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.     

Two new cases of rank reversals when the AHP and some of its additive variants are used that do not occur with the multiplicative AHP

Many researchers have long observed some cases in which certain ranking irregularities can occur when the original analytic hierarchy process (AHP), or some of its variants, are used. This paper presents two new categories of ranking irregularities which defy common intuition. These ranking irregularities occur when one decomposes a decision problem into a set of smaller problems each defined on two alternatives and the same criteria as the original problem. These irregularities are possible when the original AHP, or some of its additive variants, are used. Computational experiments on random test problems and an examination of some real‐life case studies suggest that these ranking irregularities are dramatically likely to occur. This paper also proves that these ranking irregularities are not possible when a multiplicative variant of the AHP is used. Copyright © 2001 John Wiley & Sons, Ltd.     

Time complexity and consistency issues in using the AHP for making group decisions

Two different ways of using the AHP in making group decisions are compared and evaluated. The first method combines different experts’ opinions before applying an eigenvalue method to obtain final weights for decision alternatives. The second, in contrast, derives each expert's rating for the decision alternatives before combining them. Both methods take into account the relative importance of different experts in making decisions. Comparison and evaluation of these two methods are made by using two criteria: time complexity and consistency indices. A numerical example is provided to illustrate the use of these two methods, and results of a mathematical simulation are presented for comparing the time complexity in different-sized problems. © 1998 John Wiley & Sons, Ltd.     

Origins,uses of,and relations between goal programming and data envelopment analysis

Origins and uses of ‘goal programming’ and ‘data envelopment analysis’ (DEA) are identified and discussed. The purpose of this paper is not only to review some of the history of these developments, but also to show some of their uses (e.g. in statistical regression formulations) in order to suggest paths for possible further developments. Turning to how the two types of models relate to each other, the ‘additive model’ of DEA is shown to have the same structure as a goal programming model in which only ‘one‐sided deviations’ are permitted. A way for formally relating the two to each other is then provided. However, the objectives are differently oriented because goal programming is directed to future performances as part of the planning function whereas DEA is directed to evaluating past performances as part of the control function of management. Other possible ways of comparing and combining the two approaches are also noted including statistical regressions that utilize goal programming to ensure that the resulting estimates satisfy the multi‐criteria conditions that are often encountered in managerial applications. Both goal programming and DEA originated in actual applications that were successfully addressed. The research was then generalized and published. This leads to what is referred to as an ‘applications‐driven theory’ strategy for research that is also described in this paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Some results concerning the quality of vertex solutions found by a method for multiple-objective linear programming

The Zionts-Wallenius algorithm for multiple-objective linear programming terminates with an extreme point solution that is locally but not necessary globally optimal. To find the globally optimal solution, a search along the facets of the solution space polyhedron may be required. In this paper we report the results of an experiment to determine how close the local and global optima are. We discuss the concept of closeness and propose one measure. Computer simulation is used to determine, in general, the quality of the solution found by the Zionts-Wallenius method for two types of non-linear utility functions. The merits of a search procedure are discussed in the context of the results.     

An application of visual interactive goal programming: a case in vendor selection decisions

This article presents the vendor selection problem of the hydraulic pump division of a US original equipment manufacturing company. The division wants to identify appropriate vendors and allocate purchase orders among them while minimizing product acquisition costs and maximizing total product quality and delivery reliability. Visual interactive goal programming is used as a multi‐criteria decision analysis tool. Interaction with decision makers during the model building and solution process, and implications are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

An imprecise goal programming approach for modeling design team's preferences in quality function deployment planning process

The Quality Function Deployment (QFD) is an approach that facilitates designing product by analyzing and projecting the Customer's Needs (CNs) in the Engineering Characteristics (ECs) of a product. The aim of QFD planning process is to determine the target levels for ECs of a product that achieve high level of overall customers' satisfaction. However, integrating design team's preferences in this preliminary stage of product design could make the design more realistic and could also avoid unfeasibility in posterior phases of the product development processes. Moreover, this process is performed within an imprecise environment, and more than one factor must be taken into account in determining targets levels of ECs; especially, the limited resources and increased market competition. This paper presents an imprecise goal programming approach to determine the best aspiration levels of ECs in QFD planning process. Based on benchmarking data of ECs, the concept of satisfaction functions will be utilized to integrate explicitly the design team's preferences and incorporate the competitive analysis of target market into the modelling and solution processes. In addition, the relationships linking CNs and ECs and the ECs to each other are integrated by functional relationships. The proposed approach will be illustrated through an example of product development of an emulsification dynamite packing machine. Copyright © 2011 John Wiley & Sons, Ltd.     

