Scale sensitivity in the multiplicative AHP and SMART

We consider first a variant of the analytic hierarchy process (AHP) with a one-parametric class of geometric scales to quantify human comparative judgement and with a multiplicative structure: logarithmic regression to calculate the impact scores of the alternatives at the first evaluation level and a geometric-mean aggregation rule to calculate the final scores at the second level. We demonstrate that the rank order of the impact scores and final scores is scale-independent. Finally we show that the multiplicative AHP is an exponential version of the simple multi-attribute rating technique (SMART). In fact, the multiplicative AHP is concerned with ratios of intervals on the dimension of desirability, whereas SMART analyses differences in the corresponding orders of magnitude.     

Linking Disjoint Supermatrices and Criteria Clusters

An axiom of the Analytic Network Process (ANP) requires the elements being considered to be strongly connected in order to obtain a meaningful priority vector. A simple example demonstrates the issues that can arise when a decision contains disjoint clusters within the Supermatrix. From the example it can be observed that the necessary information to complete additional linking pin comparisons would have already been collected; and by performing linking pin comparisons a decision maker can convert a disjoint Supermatrix into a strongly connected Supermatrix. The linking process is summarized in five steps and provided in the general form. This linking comparison methodology exploits the fundamental advantages of pairwise comparisons and can also be used to weight the criteria clusters within a decision network. Linking pin comparisons performed at the level of a criterion of a single alternative with respect to another criterion of that same alternative can be used to obtain the criteria cluster weights. Linking pin comparisons at this level can reduce the decision maker's cognitive burden in comparison to totality comparisons. The ability to strongly connect an otherwise disjoint Supermatrix and reduce the decision maker's cognitive burden demonstrates the usefulness of linking pin comparisons in ANP decision models. Copyright © 2016 John Wiley & Sons, Ltd.     

A Psychometric Analysis of the “Divide and Conquer” Principle in Multicriteria Decision Making

The principle of “Divide and Conquer” (DAC) suggests that: (1) complex decision problems should be decomposed into smaller, more manageable parts and (2) these smaller parts should be logically aggregated to derive an overall value for each alternative. Typically, decompositional procedures have been compared to holistic evaluations that require decision makers to simultaneously consider all of the relevant attributes in the evaluation of the objects under consideration. These comparisons between decompositional and holistic judgments have primarily used a variant of Multiattribute Utility Theory (MAUT).We presented a general experimental framework that allows for a more extensive assessment of the DAC principle, as well as the effects of decision complexity on both holistic and decompositional procedures. We illustrate this approach with a study that uses the Simple Multiattribute Rating Technique with Swing Weights (SMARTS; Edwards & Barron, 1994) and the Analytic Hierarchy Process (AHP; Saaty, 1980). We report data comparing the convergent validity (e.g the agreement between decompositional and holistic strategies) and the temporal stability for decompositional and holistic judgments on a variety of dependent measures. Decision complexity did not significantly affect the correspondence between decompositional and holistic judgments for both SMARTS and AHP judgments. Results from an ordinal measure of temporal stability indicated the DAC principle was violated for the AHP judgments. For a linear measure of temporal stability, trends in the data indicated that the predicted effects of decision complexity on the DAC principle was violated for the SMARTS judgments.     

An empirical comparison of three variants of the AHP and two variants of conjoint analysis

This paper provides an empirical comparison of two methods of attribute valuation: the analytic hierarchy process (AHP) and conjoint analysis. Variants within each approach are also examined. The results of two empirical studies indicate that the methods differ in their predictive and convergent validity. Within the AHP methods no significant difference in predictive validity was found. Within the conjoint methods, the ranking method significantly outperformed the rating method. The difference in predictive validity between the AHP and conjoint methods was significant in the second study but not in the first study, suggesting superior performance of the AHP over conjoint analysis in complex problems. Copyright© 1998 John Wiley & Sons, Ltd.     

Stochastic pairwise comparative judgements and direct ratings of alternatives in the REMBRANDT system

The REMBRANDT system for multicriteria decision analysis consists of both the multiplicative variant of the AHP (which employs a method of pairwise comparative judgements by a decision maker to arrive at final impact scores for the alternatives under consideration) and SMART, the simple multiattribute rating technique (which utilizes direct rating of alternatives to achieve final impact scores). This paper examines the effect of imprecision or uncertainty in the decision maker's pairwise judgements or ratings of alternatives by expressing each pairwise judgement or rating as a probability distribution, and the structure of REMBRANDT's component models is exploited to derive interval judgements or interval ratings of the alternatives’ final impact scores. These interval judgements or interval ratings can be used to determine the probability of rank reversal amongst alternatives, i.e. to assess the stability of the final impact score vector. © 1998 John Wiley & Sons, Ltd.     

