Antti Punkka

Rank inclusion in criteria hierarchies

This paper presents a method called Rank Inclusion in Criteria Hierarchies (RICH) for the analysis of incomplete preference information in hierarchical weighting models. In RICH, the decision maker is allowed to specify subsets of attributes which contain the most important attribute or, more generally, to associate a set of rankings with a given set of attributes. Such preference statements lead to possibly non-convex sets of feasible attribute weights, allowing decision recommendations to be obtained through the computation of dominance relations and decision rules. An illustrative example on the selection of a subcontractor is presented, and the computational properties of RICH are considered.

Preference Programming with incomplete ordinal information

This paper extends possibilities for analyzing incomplete ordinal information about the parameters of an additive value function. Such information is modeled through preference statements which associate sets of alternatives or attributes with corresponding sets of rankings. These preference statements can be particularly helpful in developing a joint preference representation for a group of decision-makers who may find difficulties in agreeing on numerical parameter values. Because these statements can lead to a non-convex set of feasible parameters, a mixed integer linear formulation is developed to establish a linear model for the computation of decision recommendations. This makes it possible to complete incomplete ordinal information with other forms of incomplete information.

Baseline value specification and sensitivity analysis in multiattribute project portfolio selection

A key issue in applying multi-attribute project portfolio models is specifying the baseline value – a parameter which defines how valuable not implementing a project is relative to the range of possible project values. In this paper we present novel baseline value specification techniques which admit incomplete preference statements and, unlike existing techniques, make it possible to model problems where the decision maker would prefer to implement a project with the least preferred performance level in each attribute. Furthermore, we develop computational methods for identifying the optimal portfolios and the value-to-cost -based project rankings for all baseline values. We also show how these results can be used to (i) analyze how sensitive project and portfolio decision recommendations are to variations in the baseline value and (ii) provide project decision recommendations in a situation where only incomplete information about the baseline value is available.

Scale Dependence and Ranking Intervals in Additive Value Models under Incomplete Preference Information

A multiattribute additive value function that has been built from a complete specification of the decision makers (DMs) preferences gives scale-independent decision recommendations, which do not depend on how the value function is normalized. In this paper, we show that if the preference specification is incomplete, many widely employed decision rules for comparing alternatives give scale-dependent decision recommendations in which the relative ranking of alternatives depends not only on the DMs preferences but also on the normalization of the value function. But because normalization does not involve preference statements, the recommendations should be scale independent so that they do not depend on the chosen normalization. To provide such recommendations, we propose ranking intervals , which show how a given alternative compares with all other alternatives for all value functions that are consistent with the stated preference information. These intervals can be computed from mixed integer linear optimization problems that are constrained by inequalities implied by the DMs preference statements. We illustrate the use of ranking intervals by analyzing university rankings and discuss their uses in project portfolio selection.