Assigning machines to incomparable maintenance strategies with ELECTRE-SORT

The increasing demand on productivity and quality requires machines to be constantly available for production. It is therefore crucial to develop an adequate maintenance programme. To facilitate this, several criteria need to be considered, such as: downtime, maintenance frequency, spare parts costs, bottleneck impacts, etc. In the literature, a strategy is selected for each machine with a multi-criteria decision choice method. However, before making an informed decision, each strategy needs to be tested on each machine and then their performances evaluated with a multicriteria decision method. This is time-consuming, inefficient and often unfeasible. As machines׳ performances are usually systematically collected by industries, a much more practical approach is to assign machines to a maintenance strategy. This is referred to as a sorting problem. However, this problem cannot be solved by existing multi-criteria sorting methods because maintenance strategies cannot always be completely ordered: incomparable strategies exist. Recently, a Decision Making Grid was proposed to allocate machines to incomparable strategies. However, this technique can only be applied to problems with two criteria. In this paper, we have developed ELECTRE-SORT, a new sorting method that is able to consider an unlimited number of criteria in order to assign machines to incomparable strategies. A case study illustrates that ELECTRE-SORT provides more precise and flexible maintenance strategies than the Decision Making Grid.     

A unicriterion analysis based on the PROMETHEE principles for multicriteria ordered clustering

We consider multicriteria clustering problems where the groups are defined by a total order. We assume that the pairwise comparisons between the alternatives are expressed by a valued preference model built by PROMETHEE. In order to analyze the characteristics of each cluster on the different criteria, we propose three concepts based on the PROMETHEE principles: the preference profile of a cluster, the similarity profile of a cluster and the inconsistency profile of a cluster. These notions are illustrated based on a real application on the supplier segmentation.     

R&D portfolio selection by using qualitative pairwise comparisons

A new multicriteria decision aid, QualScal, is applied to the problem of selecting an extramural Fisheries R&D portfolio in the Ministry of Agriculture, Fisheries and Food. QualScal has been developed for the situation where the characteristics of the decision alternatives cannot be readily quantified. The decision-maker is only required to state either indifference or preference for each pair of the alternatives. A map representing the preference structure of the decision maker is produced with the aid of an enhanced version of the traditional nonmetric multidimensional scaling procedure, capable of scaling disjoint subsets of alternatives. Averaged results for the group of decision-makers facilitate a discussion to determine a mutually acceptable portfolio.     

INCORPORATING SALES FORCE PREFERENCES IN A GOAL PROGRAMMING MODEL FOR THE SALES RESOURCE ALLOCATION PROBLEM

This note presents a model for the sales territory assignment and resource allocation problem. The integer-goal-programming model includes input from the sales representatives in the form of preference values along with organizational goal values from management. The approach integrates the multiple objectiive inputs both for individual sales reprresentatives and for the organization into a single model by employing the approaches of multiattribute utility theory and multicriteria decision making. The purpose of the model is to provide a vehicle for testing various strategies and assessing the impact of those strategies on the sales representatives’utilities and the organization's goals.     

PAHAP: A Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences

In this paper, we present a Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences (PAHAP), a new method for solving discrete alternative multicriteria decision problems. Following the Analytic Hierarchy Process (AHP), PAHAP uses pairwise preference judgments to assess the relative attractiveness of the alternatives. By first aggregating the pairwise judgment ratios of the alternatives across all criteria, and then synthesizing based on these aggregate measures, PAHAP determines overall ratio scale priorities and rankings of the alternatives which are not subject to rank reversal, provided that certain weak consistency requirements are satisfied. Hence, PAHAP can serve as a useful alternative to the original AHP if rank reversal is undesirable, for instance when the system is open and criterion scarcity does not affect the relative attractiveness of the alternatives. Moreover, the single matrix of pairwise aggregated ratings constructed in PAHAP provides useful insights into the decision maker's preference structure. PAHAP requires the same preference information as the original AHP (or, altematively, the same information as the Referenced AHP, if the criteria are compared based on average (total) value of the alternatives). As it is easier to implement and interpret than previously proposed variants of the conventional AHP which prevent rank reversal, PAHAP also appears attractive from a practitioner's viewpoint.     

