Robustness in the Pareto‐solutions for the multi‐criteria minisum location problem

In this paper, a new trend is introduced into the field of multi‐criteria location problems. We combine the robustness approach using the minmax regret criterion together with Pareto‐optimality. We consider the multi‐criteria squared Euclidean minisum location problem which consists of simultaneously minimizing a number of weighted sum‐distance functions and the set of Pareto‐optimal locations as its solution concept. The Pareto‐optimal solutions for the set of robust locations with respect to the original weighted sum‐distance functions is completely characterized. These Pareto‐optimal solutions have both the properties of stability and non‐domination which are required in robust and multi‐criteria programming. Copyright © 2001 John Wiley & Sons, Ltd.     

A parameter analysis method for the weight‐set to satisfy preference orders of alternatives in additive multi‐criteria value models

In the context of the additive multi‐criteria value model, this paper investigates how the set of criteria weights (weight‐set hereafter) can be determined according to the preference orders of alternatives given by the decision maker. A construction method is proposed for the weight‐set for different intervals of β, where β is a differential amount of value between the preference information on two alternatives. The results of this paper are important for sensitivity analysis in multi‐criteria decision making (MCDM) problems and multi‐criteria group decision analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

Indifference sets of reference points in multi‐objective integer linear programming

Reference point approaches for multi‐objective problems rely on the definition of an achievement scalarizing function that projects reference points onto the non‐dominated solution set. In this paper, we investigate the behaviour of reference points using a Tchebycheff metric‐based scalarizing function in multi‐objective pure integer linear programming (MOILP). Since the non‐dominated solutions are discrete in MOILP, there are multiple reference points that lead to the same solution, i.e. there are indifference sets on the reference point space. We investigate some properties of the reference points in MOILP and also the graphical representation of indifference sets for tri‐objective problems. We further investigate properties of the reference points when additional limitations on the objective function values are introduced. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

Material handling device selection in cellular manufacturing

This paper presents a new multi‐criteria decision model for the material handling device (MHD) selection problem in cellular manufacturing systems. Given a set of manufacturing cells based on several automatic work‐centres, the technique makes it possible to select a particular MHD for each cell in an integrated way, with different constraints being taken into consideration. The approach is based on two different multi‐attribute analyses executed with analytic hierarchy process (AHP) methodology, and a final integer linear programming including important limitations faced by the designer when making MHD investment decisions. An example using real data is provided to illustrate this methodology. Copyright © 2002 John Wiley & Sons, Ltd.     

A Multicriteria Decision‐Making Application to the Conceptual Design of Mechanical Components

Early design is crucial for the success of the final product. In the conceptual design phase, several constraints, criteria, objectives and disciplines have to be considered. To this aim, multidisciplinary optimization has proven effective for the solution of engineering design problems, even in the industrial every‐day practice, to improve and simplify the work of designers in a successful quest of the best compromise solution. In this paper, a multicriteria decision‐making (MCDM)‐based design platform for early optimal design of industrial components is proposed. In a group decision‐making context, the selection of the most suitable component among several possible layouts is performed by means of a group Fuzzy Technique for Order of Preference by Similarity to Ideal Solution approach. Hence, a multi‐objective optimization is performed on the selected component by applying a multi‐objective particle swarm optimization for finding optimal component dimensions. An industrial case study is presented for showing the efficiency of the multicriteria decision‐making‐based design platform, regarding an innovative and low‐cost solution to increase the duration of heel tips in women's shoes. Copyright © 2016 John Wiley & Sons, Ltd.     

Scientific value

Criteria of scientific value are of different kinds. This paper concerns ultimate criteria, i.e. the axiology of science. Most ultimate criteria are multi‐dimensional. This gives rise to an aggregation problem, which cannot be adequately solved with reference to attitudes and behaviour within the scientific community. Therefore, in many cases, there is no fact of the matter as to whether one theory is better than another. This, in turn, creates problems for methodology.     

