A convex approach for multicriteria decision making in hierarchical systems

In this paper hierarchical multicriteria optimization problems are addressed in a convex programming framework. It is assumed that the criteria are aggregated into a nonlinear function, which renders the problem nonseparable, in general. The projection of the problem onto the criteria space is used to obtain an equivalent separable problem, solved through a relaxation procedure implemented on basis of a multilevel structure. At the upper level of the structure, the decision making process involves the solution of a multicriteria problem formulated in the criteria space. The solution encountered at the upper level originates a lower level parametric optimization problem with separable structure that can be treated by standard coordination-decomposition techniques. The convergence of the overall procedure is ensured. The paper includes an application of the approach proposed for the control of dynamic systems with linear quadratic structure. © 1998 John Wiley & Sons, Ltd.     

Experimental consideration of preference in decision making under certainty

This paper describes an experiment in decision making under certainty with multiple, conflicting objectives and continuous decision variables. Two techniques for analysing such problems are considered: one taken from the paradigm of multicriteria decision making (MCDM), a non-directed approach called the NAIVE technique, and one from the paradigm of multiattribute decision analysis (D/A), the SMART technique. While the two techniques seek and are throught to arrive at the same end—a solution which is in some sense optimal for the decision maker (DM)—the former approach implicitly incorporates DM preferences while the latter approach considers preferences explicitly. The setting is a laboratory study using a sample of university students on a three-criteria problem which is designed to study the extent to which value functions implied/assessed by the techniques are consistent with DMs' holistic ranking of alternatives. Results show that (1) the two techniques of interest show significantly better rank order correlation with holistic judgement compared with other techniques, (2) DMs prefer the non-directed MCDM approach and (3) subjects break down into two groups: those that use assessable value functions when ranking and those that do not. This implies that for small-dimensioned problems DMs may first need to be classified as to the assessability of their value functions before a solution method is chosen.     

Relating reference points and weights in MOLP

A frequent problem for decision makers (DMs) analysing decisions involving multiple objectives is the identification and selection of the most preferred option from the set of non‐dominated solutions. Two techniques, weighted sum optimization and reference point optimization, have been developed to address this problem for multiobjective linear programming problems (MOLP). In this paper, we examine the relationship between these two techniques. We demonstrate that the values of the dual variables associate with auxiliary constraints of the reference point technique are equal to the weight values used to compute the same non‐dominated solution via the weighted sum technique. This insight will enable the development of new interactive solution procedures for MOLPs which allow the DM to readily switch from one method to the other during the search for the most preferred non‐dominated solution. The advantages of the approach are discussed in the paper. Copyright © 1999 John Wiley & Sons, Ltd.     

Dynamic multi-criteria decision making

Most medium-and long-term decision making in industry and government can be viewed as dynamic multi-criteria decision making (MCDM), in which the decision makers are free to alter the emphasis placed on each objective in the light of developing circumstances. In this paper the problem of time-dependent weights in MCDM is discussed and an analysis of empirical data associated with dynamic decision making is presented.     

Integration of Analytic Hierarchy Process with Regression Analysis to Identify Attractive Locations for Market Expansion

Selection of new geographies in which to expand is a key decision for businesses aspiring to go beyond the opportunities in the existing markets. The conventional approaches of market selection can only provide a set of systematic steps for problem solving without considering the relationships between the decision factors. Decision models based on statistical techniques are able to examine the relationship between decision factors but are unable to effectively assist decision makers in identifying the most promising market, particularly in terms of prioritizing across decision factors. Analytic Hierarchy Process (AHP) is a commonly used approach for choosing alternatives by prioritizing across multiple decision factors. The typical AHP modelling requires knowledge of criteria and/or alternatives along with their relative weights, generally elicited from field experts. Quite often, firms encounter situations where decision makers are aware of only the overall objective and a set of earmarked geographies for setting up market locations while being relatively unaware of decision criteria and relative weights. This precludes using AHP to identify promising market locations. This paper conceptualizes a market selection decision model that integrates AHP with statistical modelling techniques to identify the attractive market locations for the purpose of expansion. The model first uses principal component analysis and multiple regression to determine significant decision criteria and their weights. Thereafter, it applies AHP to prioritize the market locations across the decision criteria. This integrative approach is illustrated for identifying the attractive locations in rural markets for a steel firm in India. The major advantage of this approach is that unlike the existing models, it works in situations when firms have not enough knowledge about factors for evaluating alternative market locations. Another key advantage of the proposed model is that of economizing resources for data collection on variables representing decision factors. Copyright © 2012 John Wiley & Sons, Ltd.     

