RANK GENERATION,PRESERVATION, AND REVERSAL IN THE ANALYTIC HIERARCHY DECISION PROCESS

Decision making has the objective of finding the best alternative or set of alternatives by considering a number of goals, objectives, criteria, competitors, and other important factors. The analytic hierarchy process is a decision aid used to assist a decision maker in sorting out the complexity of a decision problem and making use of his or her judgments. A decision maker must be assured that the arithmetic operations of any such decision process are the right ones—that they surface the correct ranking and values of the alternatives and preserve or alter ranks appropriately when new alternatives are added or deleted. In this paper it will be shown that with absolute measurement, rank always is preserved, with relative measurement, rank changes with nspect to scveral criteria only because of the structural dependence (involving both numbers and measurements) of criteria on alternatives. A discussion of the effect on rank of replicas and near replicas of the alternatives also is given.     

考虑决策者损失规避的异质信息多属性变权决策方法

现实中存在大量异质信息（或数据）和需要考虑权重随属性值变化的多属性决策问题。针对这类异质信息多属性决策问题，本文提出了一种基于前景理论的变权综合求解方法。首先，构建了异质信息的统一距离计算公式，进而计算各个决策方案的相对贴近度；然后，提出基于不同类型效用函数的变权向量构造方法；其次，以初始权重为参考点，计算变权向量相对于参考点的益损决策矩阵，进而计算考虑决策者权重损失和收益的风险态度的各个决策方案的前景综合值，据此确定方案优劣排序和最优方案。通过数值例子的计算分析说明，文中所提决策模型与方法具有较好的有效性和合理性，可为解决复杂情景的决策问题提供理论依据与方法支持。     

Sequential Search and Selection Problem Under Uncertainty

This paper formulates and discusses a series of sequential decision problems of the following common structure: A decision alternative of multiple attributes‐that is, a job, an employee, or an investment alternative‐is to be selected within a certain fixed length of time. An unknown number of alternatives are presented sequentially, either deterministically or in a random manner. The decision maker can rank all the alternatives from best to worst without ties, and the decision to accept or reject an alternative is based solely on the relative ranks of those alternatives evaluated so far. The nonparametric sequential decision problem is first studied for a model involving a discrete time period and then generalized in terms of continuous time. Also considered is a variant of this problem involving a Bayesian estimation of (1) the uncertain probability of having an alternative at a given stage in the discrete‐time model and (2) the arrival rate of alternatives in the continuous‐time model. The optimal selection strategy that maximizes the probability of selecting the absolute best alternative is illustrated with the job search problem and the single‐machine job assignment problem.     

RUTA: A framework for assessing and selecting additive value functions on the basis of rank related requirements

In this paper, we present a new preference disaggregation method, called RUTA, which infers a set of additive value functions from the preference information referring to the desired ranks of some reference alternatives. Real-life experience indicates that people willingly refer to the range of allowed ranks that a particular alternative should attain, or to constraints on the final scores of the alternatives. We develop a mathematical model for incorporating such preference information via mixed-integer linear programming (MILP). Then, we discuss how decision making could be supported with the use of the already proposed extreme ranking analysis (ERA), which indicates the best and worst ranks gained by each alternative over the set of compatible preference model instances. We also introduce a new interactive UTA-like technique, which aims at selecting a single value function representing the outcomes of ERA. In the interactive process, the decision maker (DM) is assigning priorities to different pre-defined targets, which are built on results of ERA, and refer to the comparison of the best and/or worst ranks for pairs of alternatives. In particular, the DM may choose to emphasize or neglect the advantage of some alternatives over the others, in terms of results of ERA. In this way, one obtains a synthetic representation of extreme ranking analysis at a higher level of abstraction.     

Screening alternatives graphically by an extended case-based distance approach

Screening is a helpful process of multiple criteria decision aid (MCDA) to reduce a larger set of alternatives into a smaller one containing the best alternatives; thereby, decision makers are able to concentrate on evaluating alternatives within a smaller set. Therefore, determining how to assist decision makers in screening is an important issue for MCDA. This study proposes an extended case-based distance approach incorporating the advantages of a case-based distance method, a mixed-integer programming approach of discriminant analysis, and a multidimensional scaling technique to help decision makers screen alternatives visually in MCDA. The proposed approach can screen alternatives by evaluating sets of cases selected by decision makers, providing visual aids to observe decision context, reducing the number of misclassifications, and improving multiple solution problems. An interactive screening procedure is also developed to provide flexibility so that decision makers can check and adjust screening results iteratively.     