Reduction of pairwise comparisons in decision making via a duality approach

Although pairwise comparisons have been seen by many as an effective and intuitive way for eliciting qualitative data for multi‐criteria decision making problems, a major drawback is that the number of the required comparisons increases quadratically with the number of the entities to be compared. Thus, often even data for medium size decision problems may be impractical to be elicited via pairwise comparisons. The more the comparisons are, the higher is the likelihood that the decision maker will introduce erroneous data. This paper introduces a dual formulation to a given multi‐criteria decision making problem, which can significantly alleviate the previous problems. Some theoretical results establish that this is possible when the number of alternatives is greater than the number of decision criteria plus one. Copyright © 1999 John Wiley & Sons, Ltd.     

A Recourse Stochastic Goal Programming Approach for the Multi‐objective Stochastic Vehicle Routing Problem

This paper addresses a multi‐objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic nature. In order to build a certainty equivalent program to the multi‐objective stochastic vehicle routing problem, we propose a solution strategy based on a recourse approach, a chance‐constrained approach and a goal‐programming approach. The resulting certainty equivalent program is solved to optimality using CPLEX. Copyright © 2016 John Wiley & Sons, Ltd.     

Distance‐Based Measures of Specialization and Balance in Multi‐Criteria: A DEA‐Integrated Method

Decision makers pursuing several distinct goals may differ in their behaviour. Some try to achieve all goals simultaneously, whereas others concentrate on only certain ones and are therefore specialized. We present a new method of measuring the specialization degree with respect to a given standard balanced relation of the goals. The measurement is integrated into data envelopment analysis (DEA) methodology, uses a non‐compensative distance measure, permits optional convex polyhedral cones as predefined balance sets and guarantees feasible solutions. Geometrically, it is based on the angle between the balance cone and the ray through the point of investigation. The proposed models can be used to support and complement the usual effectiveness and efficiency analysis in multi‐criteria decision analysis and DEA. They are motivated and illustrated by a simple numerical example, compared with an alternative method recently published and applied to real data from the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Triple Bottomline Many‐Objective‐Based Decision Making for a Land Use Management Problem

A land use many‐objective optimization problem for a 1500‐ha farm with 315 paddocks was formulated with 14 objectives (maximizing sawlog production, pulpwood production, milksolids, beef, sheep meat, wool, carbon sequestration, water production, income and Earnings Before Interest and Tax; and minimizing costs, nitrate leaching, phosphorus loss and sedimentation). This was solved using a modified Reference‐point‐based Non‐dominated Sorting Genetic Algorithm II augmented by simulated epigenetic operations. The search space had complex variable interactions and was based on economic data and several interoperating simulation models. The solution was an approximation of a Hyperspace Pareto Frontier (HPF), where each non‐dominated trade‐off point represented a set of land‐use management actions taken within a 10‐year period and their related management options, spanning a planning period of 50 years. A trade‐off analysis was achieved using Hyper‐Radial Visualization (HRV) by collapsing the HPF into a 2‐D visualization capability through an interactive virtual reality (VR)‐based method, thereby facilitating intuitive selection of a sound compromise solution dictated by the decision makers' preferences under uncertainty conditions. Four scenarios of the HRV were considered emphasizing economic, sedimentation and nitrate leaching aspects—giving rise to a triple bottomline (i.e. the economic, environmental and social complex, where the social aspect is represented by the preferences of the various stakeholders). Highlights of the proposed approach are the development of an innovative epigenetics‐based multi‐objective optimizer, uncertainty incorporation in the search space data and decision making on a multi‐dimensional space through a VR‐simulation‐based visual steering process controlled at its core by a multi‐criterion decision making‐based process. This approach has widespread applicability to many other ‘wicked’ societal problem‐solving tasks. Copyright © 2014 John Wiley & Sons, Ltd.     