Sequential decision making: An aggregate scheduling methodology

Recent studies of sequential decision making performance have utilized optimal dynamic programming solutions as the criteria for evaluating the quality of human decisions. The difficulties incumbent in increasing the dimensionality of dynamic programming formulations effectively prohibit their extension beyond the case of a single decision variable. In the following article an alternative optimization formulation for a two-decision-variable case is presented, followed by the development of a corresponding one-decision-variable problem. In addition, related methodological problems limiting the comparability of results among previous studies are presented. It is suggested that the proposed problem formulation and its accompanying interpretation for the decision maker largely eliminate these previous methodological problems. Furthermore, the problem formulation permits quantification of the relative weights that should optimally be placed on future decision periods in the multiple-stage decision problem.     

An Approach to Multi‐Criteria Decision Problems Under Severe Uncertainty

Solving complex decision problems is a demanding task; it requires determining and evaluating the consequences of decision alternatives. To this end, uncertain factors that can only partly be influenced by the decision makers, and their interdependencies need to be considered. Scenarios focus on this part of the decision problem; they enable a systematic exploration of a multitude of possible future developments that are relevant for the decision including external events and decisions made. Scenarios are particularly useful when the problem is pervaded by severe uncertainties that cannot be quantified. For the evaluation of alternatives, multiple objectives and the potentially diverging preferences of the involved actors need to be respected. Multi‐criteria decision analysis aims at structuring the problem, evaluating the alternatives and supporting decision makers pursuing multiple goals. We propose an approach integrating scenarios and multi‐criteria decision analysis that focuses on the robustness of alternatives in complex, dynamic, uncertain and time‐bound situations. In this integrated framework, the scenarios provide the basis for evaluating a set of alternatives. Ideally, the set of scenarios considered captures all possible future developments. To appropriately explore this set, formal or analytical approaches to scenario construction generate a large number of scenarios. This challenges the decision makers' information‐processing capacity. To support them in managing the richness of information, a two‐fold approach that uses selection and aggregation is presented. By using a selection method, the scenarios that are deemed most relevant are identified, and their evaluations are presented in detail to decision makers. This approach is complemented by an aggregation of scenario evaluations on the basis of the decision makers' preferences. We present two approaches to facilitate the preference elicitation process. Copyright © 2013 John Wiley & Sons, Ltd.     

Rank disagreement: A comparison of multi-criteria methodologies

A number of multi-criteria decision support techniques have emerged in recent years that use varying computational approaches to arrive at the most desirable solution and thereby ‘recommend’ a course of action. Decision makers who use the results of this analytic work should be assured that the computational schemes used by their supporting analysts or decision support software produce the appropriate solutions. We conducted a series of simulation experiments that compared the top-ranked options resulting from the computational algorithms that support Multi-Attribute Value Theory (MAVT) and three methods that are reported in the literature that allow rank reversals, the change in rank order of two options when an unrelated option is added or deleted from the analysis: the Analytical Hierarchy Process (AHP), Percentaging and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). We also included a Fuzzy algorithm proposed by Yager to gauge its consistency with the other algorithms, even though it is not subject to rank reversals. These experiments demonstrated that the MAVT and AHP techniques, when provided with the same decision outcome data, very often identify the same alternative as ‘best’. The other techniques are noticeably less consistent with MAVT, the Fuzzy algorithm being the least consistent. The situations under which the most frequent and significant differences occurred were dependent upon the method. The results of our experiments indicate that other issues (e.g. the processes used for problem structuring and the elicitation of value weights) are likely to be of greater significance to problem outcome (based on our experience) than the choice between the computational algorithms of MAVT and AHP. The results cause us to be concerned about the use of the other methods.     

Generating consensus priority interval vectors for group decision‐making in the AHP

Many practical and important decision‐making problems are complicated by at least two factors: (1) the qualitative/subjective nature of some criteria often results in uncertainty in the individual ratings; and (2) group decision‐making is involved and some means of aggregating individual ratings is required. Traditionally, both individual and group priorities have been represented as point estimates, but this approach presents severe limitations for accommodating imprecision in the decision‐making process. This paper examines the group decision‐making problem in the context where priorities are represented as numeric intervals. A set of techniques that could be used at some of the phases of an analytic hierarchy process (AHP)‐based group decision‐making process, which has the objective of generating a ‘consensus’ priority that represents the group's opinion with regards to the relative importance of a set of N objects (e.g. criteria, alternatives), is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