R&D portfolio selection by using qualitative pairwise comparisons

A new multicriteria decision aid, QualScal, is applied to the problem of selecting an extramural Fisheries R&D portfolio in the Ministry of Agriculture, Fisheries and Food. QualScal has been developed for the situation where the characteristics of the decision alternatives cannot be readily quantified. The decision-maker is only required to state either indifference or preference for each pair of the alternatives. A map representing the preference structure of the decision maker is produced with the aid of an enhanced version of the traditional nonmetric multidimensional scaling procedure, capable of scaling disjoint subsets of alternatives. Averaged results for the group of decision-makers facilitate a discussion to determine a mutually acceptable portfolio.     

Missing consequences in multiattribute utility theory

This paper addresses how to deal with decision alternatives with missing consequences in multicriteria decision-making problems. We propose disregarding the attributes for which a decision alternative provides no consequence by redistributing their respective weights throughout the objective hierarchy in favor of a straightforward idea: the assignation of the respective attribute range as a default value for missing consequences due to possible uncertainty about the decision alternative consequences. In both cases, decision alternatives are evaluated by means of an additive multi-attribute utility model. An illustrative example of the restoration of radionuclide contaminated aquatic ecosystems is shown.     

Applications and Implementation DECISION SUPPORT SYSTEMS: AN EMPIRICAL ASSESSMENT FOR DECISION MAKING

A laboratory experiment examined the effects of applying decision support system (DSS) technology to decision making in ill-structured problem environments under varying information conditions. Marketing executives participated in the experiment which investigated the effects of DSS availability, DSS training, and data availability on dependent variables that included: (1) the number of alternatives considered by a subject during decision making, (2) the period of time spent by a subject to complete the decision-making process, (3) the subject's perceived confidence in the decisions he or she had made, (4) the amount of data considered by a subject's during decision making, (5) the individual subject's decision processing, and (6) the subject's performance overall. Our results indicate that all three factors significantly affect the number of alternatives considered by subjects during the decision-making process. We therefore suggest that DSS training be coordinated with decision training in order to realize the potential of DSSs as described in the DSS literature.     

Expanding the Reach of Participatory Risk Management: Testing an Online Decision‐Aiding Framework for Informing Internally Consistent Choices

This article presents research aimed at developing and testing an online, multistakeholder decision‐aiding framework for informing multiattribute risk management choices associated with energy development and climate change. The framework was designed to provide necessary background information and facilitate internally consistent choices, or choices that are in line with users’ prioritized objectives. In order to test different components of the decision‐aiding framework, a six‐part, 2 × 2 × 2 factorial experiment was conducted, yielding eight treatment scenarios. The three factors included: (1) whether or not users could construct their own alternatives; (2) the level of detail regarding the composition of alternatives users would evaluate; and (3) the way in which a final choice between users’ own constructed (or highest‐ranked) portfolio and an internally consistent portfolio was presented. Participants’ self‐reports revealed the framework was easy to use and providing an opportunity to develop one's own risk‐management alternatives (Factor 1) led to the highest knowledge gains. Empirical measures showed the internal consistency of users’ decisions across all treatments to be lower than expected and confirmed that providing information about alternatives’ composition (Factor 2) resulted in the least internally consistent choices. At the same time, those users who did not develop their own alternatives and were not shown detailed information about the composition of alternatives believed their choices to be the most internally consistent. These results raise concerns about how the amount of information provided and the ability to construct alternatives may inversely affect users’ real and perceived internal consistency.     

