined by the objective function used in the model. The constraints embody the decision maker's anxieties and minimal desires.     

Stochastic Judgments in the AHP: The Measurement of Rank Reversal Probabilities

This paper presents a methodology for analyzing Analytic Hierarchy Process (AHP) rankings if the pairwise preference judgments are uncertain (stochastic). If the relative preference statements are represented by judgment intervals, rather than single values, then the rankings resulting from a traditional (deterministic) AHP analysis based on single judgment values may be reversed, and therefore incorrect. In the presence of stochastic judgments, the traditional AHP rankings may be stable or unstable, depending on the nature of the uncertainty. We develop multivariate statistical techniques to obtain both point estimates and confidence intervals of the rank reversal probabilities, and show how simulation experiments can be used as an effective and accurate tool for analyzing the stability of the preference rankings under uncertainty. If the rank reversal probability is low, then the rankings are stable and the decision maker can be confident that the AHP ranking is correct. However, if the likelihood of rank reversal is high, then the decision maker should interpret the AHP rankings cautiously, as there is a subtantial probability that these rankings are incorrect. High rank reversal probabilities indicate a need for exploring alternative problem formulations and methods of analysis. The information about the extent to which the ranking of the alternatives is sensitive to the stochastic nature of the pairwise judgments should be valuable information into the decision-making process, much like variability and confidence intervals are crucial tools for statistical inference. We provide simulation experiments and numerical examples to evaluate our method. Our analysis of rank reversal due to stochastic judgments is not related to previous research on rank reversal that focuses on mathematical properties inherent to the AHP methodology, for instance, the occurrence of rank reversal if a new alternative is added or an existing one is deleted.     

An extension of the Electre I method for group decision-making under a fuzzy environment

Many real-world decision problems involve conflicting systems of criteria, uncertainty and imprecise information. Some also involve a group of decision makers (DMs) where a reduction of different individual preferences on a given set to a single collective preference is required. Multi-criteria decision analysis (MCDA) is a widely used decision methodology that can improve the quality of group multiple criteria decisions by making the process more explicit, rational and efficient. One family of MCDA models uses what is known as “outranking relations” to rank a set of actions. The Electre method and its derivatives are prominent outranking methods in MCDA. In this study, we propose an alternative fuzzy outranking method by extending the Electre I method to take into account the uncertain, imprecise and linguistic assessments provided by a group of DMs. The contribution of this paper is fivefold: (1) we address the gap in the Electre literature for problems involving conflicting systems of criteria, uncertainty and imprecise information; (2) we extend the Electre I method to take into account the uncertain, imprecise and linguistic assessments; (3) we define outranking relations by pairwise comparisons and use decision graphs to determine which action is preferable, incomparable or indifferent in the fuzzy environment; (4) we show that contrary to the TOPSIS rankings, the Electre approach reveals more useful information including the incomparability among the actions; and (5) we provide a numerical example to elucidate the details of the proposed method.     

基于前景理论的多阶段随机多准则决策方法

研究一种基于动态参考点的多阶段随机多准则决策方法。考虑多阶段决策过程中决策者的风险偏好,建立了基于前景理论的多阶段随机多准则决策分析框架,提出了一种基于阶段发展特征的动态参考点设置方法;构建准则权重的目标规划模型,结合阶段参考点动态变化的特征测算各阶段备选方案的综合前景值;设计方案综合前景值的范围估算模型,以反映决策风险对评价结果的影响;案例研究验证了上述方法的可行性和实际效果。     

Risk Averse Decisions in Business Planning

Second-order stochastic dominance is used to determine preferences among various investments for any risk-averse decision maker. On the other hand, when faced with choosing between different insurance policies or disaster plans, a risk-averse decision maker should use a type of stochastic dominance called variability ordering. In this situation, second-order stochastic dominance has been used in previous research and is incorrect.     

Stochastic Choice and Revealed Perturbed Utility

Perturbed utility functions—the sum of expected utility and a nonlinear perturbation function—provide a simple and tractable way to model various sorts of stochastic choice. We provide two easily understood conditions each of which characterizes this representation: One condition generalizes the acyclicity condition used in revealed preference theory, and the other generalizes Luce's IIA condition. We relate the discrimination or selectivity of choice rules to properties of their associated perturbations, both across different agents and across decision problems. We also show that these representations correspond to a form of ambiguity‐averse preferences for an agent who is uncertain about her true utility.     

不确定环境下考虑风险厌恶的生产-分销网络优化模型及试验设计

考虑上游生产和下游需求不确定性，研究了由工厂、分销中心及终端市场构成的生产-分销网络优化设计问题。针对上游生产不确定性，考虑产生故障和无故障两种状态；针对下游市场需求不确定性，考虑其具有低、中和高三种状态。由于生产发生故障可能导致不合格品的产生，进一步考虑了在上游生产环节是否实施产品监测问题。综合网络运作成本和由不确定性导致的绩效风险，建立了由风险厌恶水平和悲观系数刻画的基于均值-条件风险值（CVaR）准则的生产-分销网络两阶段随机规划模型。特别地，针对由网络潜在节点数众多所导致的不确定情景规模过大的问题，采用情景缩减技术进行了情景筛选，降低了所建模型的求解难度。最后，进行了数值计算，分析了相关参数对网络运作绩效的影响，并给出了期望成本和条件风险值两个目标权衡的帕累托有效前沿。进一步，通过回归试验设计检验了决策者风险厌恶水平和悲观系数对所设计的生产-分销网络绩效的影响程度。结果表明，相对于决策者的风险厌恶程度，悲观系数对网络运作绩效的影响更大。     