Gaussian model‐based partitioning using iterated local search

The emergence of Gaussian model‐based partitioning as a viable alternative to K‐means clustering fosters a need for discrete optimization methods that can be efficiently implemented using model‐based criteria. A variety of alternative partitioning criteria have been proposed for more general data conditions that permit elliptical clusters, different spatial orientations for the clusters, and unequal cluster sizes. Unfortunately, many of these partitioning criteria are computationally demanding, which makes the multiple‐restart (multistart) approach commonly used for K‐means partitioning less effective as a heuristic solution strategy. As an alternative, we propose an approach based on iterated local search (ILS), which has proved effective in previous combinatorial data analysis contexts. We compared multistart, ILS and hybrid multistart–ILS procedures for minimizing a very general model‐based criterion that assumes no restrictions on cluster size or within‐group covariance structure. This comparison, which used 23 data sets from the classification literature, revealed that the ILS and hybrid heuristics generally provided better criterion function values than the multistart approach when all three methods were constrained to the same 10‐min time limit. In many instances, these differences in criterion function values reflected profound differences in the partitions obtained.     

Evolution of multi‐criteria analysis: a scientometric analysis

The field of multi‐criteria analysis has known very important developments during the last 20 years, if one considers the very large amount of activities that it has generated and continues to generate (papers in journals, a dedicated journal, books, meetings, applications, …). Even if multi‐criteria analysis has reached some maturity, its future is subject to questions and debate among its researchers: what is the evolution of the field? What is its structure? Is it integrating new topics? In order to answer such questions at least partially, we have studied multi‐criteria analysis literature by means of the method of associated words (scientometric analysis) and the software ‘Leximappe’. All the abstracts of the papers which are relative to multi‐criteria analysis and are included in the bibliographic ABI‐INFORM database from 1985 to 1996 have been analysed. In this paper, we will present some results of this study. Copyright © 1999 John Wiley & Sons, Ltd.     

A real‐world MCDA application: evaluating software

A real‐world multi‐criteria decision aid (MCDA) application on software evaluation is presented in this paper. The decision process concerned a big Italian company faced with the management of a call for tenders for a very important software acquisition. The decision aiding process is extensively presented and discussed, mainly as far as its products are concerned, i.e. –the problem situation; –the problem formulation; –the evaluation model; –the final recommendation. The results of the experience are discussed using the comments of the client of the study. Copyright © 2000 John Wiley & Sons, Ltd.     

A Fuzzy Goal Programming Formulation with Multiple Target Levels

The essential activity of a manager is decision making, which is becoming more and more complex, mainly in the multi‐criteria problems. Multi‐choice goal programming (MCGP) is considered as a robust tool in operational research to solve this type of problem. However, in real world problems, determining precise targets for the goals is a difficult task. To deal with such situation, Tabrizi introduced and used in 2012 the concept of membership functions in the MCGP model in order to model the targets fuzziness of each goal. In their model, they considered just only one type of functions (triangular form), which does not reflect adequately the decision maker's preferences that are considered as an essential element for modelling the goal's fuzziness. Their model is called Fuzzy MCGP. In this paper, new ideas are presented to reformulate MCGP model to tackle all types of functions by introducing the (decision maker's) preferences. The concept of indifference thresholds is used in the new formulation for characterizing the imprecision and the preferences associated with all types of the goals. The proposed formulation provides useful insight about the solution of a new class of problems. A numerical example is given to demonstrate the validity and strength of the new formulation. Copyright © 2013 John Wiley & Sons, Ltd.     