Market segmentation: A multiple criteria approach combining preference analysis and segmentation decision

We propose a new multiple criteria decision aiding approach for market segmentation that integrates preference analysis and segmentation decision within a unified framework. The approach employs an additive value function as the preference model and requires consumers to provide pairwise comparisons of some products as the preference information. To analyze each consumer’s preferences, the approach applies the disaggregation paradigm and the stochastic multicriteria acceptability analysis to derive a set of value functions according to the preference information provided by each consumer. Then, each consumer’s preferences can be represented by the distribution of possible rankings of products and associated support degrees by applying the derived value functions. On the basis of preference analysis, a new metric is proposed to measure the similarity between preferences of different consumers, and a hierarchical clustering algorithm is developed to perform market segmentation. To help firms serve consumers from different segments with targeted marketing policies and appropriate products, the approach proposes to work out a representative value function and the univocal ranking of products for each consumer so that products that rank in the front of the list can be presented to her/him. Finally, an illustrative example of a market segmentation problem details the application of the proposed approach.     

Super-stability in the student-project allocation problem with ties

The Student-Project Allocation problem with lecturer preferences over Students (spa-s) involves assigning students to projects based on student preferences over projects, lecturer preferences over students, and the maximum number of students that each project and lecturer can accommodate. This classical model assumes that each project is offered by one lecturer and that preference lists are strictly ordered. Here, we study a generalisation of spa-s where ties are allowed in the preference lists of students and lecturers, which we refer to as the Student-Project Allocation problem with lecturer preferences over Students with Ties (spa-st). We investigate stable matchings under the most robust definition of stability in this context, namely super-stability. We describe the first polynomial-time algorithm to find a super-stable matching or to report that no such matching exists, given an instance of spa-st. Our algorithm runs in O(L) time, where L is the total length of all the preference lists. Finally, we present results obtained from an empirical evaluation of the linear-time algorithm based on randomly-generated spa-st instances. Our main finding is that, whilst super-stable matchings can be elusive when ties are present in the students’ and lecturers’ preference lists, the probability of such a matching existing is significantly higher if ties are restricted to the lecturers’ preference lists.

     

A New Approach to the Group Ranking Problem: Finding Consensus Ordered Segments from Users’ Preference Data

The group ranking problem involves constructing coherent aggregated results from users’ preference data. The goal of most group ranking problems is to generate an ordered list of all items that represents the user consensus. There are, however, two weaknesses to this approach. First, a complete list of ranked items is always output even when there is no consensus or only a slight consensus. Second, due to similarity of performance, in many practical situations, it is very difficult to differentiate whether one item is really better than another within a set. These weaknesses have motivated us to apply the clustering concept to the group ranking problem, to output an ordered list of segments containing a set of similarly preferred items, called consensus ordered segments. The advantages of our approach are that (i) the list of segments is based on the users’ consensuses, (ii) the items with similar preferences are grouped together in the same segment, and (iii) the relationships between items can be easily seen. An algorithm is developed to construct the consensus of the ordered segments from the users’ total ranking data. Finally, the experimental results indicate that the proposed method is computationally efficient, and can effectively identify consensus ordered segments.     

A modified DEA model to estimate the importance of objectives with an application to agricultural economics

This paper demonstrates a connection between data envelopment analysis (DEA) and a non-interactive elicitation method to estimate the weights of objectives for decision-makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows us to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of multiple attribute decision analysis the basic contribution of this paper is a new interpretation in terms of efficiency of the non-interactive methodology employed to estimate weights in a multicriteria approach. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures that does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.     

