Ahti Salo

On the measurement of preferences in the analytic hierarchy process

In this paper we apply multiattribute value theory as a framework for examining the use of pairwise comparisons in the analytic hierarchy process (AHP). On one hand our analysis indicates that pairwise comparisons should be understood in terms of preference differences between pairs of alternatives. On the other hand it points out undesirable effects caused by the upper bound and the discretization of any given ratio scale. Both these observations apply equally well to the SMART procedure which also uses estimates of weight ratios. Furthermore, we demonstrate that the AHP can be modified so as to produce results similar to those of multiattribute value measurement; we also propose new balanced scales to improve the sensitivity of the AHP ratio scales. Finally we show that the so-called supermatrix technique does not eliminate the rank reversal phenomenon which can be attributed to the normalizations in the AHP.

Preference programming through approximate ratio comparisons

Abstract In the context of hierarchical weighting, this paper operationalizes interval judgments which allow the decision maker to enter ambiguous preference statements by indicating the relative importance of factors as intervals of values on a ratio scale. Through such judgments the decision maker can capture the subjective uncertainty in his preferences and thus avoid the often cumbersome elicitation of exact ratio estimates. After each new statement the interval judgments are synthesized into dominance relations on the alternatives by solving a series of linear programming problems. This leads to an interactive process of preference programming which provides more detailed results as the decision maker gradually enters a more specific preference description. Moreover, the overall effort of preference elicitation is smaller than in the analytic hierarchy process because the most preferred alternative can usually be identified before all possible comparisons between pairs of factors have been completed.

Preference assessment by imprecise ratio statements

The PAIRS method developed in this paper introduces imprecise preference statements into value trees. The assessment of attribute weights in PAIRS extends the well known SMART technique so that in addition to exact statements the decision maker can enter interval judgments which indicate ranges for the relative importance of the attributes. The interval judgments and the possibly range-valued information about the outcomes of the alternatives are processed with linear programming into value intervals and dominance relations. As the decision maker refines the description of his preferences, either by entering new statements or by tightening his earlier judgments, these results become more detailed and convey more information about which alternatives are preferred. Throughout the interactive refinement process PAIRS supports the decision maker by deriving and displaying the consequences of his earlier judgments.

Preference Programming for Robust Portfolio Modeling and Project Selection

In decision analysis, difficulties of obtaining complete information about model parameters make it advisable to seek robust solutions that perform reasonably well across the full range of feasible parameter values. In this paper, we develop the Robust Portfolio Modeling (RPM) methodology which extends Preference Programming methods into portfolio problems where a subset of project proposals are funded in view of multiple evaluation criteria. We also develop an algorithm for computing all non-dominated portfolios, subject to incomplete information about criterion weights and project-specific performance levels. Based on these portfolios, we propose a project-level index to convey (i) which projects are robust choices (in the sense that they would be recommended even if further information were to be obtained) and (ii) how continued activities in preference elicitation should be focused. The RPM methodology is illustrated with an application using real data on road pavement projects.

Preference ratios in multiattribute evaluation (PRIME)-elicitation and decision procedures under incomplete information

This paper presents the preference ratios in multiattribute evaluation (PRIME) method which supports the analysis of incomplete information in multiattribute weighting models. In PRIME, preference elicitation and synthesis is based on 1) the conversion of possibly imprecise ratio judgments into an imprecisely specified preference model, 2) the use of dominance structures and decision rules in deriving decision recommendations, and 3) the sequencing of the elicitation process into a series of elicitation tasks. This process may be continued until the most preferred alternative is identified or, alternatively, stopped with a decision recommendation if the decision maker is prepared to accept the possibility that the value of some other alternative is higher. An extensive simulation study on the computational properties of PRIME is presented. The method is illustrated with a re-analysis of an earlier case study on international oil tanker negotiations.

Forecasting with scenarios

Abstract It is often argued that scenario development is different from forecasting, but the analysis presented here reevaluates how it is converging with contemporary forecasting practice. The most common aspects of scenario analysis are discussed, with an emphasis on their support for strategic modelling and in the light of relevant research on human cognition and judgemental forecasting. The paper also offers some practical guidelines and a more integrative perspective on using scenarios to support strategic planning.

Robust portfolio modeling with incomplete cost information and project interdependencies

Robust portfolio modeling (RPM) [Liesio, J., Mild, P., Salo, A., 2007. Preference programming for robust portfolio modeling and project selection. European Journal of Operational Research 181, 1488-1505] supports project portfolio selection in the presence of multiple evaluation criteria and incomplete information. In this paper, we extend RPM to account for project interdependencies, incomplete cost information and variable budget levels. These extensions lead to a multi-objective zero-one linear programming problem with interval-valued objective function coefficients for which all non-dominated solutions are determined by a tailored algorithm. The extended RPM framework permits more comprehensive modeling of portfolio problems and provides support for advanced benefit-cost analyses. It retains the key features of RPM by providing robust project and portfolio recommendations and by identifying projects on which further attention should be focused. The extended framework is illustrated with an example on product release planning.

Decision support by interval SMART/SWING - incorporating imprecision in the SMART and SWING methods

Interval judgments are a way of handling preferential and informational imprecision in multicriteria decision analysis (MCDA). In this article, we study the use of intervals in the simple multiattribute rating technique (SMART) and SWING weighting methods. We generalize the methods by allowing the reference attribute to be any attribute, not just the most or the least important one, and by allowing the decision maker to reply with intervals to the weight ratio questions to account for his/her judgmental imprecision. We also study the practical and procedural implications of using imprecision intervals in these methods. These include, for example, how to select the reference attribute to identify as many dominated alternatives as possible. Based on the results of a simulation study, we suggest guidelines for how to carry out the weighting process in practice. Computer support can be used to make the process visual and interactive. We describe the WINPRE software for interval SMART/SWING, preference assessment by imprecise ratio statements (PAIRS), and preference programming. The use of interval SMART/SWING is illustrated by a job selection example.

An Experiment on the Numerical Modelling of Verbal Ratio Statements

Verbal statements are intuitively attractive for preference elicitation. In the analytic hierarchy process (AHP) the verbal responses to pairwise comparisons of relative importance are converted into real numbers according to the nine-point integer scale. Several alternative scales have been proposed for the conversion, but sufficient empirical evidence has not been produced to support the choice among these scales. We performed a comparative study in which subjects were requested to quantify verbal ratio statements by adjusting the heights of visually displayed bars. Subjects were also asked to employ verbal expressions in pairwise comparisons of areas of figures with different shapes. The principal result of the experiment was that the perceived meaning of the verbal expressions varies from one subject to the next and also depends on the set of elements involved in the comparison. Our results indicate that there are alternative numerical scales which yield more accurate estimates than the usual 1-to-9 scale and reduce the inconsistency of the comparison matrices. Alternative ways of using verbal preference statements are suggested to overcome the difficulties that arise from the context dependence of verbal pairwise comparisons.

Rationales for Government Intervention in the Commercialization of New Technologies

The paper examines rationales relevant to the evolving roles of government intervention and private venture capital industry in the commercialization of new technologies. Specifically, government interventions may aim to mitigate market and systemic failures, eliminate structural rigidities, or respond to anticipatory myopia. Ex ante , constructive, and ex post evaluations are discussed in relation to the possibility that agencies responsible for policy implementation may intervene even in situations in which the benefits of their interventions are not necessarily transparent.