Behavior in a Dynamic Decision Problem: An Analysis of Experimental Evidence Using a Bayesian Type Classification Algorithm

Different people may use different strategies, or decision rules, when solving complex decision problems. We provide a new Bayesian procedure for drawing inferences about the nature and number of decision rules present in a population, and use it to analyze the behaviors of laboratory subjects confronted with a difficult dynamic stochastic decision problem. Subjects practiced before playing for money. Based on money round decisions, our procedure classifies subjects into three types, which we label “Near Rational,”“Fatalist,” and “Confused.” There is clear evidence of continuity in subjects' behaviors between the practice and money rounds: types who performed best in practice also tended to perform best when playing for money. However, the agreement between practice and money play is far from perfect. The divergences appear to be well explained by a combination of type switching (due to learning and/or increased effort in money play) and errors in our probabilistic type assignments.     

Quantitative Comparison of Approximate Solution Sets for Bi‐criteria Optimization Problems*

We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near‐pareto‐optimal solutions to bi‐criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives.     

A two-stage stochastic programming approach for identifying optimal postponement strategies in supply chains with uncertain demand

In the course of globalization, applying mass-customization strategies has led to a high diversity of variants in many economic sectors. Thus, customer demands are often less predictable, and handling increasing inventory stocks as well as avoiding shortfalls have become particularly important. All these complexity drivers result in higher supply chain risks. Postponement strategies have been proposed as a suitable approach to address these problems. Although the concept of postponement and its impact on the supply chain are theoretically well discussed, optimally configuring the entire production and distribution activities is still challenging. We present a two-stage stochastic mixed-integer linear programming model, which comprises an integrated production and distribution planning approach, and considers postponement concepts. In comparison to earlier approaches that examine postponement strategies, our model supports the decision maker under demand uncertainty and considers lead times, penalty costs for shortfalls, as well as inventory-keeping decisions over a tactical planning horizon. This allows an integrated investigation of both form and logistics postponement concepts. Moreover, we consider the decision maker’s risk attitude identifying non-dominated profitable and risk-averse strategies. We illustrate the benefits of the model by using a case study from the apparel industry, and present the results of a sensitivity analysis with respect to varying demand uncertainty and demand correlations as well as different preferences regarding risk aversion. Furthermore, we carry out performance and quality benchmarks and compare the results of a standard mixed-integer linear programming solver, a parallel nested Benders approach and a sample average approximation technique.     

Planning with multiple objectives

Planning any task that is characterised by the presence of multiple objectives presents the decision maker with a set of special considerations which are not present in the case of decision making with one unique objective. The paper outlines the stages in the formulation of a dynamic multiple-objective objective function and introduces the criterion complex as a decision making construct particularly suited to formulating and solving problems with multiple objectives. The paper then considers some of the mathematical properties of the alternative formulations of criterion complex.     

An Experimental Evaluation of Articulation of Preferences in Multiple Criterion Decision-Making (MCDM) Methods

This paper describes the results of a study done to determine how well multiple criterion decision-making methods perform in helping a decision maker arrive at a preferred solution to a multicriterion problem with conflicting objectives. The study used a factorial experiment and doctoral students as subjects. Two competing methods for solving multicriterion problems were compared along with the influence of problem complexity. The methods differed in the way preferences were articulated by decision makers. The results showed that there was no difference between the methods for several performance measures, disaffirming some prior expectations. From an actual use point of view, the study suggests that methodological improvements to existing techniques must be matched by efforts to improve information presentation and interpretation to facilitate preference judgments.     

Relative Objective Functions in Multiobjective Decision Support Models*

This paper considers the importance of using the nondominated minimum in forming relative objective functions. Other minima can prevent the decision maker from reaching a preferred decision. They disturb the zero and distort the scale, thereby misguiding the decision maker by falsifying trade-off possibilities. Worse, some of these other minima can inadvertently hide whole regions of preferred solutions. Zeleny's multiple criteria simplex method is used to find the nondominated minimum for the linear case.     

Parametric discounting

A parametric approach to the problem of selection from amongst alternative investment opportunities is considered in a discounted cash flow framework. The approach employs differential cash flows, an uncertain planning horizon and a nested approach to composing cash flow parameters. This promotes consistent treatment of alternative investments, clarifies the effects of uncertainty, avoids some of the defects of internal rate of return and payback period criteria and allows direct comparison of best and next best options as primal and dual versions of the same model. Net present value, internal rate of return, annual average cost or payback period assessments may be selected post analysis. A domestic wall insulation example is used for illustrative purposes. This example is related to the hydroelectric power development decision which gave rise to the approach.     

Expected Uncertain Utility Theory

We introduce and analyze expected uncertain utility (EUU) theory. A prior and an interval utility characterize an EUU decision maker. The decision maker transforms each uncertain prospect into an interval‐valued prospect that assigns an interval of prizes to each state. She then ranks prospects according to their expected interval utilities. We define uncertainty aversion for EUU, use the EUU model to address the Ellsberg Paradox and other ambiguity evidence, and relate EUU theory to existing models.