A Fuzzy Topsis Method for Prioritized Aggregation in Multi‐Criteria Decision Making Problems

Aggregation in a decision making environment requires the fusion of opinions of a group of decision makers. The group of decision makers are required to analyse a set of interrelated criteria that are usually measured on a linguistic scale. This process requires, in many instances, to capture experts experience, intuition and thinking that are traditionally expressed in a linguistic fashion rather than a numerical fashion. Furthermore, the necessity of considering the relationship between the criteria to the overall decision must be considered by the group of decision makers. This paper extends the application of fuzzy numbers, fuzzy relative importance scores (FRIS), fuzzy relative weights (FRW) and the fuzzy technique of order preference by similarity to ideal solution (TOPSIS) in prioritized aggregation. This extension provides a mean to systematically aggregate a group of decision makers' views for a set of interrelated criteria that are measured on a linguistic scale. First, an overview of the application of fuzzy numbers and the characteristics of aggregating fuzzy numbers in multi‐criteria decision making problems are presented. Then, the application of TOPSIS in fuzzy environments is presented. Next, past research is highlighted to present prioritized aggregation and the different aggregation operators' classes. Subsequently, a new prioritized aggregation method is presented. This method utilizes fuzzy TOPSIS with prioritized aggregation in fuzzy environments. Finally, the fuzzy prioritized aggregation method presented in this paper is applied on an actual case study. According to the results, the method presented in this paper provides a systematic approach to capture the uncertainty and imprecision associated with quantifying linguistic measurements in multi‐criteria decision making problems. Furthermore, it considers the relationship between the set of linguistically measured criteria undergoing prioritized aggregation in a fuzzy environment. Lastly, findings, conclusions and future work are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Decision Support System and Multi‐Criteria Decision Aid: A State of the Art and Perspectives

The aim of this paper is to highlight the role of the Decision Support System within the field of multi‐criteria decision aid (MCDA). The MCDA tools have been incorporated into systems to create Multi‐Criteria Decision Support Systems (MCDSSs). In our literature review, we noticed that more than 100 papers have been written over a 20‐year period in which MCDSS was used as a decision‐making tool. The present paper describes some real applications of MCDSS in different fields, harmoniously combined with decision‐making methods such as analytic hierarchy process, Utility Additive, and Goal Programming. The present study proposes an integrative MCDSS evaluation through guidance on the tools most useful for a specific user with a particular decision problem. Copyright © 2014 John Wiley & Sons, Ltd.     

Multicriteria Classification with Unknown Categories: A Clustering–Sorting Approach and an Application to Conflict Management

This work proposes an approach to cluster and sort a set of alternatives considering multi‐criteria categories with a partial order structure. It can be considered a heuristic approach because it does not attempt to derive an optimal partial order among all conceivable clusters of alternatives. Rather than this, it intends to be a simple approach that is transparent to the Decision Maker (DM) whose assistance is sought to help shaping the results. The approach proposed arises from the conjugation of traditional Clustering analysis and Multi‐criteria sorting tools. At the outset, the number of categories and their characteristics is unknown. First, we need to detect only the clusters themselves on the basis of a similarity measure independent of the preferences of the DM. Next, we detect potential partial order relations that might exist between them, according to the subjective preferences of the DM. Such preferences are elicited only after the DM has examined the clusters detected and deemed that these categories made sense. The new approach performs very well in a real‐world problem of management of intragroup conflicts and conflict handling strategies. Copyright © 2012 John Wiley & Sons, Ltd.     

A multicriteria approach for material yard planning

The material yard is the origin of the production process for manufacturing firms. If materials are not stored at appropriate locations of the yard, then the stacking operation and the subsequent reclaiming operation will be inefficient in terms of time. In this paper a multicriteria approach which utilizes local trade-offs between different criteria in the absence of an explicit overall preference function is proposed to solve the material yard planning problem. The idea is to linearize the unknown preference function at a given point in the solution space. If the trade-offs between different criteria at this point can be determined via some mechanism, then a better solution can be derived. This process is continued until it converges to a stationary point, namely the optimal solution. To illustrate this idea, a case of the China Steel Co. in Taiwan is presented. The results from a simulation study indicate that the proposed approach is able to find a very good solution which satisfies all the criteria in a rather short transition period. © 1997 John Wiley & Sons, Ltd.