R&D Project Selection: A Decision Process Approach

The fundamental decision problem of an R&D firm is to select projects in which to invest. Most reported models dealing with this subject use sophisticated mathematical models maximizing specific attributes of the projects without dealing with the underlying motivation of the decision maker. This paper summarizes a successful application of a decision-making process involving multicriteria in the selection of R&D projects in the Ecogen Israel Partnership. We emphasize the structure of the decision problem, with the main goal of helping the decision maker to better understand the nature of his problem. We systematically generate the objective hierarchy of the decision maker, including his main criteria, subcriteria attributes and alternatives. The ‘best’ alternative can then be found using most interactive procedures found in the literature. As the decision maker is totally involved in the entire decision-making process he is better able to understand his problem and preferences.     

Decision making in a dynamic situation: The effect of false alarms and time pressure

An experiment was conducted to investigate the effect of a priori probability of false alarms and time pressure on decision-making behaviour in a dynamic task environment. In order to assess whether strategy selection in a dynamic task environment would be adaptive, we modelled the task mathematically, and compared actual decision strategies to the optimal ones. In addition to the selected strategy, we also studied decision-making behaviour at a lower operational level, reflecting the amount of effort subjects are willing to spend on the decision process. Subjects were required to monitor the fitness level of a simulated athlete, who was running a race, and had to provide treatments whenever the athlete's fitness level suggested a real physiological problem. When a decline of the athlete's fitness was caused by a false alarm, a spontaneous recovery would occur after some time, without any need for intervention. Time pressure was manipulated by the rate at which the athlete's fitness level declined. Overall, subjects did not select the most efficient strategy: they dominantly selected information before applying an action, even though it would have been more profitable, and less effortful, just to apply actions. At the operational level, subjects appeared to invest less effort when the probability of false alarms increased and to invest more effort when time pressure increased. However, in contrast to the outcomes of our mathematical model, subjects adjusted the amount of intervention to the a priori probability of false alarms and not to time pressure. Together, the results indicate that the selection of a decision strategy in a dynamic task is less adaptive then is generally concluded from studies with static tasks.     

动态重复决策中先前结果对风险偏好的影响

在没有轮次限制的轮盘赌任务中考察了先前一轮及多轮的决策结果对后续决策风险偏好的影响模式, 结果表明：(1)无论盈亏, 前一轮获益或损失的程度越大后一轮的风险偏好越大; (2)先前获益后, 接下来的下注投入的金额小于先前一轮的获益金额, 先前损失后, 接下来的下注的潜在获益金额大于先前一轮的损失金额。实验结果定量地验证和拓展了私房钱效应(house money effect)和保本效应(break even effect), 在此基础上归纳出了动态重复决策中“决策前景与先前结果合并后规避损失”的决策标准, 即当决策情景具有重复性且可以自由制定决策方案时, 决策的标准是使得先前一次的获益(或损失)与下一次决策的潜在损失(或获益)合并后可以规避损失。实验结果还表明决策者仅合并最近一次的先前结果而不会合并先前连续获益或损失的结果。     

Simplified approaches for multicriteria decision making under uncertainty

The problem of uncertainty in the outcome of decisions has tended to be glossed over by many MCDM methods, with the exception of multiattribute utility theory (MAUT). MAUT does, however, require quite complicated preference elicitations and knowledge of the full multivariate distribution of outcomes. Results from a series of simulation studies indicate that the preference orderings of MAUT are only minimally changed when using a simple additive aggregation of marginal utilities, especially in relation to the natural imprecisions inherent in preference elicitation. It is shown in the simulations that by far the most critical aspect of multicriteria decision analysis under uncertainty is not the form of aggregation, but the correct elicitation of marginal utilities which properly represent decision maker preferences over gambles. We relate the results obtained here to other results on the approximation of distributions by three- or five-point discrete distributions, and suggest that the use of deterministic MCDM methods of any form (not necessarily value function techniques), applied to an extended formulation in which each criterion measure is repeated for three or five ‘scenarios’, can be justified.     