A multiple-objective linear programming model for the citrus rootstock selection problem in Florida

Citrus is one of Florida's key agricultural crops, with annual production accounting for over 70% of all U.S. production. During the 1970s and 1980s, citrus blight, tristeza and freezes caused citrus rootstock selection to become a critical issue in Florida, and it remains so today. This paper describes a multiple-objective linear programming model that we have developed for solving the citrus roostock selection problem in Florida. The model has four objective functions. These functions, together with the constraints of the model, capture the main factors that Florida citrus growers use in choosing portfolios of rootstocks for planting in their groves. We tested the usefulness of this model by solving an experimental application for the Fort Pierce area with the interactive STEM algorithm. From our research we conclude that, when properly solved with the aid of STEM, the multiple-objective linear programming model has the potential to serve Florida citrus growers as a useful decision aid in formulating rootstock selection plans. © 1997 John Wiley & Sons, Ltd.     

On the Proper Interpretation and Impact of the AHP Axiom of Independence in Single-Criterion and Multiple-Criteria Problems

Some authors have proposed that the analytic hierarchy process (AHP) axiom of independence be relaxed to accommodate observations drawn from (a) examples of pairwise comparisons of alternatives in clusters in single-criterion AHP problems and (b) examples of problems in which the criteria have the same underlying measurement and both the achievement of the goal and the alternatives are measured objectively. We show that the illustrations given are actually single-criterion problems according to the AHP. Thus the AHP axiom of independence is inapplicable in both situations and therefore not violated. We also consider the consequence of failure to distinguish between a criterion as an attribute of alternatives and cluster of alternatives, the two being different in the hierarchic structure. Finally, we discuss transformable problems, which look like multicriteria problems but are actually single-criterion problems, and how failure to recognize this fact may lead to incorrect syntheses and false conclusions.     

An investigation of the role of scale values in the DS/AHP method of multi‐criteria decision making

DS/AHP is a method of multi‐criteria decision making based on the Dempster–Shafer theory of evidence and the analytic hierarchy process. Central to the utilization of DS/AHP is the composing of preference judgements on identified groups of decision alternatives (DA) across a number of criteria against all the DA present in the problem in question. This paper exposits a series of results whose objectives are to aid in the development of an effective set of preference scale values for use within DS/AHP. These results relate directly to the concomitant level of ignorance (uncertainty) with the judgements made on a single criterion. Two particular directions of investigation are undertaken, firstly in determining the necessary number of scale values available and secondly finding the necessary differences between scale values, dependent on whether an arithmetic or geometric progression is the basis for the scale values. Through an example, the implications and utilization of these results within DS/AHP are illustrated. Copyright © 2003 John Wiley & Sons, Ltd.     

Generating interior search directions for multiobjective linear programming

A new multiobjective linear programming (MOLP) algorithm is presented. The algorithm uses a variant of Karmarkar's interior-point algorithm known as the affine-scaling primal algorithm. Using this single-objective algorithm, interior search directions are generated and used to provide an approximation to the gradient of the (implicitly known) utility function. The approximation is guided by assessing locally relevant preference information for the various interior directions through interaction with a decision maker (DM). The resulting algorithm is an interactive approach that makes its progress towards the solution through the interior of the constraints polytope.     

A cautionary note on the use of probability values to evaluate interobserver agreement

Proposed methods of assessing the statistical significance of interobserver agreements provide erroneous probability values when conducted on serially correlated data. Investigators who wish to evaluate interobserver agreements by means of statistical significance can do so by limiting the analysis to every k(th) interval of data, or by using Markovian techniques which accommodate serial correlations.     

How formulating implementation plans and remembering past actions facilitate the enactment of effortful decisions

Building on prior research studying effortful decision making and enactment processes (Bagozzi, Dholakia, & Basuroy, 2003; BDB), we identify and provide an in‐depth understanding of two specific self‐regulatory strategies: (1) formulating an implementation plan, and (2) remembering past actions, that decision makers can use in facilitating enactment of effortful decisions. The results of three experiments, in which the decision maker's goal and self‐regulatory strategy were manipulated, showed that for goals that decision makers chose volitionally, the motivational effects of both these strategies lay in increasing levels of proximal implementation‐related variables (implementation intentions, plan completeness, plan enactment, and goal realization) significantly. In contrast, for goals that were assigned to participants, these strategies' motivational effects additionally extended to significantly increasing distal goal‐related variables (goal desire, goal intentions, perceived self‐efficacy, and implementation desires). The theoretical implications of our findings are discussed, and future research opportunities are explored. Copyright © 2007 John Wiley & Sons, Ltd.     