PAHAP: A Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences

In this paper, we present a Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences (PAHAP), a new method for solving discrete alternative multicriteria decision problems. Following the Analytic Hierarchy Process (AHP), PAHAP uses pairwise preference judgments to assess the relative attractiveness of the alternatives. By first aggregating the pairwise judgment ratios of the alternatives across all criteria, and then synthesizing based on these aggregate measures, PAHAP determines overall ratio scale priorities and rankings of the alternatives which are not subject to rank reversal, provided that certain weak consistency requirements are satisfied. Hence, PAHAP can serve as a useful alternative to the original AHP if rank reversal is undesirable, for instance when the system is open and criterion scarcity does not affect the relative attractiveness of the alternatives. Moreover, the single matrix of pairwise aggregated ratings constructed in PAHAP provides useful insights into the decision maker's preference structure. PAHAP requires the same preference information as the original AHP (or, altematively, the same information as the Referenced AHP, if the criteria are compared based on average (total) value of the alternatives). As it is easier to implement and interpret than previously proposed variants of the conventional AHP which prevent rank reversal, PAHAP also appears attractive from a practitioner's viewpoint.     

应急决策方案的动态调整方法研究

本文针对应急决策中方案的动态调整问题,提出了一种风险决策方法。首先,根据突发事件的情景演变特点,描述了应急决策中方案调整的问题和过程,并对不同方案之间的相关性进行分析;然后,阐述了调整方案的生成过程;进一步地,考虑调整方案对各级别突发事件的应急处置效果和应对损失、不同方案之间的转换成本等因素,给出了应急决策方案的动态调整方法;最后,通过算例说明了该方法的有效性和可行性。     

Intelligence gathering for decision making

Empirical studies of decision making seldom consider the intelligence gathering activities required for decision making. In an attempt to fill this void, this study set out to identify and assess some of the key steps in gathering intelligence, considering the difficulty of the decision and available resources. The study found performance gapping and premising to be crucial activities and explored how each is carried out. A variety of premising and gapping tactics were uncovered, with some having better success than others. These tactics were found to influence the search approach selected to uncover alternatives and the success of the resulting decision. The best results were noted when search efforts are guided by needs documented with a quantitative performance gap; and when formal search or negotiation is used to identify alternatives. These findings hold for decisions that have high and low difficulty and for those with high and low resource support. The implications of these findings for decision makers and decision making are discussed.     

一种基于偏好分布的群决策方法

为了满足群决策的实际需求,本文提出了一种基于偏好分布的群决策方法,该方法利用完全不对称预先排序向量表示决策者的偏好,通过分析计算偏好排序向量的密度和分布结构,从可行方案集合中寻找所有决策者都能接受的优选方案集合,逐次缩小搜索空间以逼近一致满意解。该方法结合冲突分析,可进一步分析决策者之间的相互关系,集成于谈判支持系统,具有直观、实用等特点,最后给出了一个实际例子说明该方法。     

基于公理设计和功能过剩的公共住房撮合分配方法

公共住房的合理分配是关系保障性安居工程成败及可持续发展的"生命线"。公共住房分配中缺乏科学规划和依据,既难以保障公共住房资源分配的"公平正义",也在一定程度上造成了效率缺失。本文借鉴双边匹配思想,给出了一种基于公理设计和功能过剩的公共住房撮合分配方法,构建了一个公共住房撮合分配多目标优化决策模型。文中给出的公共住房分配案例计算表明,该方法有利于提高公共住房撮合分配的科学性、合理性及正确性,具有一定的可行性和适用性。基于相关系数权重的数值模拟试验,研究进一步探讨了住房保障的发展阶段、住房保障策略与最优撮合分配结果的关系,为公共住房分配提供了一些策略:在住房保障起步和发展阶段,应当优先考虑较高的保障覆盖面,同时也应避免公共住房对保障需求过剩;在住房保障发展成熟和完善阶段,则应当注重提高住房保障的保障水平,尽力满足住房保障对象更高水平的住房改善需求。     

The inferring of preferences from indifferences in multicriteria decision analysis

Rivett [5] has proposed that an approximate preference ordering may be deduced from statements of pairwise indifferences between decision alternatives by using multi-dimensional scaling. In this paper it is demonstrated that much stronger evaluations of preference are possible by applying formal statistical inferential procedures to a simple parametric model, relating indifference to closeness on a scale defined by a linear function of attribute values. This can be used to screen out a considerable proportion of less desirable decision alternatives. The method is illustrated by application to Rivett's problem of the hypothetical Town of Brove, for which a satisfactory matching with Rivett's utilities is obtained. It is also shown that the method can provide useful preference orderings on the basis of less than 20% of all possible pairwise comparisons between alternatives.     