Variation of Preference Inconsistency When Applying Ratio and Interval Scale Pairwise Comparisons

Several studies on numerical rating in discrete choice problems address the tendency of inconsistencies in decision makers' measured preferences. This is partly due to true inconsistencies in preferences or the decision makers' uncertainty on what he or she really wants. This uncertainty may be reflected in the elicited preferences in different ways depending on the questions asked and methods used in deriving the preferences for alternatives. Some part of the inconsistency is due to only having a discrete set of possible judgments. This study examined the variation of preference inconsistency when applying different pairwise preference elicitation techniques in a five‐item discrete choice problem. The study data comprised preferences of five career alternatives elicited applying interval scale and numerically and verbally anchored ratio scale pairwise comparisons. Statistical regression technique was used to analyse the differences of inconsistencies between the tested methods. The resulting relative residual variances showed that the interval ratio scale comparison technique provided the greatest variation of inconsistencies between respondents, thus being the most sensitive to inconsistency in preferences. The numeric ratio scale comparison gave the most uniform preferences between the respondents. The verbal ratio scale comparison performed between the latter two when relative residual variances were considered. However, the verbal ratio scale comparison had weaker ability to differentiate the alternatives. The results indicated that the decision recommendation may not be sensitive to the selection between these preference elicitation methods in this kind of five‐item discrete choice problem. The numeric ratio scale comparison technique seemed to be the most suitable method to reveal the decision makers' true preferences. However, to confirm this result, more studying will be needed, with an attention paid to users' comprehension and learning in the course of the experiment. Copyright © 2013 John Wiley & Sons, Ltd.     

Dealing with Dynamic Decision Problems when Knowledge of the Environment Is Limited: An Approach Based on Goal Systems

We experimentally analyzed decision procedures for dealing with a dynamic decision‐making problem in which only qualitative information about the deterministic dynamics of the environment was available to participants. A participant's task was to maximize long‐term profit in a computer‐simulated monopoly market featuring delays and inertia. The design enabled a goal‐system‐based procedure, whereby a participant could select one or several short‐term variables to be controlled (goal variables) and chose target values (aspiration levels) for each of them over a total of 50 periods. We report results based on a sample of 63 participants on the formation of goal systems and the process of aspiration adaptation. Our main findings are, first, that more frequently selecting goal systems that adequately reflect the causal structure of the underlying model is positively correlated with long‐term profit; second, that goal persistence, a measure of a participant's tendency to stick to the current goal system, is positively correlated with long‐term profit; and third, that aspiration levels tend to be adapted in strong agreement with certain basic principles of a benchmark model of aspiration adaptation. Our study thus suggests and provides empirical foundation for an approach to dealing with complex dynamic decision problems based on neither optimization nor learning. Copyright © 2011 John Wiley & Sons, Ltd.     

Decision theory and artificial intelligence II: The hungry monkey

This paper describes a problem-solving framework In which aspects of mathematical decision theory are incorporated into symbolic problem-solving techniques currently predominant in artificial intelligence. The utility function of decision theory IS used to reveal tradeoffs among competing strategies for achieving various goals, taking into account such factors as reliability, the complexity of steps in the strategy, and the value of the goal. The utility function on strategies can therefore be used as a guide when searching for good strategies. It is also used to formulate solutions to the problems of how to acquire a world model, how much planning effort is worthwhile, and whether verification tests should be performed. These techniques are illustrated by application to the classic monkey and bananas problem.     

Decision support for real-time, dynamic decision-making tasks

By definition, dynamic decision making dictates that multiple and interrelated decisions be made in a continuously changing environment. Such decision making is difficult and often taxes individuals’ cognitive resources. Here I investigated ways in which to support decision making in these environments. I evaluated three forms of decision support: outcome feedback, cognitive feedback, and feedforward that incorporated (to varying degrees) common features of learning theories associated with dynamic tasks. Participants in a laboratory experiment performed a real-time, dynamic decision-making task while receiving one of the different types of decision support. During the first 2 days, individuals received one type of decision support, but on the third day they performed the task without this support. Participants who received feedforward improved their performance considerably and continued to exhibit improved performance even after discontinuation of the decision support on the third day. Neither outcome feedback nor cognitive feedback resulted in improved performance. More research is necessary to conclusively identify the best forms of dynamic decision-making support and their durability when transferred to new tasks.     

MDFT account of decision making under time pressure

In this paper, decision making under time pressure for multiattribute choice alternatives in a risky environment is investigated. A model, multiattribute decision field theory (MDFT), is introduced that describes both the dynamic and the stochastic nature of decision making and accounts for the observed changes in choice probabilities, including preference reversals as a function of time limit. An experiment in which five different time limits were imposed on the decision maker is presented to test the predictions of the model. It is shown that MDFT is able to account for the complex decision behavior observed in the data. Furthermore, MDFT is compared with the predictions of decision field theory (Busemeyer & Townsend, 1993; Roe, Busemeyer, & Townsend, 2001).