Power Relations and Group Aggregation in the Multiplicative AHP and SMART

The relative power of the members in a group of decision makers can be incorporated in the multiplicative AHP via power coefficients in the logarithmic least squares whereby we analyse the pairwise comparison matrices. When each decision maker judges every pair of alternatives under each of the criteria, aggregation over the criteria and over the decision makers proceeds via a sequence of geometric-mean calculations which can be carried out in any order, at least with predetermined criterion weights and power coefficients. Hence, since we preserve the rank order of the alternatives, we avoid a deficiency of the original AHP. We also consider SMART, an additive method which is logarithmically related to the multiplicative AHP so that power relations can easily be incorporated in it. Finally, in order to illustrate the proposed model, we analyse a generalized version of the well-known example of Belton and Gear as well as the power relations between member countries of the European Community. © 1997 by John Wiley & Sons, Ltd. J. Multi-Crit. Decis. Anal. 6 : 155–165 (1997) No. of Figures: 0. No. of Tables: 6. No. of References: 23.     

A multicriteria framework for inventory classification and control with application to intermittent demand

Several papers have studied inventory classification in order to group items with a view to facilitating their management. The generated classes are then coupled with the specific reorder policies composing the overall inventory control system. However, the effectiveness of inventory classification and control system is strictly interrelated. That is to say, different classification approaches could show different performance if applied to a different set of reorder policies, and vice versa. Furthermore, when the cost structure is subjected to uncertainty, a pure cost‐based analysis of the inventory control system could be corrupted. This paper presents a multicriteria framework for the concurrent selection of the item classification approach and the inventory control system through a discrete‐event simulation approach. The key performance indicators provided by the simulator (i.e., average holding value, average number of backorders, and average number of emitted orders) are indicative of the multidimensional effectiveness of the adopted inventory control system when coupled with a specific classification approach. By this way, a multicriteria problem arises, where the alternatives are given by exhaustively coupling the item classes, which are generated by different classification approaches, with the reorder policies composing the inventory system. An analytical hierarchy process is then used for selecting the best alternative, as well as for evaluating the effect of the weights assigned to the key performance indicators through a sensitivity analysis. This approach has been validated in a real case study with a company operating in the field of electrical resistor manufacturing, with a view of facilitating the management of items showing intermittent demand.     

Determining Decision Values of Context Awareness in Ubiquitous Computing Environments

Research on context‐aware computing has been focusing on the technology aspect of context acquisition and interpretation of users' surrounding environment or physical context. There is no operational mechanism for integrating context awareness that is driven by user context such as users' ongoing activities and tasks. Although the necessity of integration of sensed context data with users' intent of conduct has been recognized by many researchers, it has never been empirically investigated. Using Analytic Hierarchy Process, we propose an integrated and comprehensive approach that takes into consideration both user and physical context in defining overall context awareness value. The approach is tested using secondary data of user activities in various situations and surrounding environment scenarios. The results suggest several preliminary guidelines for determining representative measures of user and physical context approaches in the design and evaluation of context‐aware systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Maintenance strategy selection with risky evaluations using RAHP

In recent years, maintenance, especially its preventive type, has been seen as an effective and considerable factor in improving the functions of machines. Maintenance plays a vital role in organizations by keeping and increasing the reliability, accessibility, the quality of products, risk mitigation, return improvement, and safety. An effective maintenance programme can be realized by implementing a proper maintenance strategy. Therefore, maintenance and its strategies have a special status in industries. However, selecting a proper maintenance strategy has always been a complex process because maintenance is a nonrepetitive task. Likewise, the lack of failure records and constant changes in the conditions of machines makes it further complicated. Hence, the decision‐making also depends on experts' opinions and because some kind of risk and uncertainty are always there in experts evaluations, the reliability of evaluations is questionable. The present study was aimed to develop a risk‐based model grounded on the analytical hierarchical process, namely, RAHP, to meet this need of maintenance. A case study from a steel rolling company was considered to evaluate the effectiveness of this model.