Screening of multiattribute alternatives

A procedure for screening multiattribute alternatives is proposed. This procedure reduces the detailed data collection needs and the information burden on the decision maker. It is shown that the inferior decision alternatives can be excluded without specifying probabilities, importance weights, and utilities with precision.     

TREATMENT OF DIFFERENTIAL COSTS AND BENEFITS UNDER RISK

In management accounting texts, the relevant costs and benefits for decision making are usually defined as those future amounts that differ between pairs of alternatives. Use of differential amounts can lead to erroneous choices in decision making under risk. This paper examines conditions under which the use of differential amounts is and is not appropriate.     

Does Concern‐Driven Risk Management Provide a Viable Alternative to QRA?

This article discusses a concept of concern-driven risk management, in which qualitative expert judgments about whether concerns warrant specified risk management interventions are used in preference to quantitative risk assessment (QRA) to guide risk management decisions. Where QRA emphasizes formal quantitative assessment of the probable consequences caused by the recommended actions, and comparison to the probable consequences of alternatives, including the status quo, concern-driven risk management instead emphasizes perceived urgency or severity of the situation motivating recommended interventions. In many instances, especially those involving applications of the precautionary principle, no formal quantification or comparison of probable consequences for alternative decisions is seen as being necessary (or, perhaps, possible or desirable) prior to implementation of risk management measures. Such concern-driven risk management has been recommended by critics of QRA in several areas of applied risk management. Based on case studies and psychological literature on the empirical performance of judgment-based approaches to decision making under risk and uncertainty, we conclude that, although concern-driven risk management has several important potential political and psychological advantages over QRA, it is not clear that it performs better than (or as well as) QRA in identifying risk management interventions that successfully protect human health or achieve other desired consequences. Therefore, those who advocate replacing QRA with concern-driven alternatives, such as expert judgment and consensus decision processes, should assess whether their recommended alternatives truly outperform QRA, by the criterion of producing preferred consequences, before rejecting the QRA paradigm for practical applications.     

A case-based distance method for screening in multiple-criteria decision aid

Screening is a process of multiple-criteria decision aid (MCDA) in which a large set of alternatives is reduced to a smaller set that most likely contains the best choice. We propose screening using a distance model calibrated on the basis of the decision-maker's own judgement. Viewing MCDA as preference aggregation based on consequence data, we define consequence and preference expressions (values and weights) and describe how they are aggregated. Then we define screening and explain some of its properties. Using an appropriate definition of distance, our case-based distance method screens a set of alternatives using criterion weights and a distance threshold obtained by quadratic optimization using the decision-maker's selection of alternatives from a test set. This case-based method can elicit the decision maker's preferences more expeditiously and accurately than direct inquiry. An application in water supply planning is used to demonstrate the procedure.     

PITFALLS OF ROUNDING IN DISCRETE MANAGEMENT DECISION PROBLEMS

A number of articles on managerial decision making have addressed the issue of whether or not to round a fractional solution to obtain a solution for a problem involving discrete alternatives. (An example is the problem in which the decision maker must select exactly one of several investment alternatives, but attaches no meaning to selecting two-thirds of one alternative and one-third of another.) Those articles which suggest that rounding can lead to undesirable answers are seemingly supported by the numerous “textbook examples” that purport to illustrate the dangers of rounding. However, the standard examples in which rounding fails to give a workable solution involve only a few rounding possibilities (usually two or four) and do not come from real world applications. Hence, it is questionable whether they provide any insight about what is likely to occur in a practical setting. This note fills a gap in previous discussions of rounding by providing two easily understood examples that dramatically portray the difficulties that rounding can encounter. The first example belongs to an important class of practical problems. We illustrate that rounding fails not only for this example, but also fails for all problems in its class. The second example is a unique “showcase” problem which can be summarized by a 5 times 5 cost matrix. This problem contains more than a million rounding alternatives, all of them infeasible! Following these examples, we present a “rounding paradox” and we show that its resolution gives analytical support to the conclusion that rounding will produce grave difficulties in a wide variety of practical situations.