1 Copyright © 2005 ASME Proceedings of IDETC/CIE 2005 ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference September 24-28, 2005, Long Beach, California, USA DETC2005-84764 PREFERENCE CONSISTENCY IN MULTIATTRIBUTE DECISION MAKING Michael Kulok University at Buffalo Department of Mechanical and Aerospace Engineering Graduate Research Assistant kulok@gmx.net Kemper Lewis University at Buffalo Department of Mechanical and Aerospace Engineering Associate Professor Corresponding Author: kelewis@eng.buffalo.edu Tel: (716) 645-2593 x2232 Fax: (716) 645-3668 ABSTRACT A number of approaches for multiattribute selection decisions exist, each with certain advantages and disadvantages. One method that has recently been developed, called the Hypothetical Equivalents and Inequivalents Method (HEIM) supports a decision maker (DM) by implicitly determining the importances a DM places on attributes using a series of simple preference statements. In this and other multiattribute selection methods, establishing consistent preferences is critical in order for a DM to be confident in their decision and its validity. In this paper a general consistency check denoted as the Preference Consistency Check (PCC) is presented that ensures a consistent preference structure for a given DM. The PCC is demonstrated as part of the HEIM method, but is generalizable to any cardinal or ordinal preference structures. These structures are important in making selection decisions in engineering design including selecting design concepts, materials, manufacturing processes, and configurations, among others. The effectiveness of the method is demonstrated and the need for consistent preferences is illustrated using a product selection case study where the decision maker expresses inconsistent preferences. 1. INTRODUCTION There are typically tradeoffs in decision making. Product design requires making a series of tradeoff decisions, including the rigorous evaluation and comparison of design alternatives using multiple, conflicting design criteria or attributes. We can be certain that no one alternative will be best in every attribute. Therefore, how to make the “best” decision when choosing from among a set of alternatives in a design process has been a common problem in research and application in product design and development. While in conceptual design, the objective may be to identify a set of promising concepts, the discussion and context of this work focuses on the decisions in design where a single concept must be selected. A number of methods have been developed to support this type of decision by capturing and quantifying decision maker preferences, such as the Analytical Hierarchy Process [1], Utility Theory [2], Decision-Based Design [3], and Conjoint Analysis [4]. In general, the multiattribute decision problem can be formulated as follows: Choose an alternative i, Maximize ∑ = = n i ij i a w j V 1 ) ( (1) Subject to 1 1 = ∑ = n i i w where V(j) is the value function for alternative j, w i is the weight for attribute i, and a ij is the normalized rating of attribute i for alternative j. While the L 1 -norm aggregation function is shown in Eqn. (1), other forms of the aggregation function have also been used [5], including the L 2 -norm and a parameterized family of aggregations, P s [6]. There are many ways to implement and solve this formulation. Most methods focus on formulating the attribute weights, w i and/or the alternative scores, a ij , indirectly or directly from the decision maker’s preferences. In new product development, a common challenge in a design process is how to capture the preferences of the end-users while also reflecting the interests of the designer(s) and producer(s). Typically, preferences of end- users are multidimensional and multiattribute in nature. If companies fail to satisfy the preferences of the end-user, the product’s potential in the marketplace will be severely limited. In this paper, we focus on the soundness and consistency of the process of making these decisions. According to Coombs’s condition, when six alternatives are ranked using multiple attributes, the process used to make the decision influences the