A Survey on Development and Applications of the Multi‐criteria Decision Making Method MULTIMOORA

This paper focuses on the MULTIMOORA method. Specifically, it discusses its development as well as extensions alongside with an overview of their applications. Indeed, the MULTIMOORA is a relatively new multi‐criteria decision making method consisting of the three parts. Therefore, it is specific with peculiarities of both complete and partial aggregation techniques. The MULTIMOORA method consists of the three parts, namely the Ratio System, the Reference Point, and the Full Multiplicative Form. The paper discussed the extensions of MULTIMOORA into the fuzzy environment and group decision making. The carried out survey identified the two major areas of application of MOORA and MULTIMOORA, namely engineering decision support for technological development and economic researches. The economic researches can further be classified into those related to micro‐level or macro‐level analyses. Copyright © 2013 John Wiley & Sons, Ltd.     

When goals loom darker: Goal ambivalence moderates the effect of goal proximity on goal-related motivation

This research extends previous work on the self-regulation of goal striving as well as effects of temporal and psychological distance on motivation. Borrowing from classic work on goal gradients and approach-avoidance conflicts, we predicted that the experience of ambivalence toward a personal goal moderates the extent to which feeling or being close to goal attainment affects motivation, such that greater proximity to the goal has a negative effect on motivation at higher levels of experienced goal ambivalence. We find evidence for the hypothesized effect across three studies examining different goals (pursuing a degree, running a half-marathon) with varying operationalizations of goal proximity (self-reported, manipulated, temporal) and motivation (goal commitment, intention strength). These results validate that classic concepts of motivation science such as goal gradients and approach-avoidance conflict are both relevant and applicable to the everyday pursuit of self-set personal goals.     

Determining the implementation order of a general plan by using a multicriteria method

We describe a real-life application of a new multicriteria method in the context of assisting the decision-making for a general plan in the municipality of Kirkkonummi in Uusimaa, Finland. At the time our group started working on the problem, a proposal for an overall plan had already been completed, but the order in which different regional parts of the plan should be implemented needed to be considered based on the environmental impact assessment (EIA) procedure. The EIA procedure generated a large amount of data about the different impacts of the alternatives. For this group decision making problem we developed the SMAA-3 decision support method which does not require any explicit preference information from the decision makers during the procedure. The uncertainty of the basic data is modelled using ELECTRE III-type pseudo-criteria with preference and indifference thresholds. © 1998 John Wiley & Sons, Ltd.     

A time–cost optimization of the national postal distribution network

The postal distribution network in the Czech Republic consists actually of 69 local transit centres (according to the administrative division of the Czech Republic). Each of them operates the post offices in the given region. Some of the important local transit centres can be selected as sorting centres—transhipment points for postal consignments. The aim of this paper is to present a bicriterial optimization model for the selection of the subset of transhipment points from the set of transit centres and choosing their appropriate equipment, such as sorting machines. Another important output of the model is the assignment of the transit centres to the sorting centres. There are two basic optimization criteria defined in this model: minimization of the sum of investment and operational costs connected with building and operating of the sorting centres and the maximization of the percentage of postal consignments delivered to the appropriate post office in the desired time (next day). The proposed model contains several thousands of zero‐one variables and constraints. The model has been verified, and the results accepted. Copyright © 1999 John Wiley & Sons, Ltd.     

The Power of Social Influence on Estimation Accuracy

Research shows that crowds can provide more accurate estimates of uncertain quantities than individuals (Surowiecki, 2004). But little is known about how to organize crowd members to maximize accuracy. When should crowd members work independently, and when should they work collaboratively? We examined the effects of social influence on estimation accuracy, consensus, and confidence. Participants first made independent estimates of uncertain quantities, such as the percentage of U.S. deaths due to heart attacks or the height of the tallest building. Then, in some conditions, they interacted with others online. After the discussion, they made second independent estimates. Social interaction improved accuracy. Despite well‐known problems with groups, such as herding and free riding, discussion resulted in more accurate estimates and greater consensus relative to independent estimates. We offer a simple model that describes the process by which group discussion improves the estimates of uncertain quantities. Copyright © 2014 John Wiley & Sons, Ltd.