Stock Evaluation Using a Preference Disaggregation Methodology

This paper presents a real application of a multicriteria decision aid (MCDA) approach to portfolio selection based on preference disaggregation, using ordinal regression and linear programming (UTADIS method; UTilités Additives DIScriminantes). The additive utility functions that are derived through this approach have the extrapolation ability that any new alternative (share) can be easily evaluated and classified into one of several user-predefined groups. The procedure is illustrated with a case study of 98 stocks from the Athens stock exchange, using 15 criteria. The results are encouraging, indicating that the proposed methodology could be used as a tool for the analysis of the portfolio managers' preferences and choices. Furthermore, the comparison with multiple discriminant analysis (either using a stepwise procedure or not) illustrates the superiority of the proposed methodology over a well-known multivariate statistical technique that has been extensively used to study financial decision-making problems.     

The popular matching and condensation problems under matroid constraints

The popular matching problem introduced by Abraham, Irving, Kavitha, and Mehlhorn is a matching problem in which there exist applicants and posts, and applicants have preference lists over posts. A matching M is said to be popular, if there exists no other matching N such that the number of applicants that prefer N to M is larger than the number of applicants that prefer M to N. The goal of this problem is to decide whether there exists a popular matching, and find a popular matching if one exists. In this paper, we first consider a matroid generalization of the popular matching problem with strict preference lists, and give a polynomial-time algorithm for this problem. In the second half of this paper, we consider the problem of transforming a given instance of a matroid generalization of the popular matching problem with strict preference lists by deleting a minimum number of applicants so that it has a popular matching. This problem is a matroid generalization of the popular condensation problem with strict preference lists introduced by Wu, Lin, Wang, and Chao. By using the results in the first half, we give a polynomial-time algorithm for this problem.     

A Multi‐Supplier Sourcing Problem with a Preference Ordering of Suppliers

We study a sourcing problem faced by a firm that seeks to procure a product or a component from a pool of alternative suppliers. The firm has a preference ordering of the suppliers based on factors such as their past performance, quality, service, geographical location, and financial strength, which are commonly included in a supplier scorecard system. Thus, the firm first uses available inventory from supplier 1, if any, then supplier 2, if any, and so on. The suppliers differ in costs and prices. The buyer firm seeks to determine which suppliers to purchase from and in what quantities to maximize its total expected profit subject to the preference ordering constraint. We present the optimal solution to this problem, and show that it has a portfolio structure. It consists of a sub‐set of suppliers that are ordered by their underage and overage costs. This portfolio achieves a substantial profit gain compared to sourcing from a unique supplier. We present an efficient algorithm to compute the optimal solution. Our model applies to component sourcing problems in manufacturing, merchandizing problems in retailing, and capacity reservation problems in services.     

A multicriteria outranking approach for modeling corporate credit ratings: An application of the Electre Tri-nC method

Corporate credit ratings are widely used in financial services for risk management, investment, and financing decisions. In this study, the use of a recently developed multicriteria outranking approach, namely the Electre Tri-nC method, is examined for constructing internal credit rating models in an expert-based judgmental framework. The models are constructed in a multicriteria classification (sorting) setting and the results are analyzed in terms of their internal properties as well as their deviations from risk rating categories defined by rating agencies (i.e. external benchmarking). A simulation/scenario analysis is conducted to examine the results and performance of the outranking models in relation to their parameters. Empirical results are provided for a sample of European firms rated by three leading rating agencies.     

PORTFOLIO MODELING IN MULTIPLE-CRITERIA SITUATIONS UNDER UNCERTAINTY: COMMENT

In a recent issue of Decision Sciences, Muhlemann, Lockett, and Gear [8] developed a multiple-objective, stochastic linear programming formulation of the multiperiod portfolio selection problem under uncertainty. The purpose of this note is to offer some extensions to their multicriteria approach which is otherwise viewed as an excellent attempt at modeling realistic aspects of the portfolio selection problem. Further, integer goal programming combined with simulation is suggested as an alternate approach for solving the dynamic multiple-objective problem.     

Concepts,Theory, and Techniques DISTRIBUTED COMPUTER SYSTEM DESIGN: A MULTICRITERIA DECISION-MAKING METHODOLOGY*

The design of distributed computer systems (DCSs) requires compromise among several conflicting objectives. For instance, high system availability conflicts with low cost which in turn conflicts with quick response time. This paper presents an approach, based on multi-criteria decision-making techniques, to arrive at a good design in this multiobjective environment. An interactive procedure is developed to support the decision making of system designers. Starting from an initial solution, the procedure presents a sequence of non-dominated vectors to designers, allowing them to explore systematically alternative possibilities on the path to a final design. The model user has control over trade-offs among different design objectives. This paper focuses on the details of the mathematical model used to provide decision support. Accordingly, a formulation of DCS design as a multicriteria decision problem is developed. The exchange search heuristic used to generate nondominated solutions also is presented. We argue that multicriteria models provide a more realistic formulation of the DCS design problem than the single-criterion models used widely in the literature. While obtaining a clear definition of design objectives (single or multiple) is an important activity, by explicitly acknowledging the trade-offs among multiple objectives in the design process, our methodology is more likely to produce a better overall design than methods addressing a single criterion in isolation.     

A Meta-Goal Programming approach to cardinal preferences aggregation in multicriteria problems

Solving multicriteria decision making problems often requires the assessment of certain preferential information. In some occasions, this information must be given by several individuals or social groups, and these individual assessments need to be aggregated into single global preferences. This cardinal preferences aggregation problem has been tackled using different techniques, including multicriteria decision making ones. In this paper, a Meta-Goal Programming approach is proposed, where different target values can be set on several achievement functions that measure the goodness of the global assessments. This methodology presents strong advantages due to its modeling flexibility and its ability to find balanced solutions. The proposed approach is demonstrated with an illustrative example and a series of computational experiments, and it is shown that the Meta-Goal Programming method produces results with better values of the achievement functions than other classical and multicriteria approaches.     

Enhancing knowledge construction processes within multicriteria decision analysis: The Collaborative Value Modelling framework

This paper proposes a new Collaborative Value Modelling framework, that combines Delphi and multicriteria decision conferencing, to build widely informed evaluation models. Multicriteria Decision Analysis (MCDA) is commonly used to help decision-makers and other stakeholders in complex evaluation contexts. Further to the technical soundness and meaningfulness of the methods and tools used, it is critical to design adequate social processes to promote shared understanding around key evaluation issues while capturing multiple stakeholders’ values and perspectives. Multicriteria decision conferencing processes have been typically adopted for collaborative modelling using MCDA methods in decision conferences with relatively small groups. Such a socio-technical approach has proven to be effective, in a variety of contexts, in creating a collaborative environment that enables surfacing individual beliefs, identifying common concerns, managing eventual value conflicts and promoting agreement in group model building. But, extending this framework to broader participatory contexts requires a different design of the social process, in order to ensure that model building captures the full panoply of points of view. This challenge can be tackled by enhancing multicriteria decision conferencing with an all-embracing (Web-)Delphi participatory process. We depart from the existing collaborative knowledge acquisition methodology to design, with the Delphi method, a participatory knowledge construction process that elicits and analyses individual judgemental knowledge from a (very) large and diverse number of stakeholders. The knowledge acquired is then digested by a small group of key-players, in a subsequent decision conferencing, to collaboratively develop a widely informed multicriteria evaluation model. This new Web-Delphi-decision conferencing social setting has been tested already in real complex evaluation contexts using a specific multicriteria method, the Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH), to develop a variety of value modelling activities. We call this socio-technical design the Collaborative Value Modelling framework. Here, we describe its real use to support the construction of value functions, focusing on how the judgemental knowledge collected flows between the participatory and collaborative stages of the framework. Results validate that enhancing MACBETH decision conferencing with an ex ante Web-Delphi process fosters higher participation and collaboration in multicriteria modelling.