This study aims to develop a Multi-Attribute Decision-Making (MADM) method, the Best-Worst Tradeoff method, which draws on the underlying principles of two popular MADM methods (the Best-Worst Method (BWM) and the Tradeoff). The traditional Tradeoff procedure, which is based on the axiomatic foundation of multi-attribute value theory, considers the ranges of the attributes, but decision-makers/analysts find it hard to check the consistency of the paired comparisons when using this method. The traditional BWM, on the other hand, uses two opposite references (best and worst) in a single optimization, which not only frames the elicitation process in a more structured way, but helps decision-makers/analysts check the consistency. However, the BWM does not explicitly considers the attributes ranges in the pairwise comparisons. The method proposed in this study uses the “consider-the-opposite-strategy” and accounts for the range effect simultaneously. Specifically, the decision-maker considers the ranges of the attributes and provide two pairwise comparison vectors, then an optimization model is designed to determine the optimal weights of the attributes based on these two vectors. After that, consistency thresholds are constructed to check the consistency of the judgements. Finally, a case study is used to examine the feasibility of the proposed method.@en

The Best-Worst Method (BWM) is a Multi-Criteria Decision Making (MCDM) method that has recently been introduced. The original BWM assumes that decision-makers are always certain about their judgments even if, in reality, decision-makers often express uncertain preferences. To deal with uncertainty, we introduce a belief structure in the BWM, a concept involving the preference degree adopted via Dempster-Shafer theory. A new approach is proposed to allow BWM to cope with this kind of information, where the level of belief in preferences being expressed is taken into account. In addition, an inconsistency measurement and an uncertainty measurement are proposed for the belief-based BWM, providing the foundation for a reliability degree of the decision-makers, after which the belief-based BWM is extended to include a group of decision-makers. Based on their reliability degrees and the weights of the criteria obtained from the various individuals, the overall criteria weights can be aggregated accordingly. Finally, a case study on the assessment of the infrastructure project criteria system in Indonesia is provided to demonstrate the applicability and feasibility of the proposed method.

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The aim of this study is to develop an inland terminal location selection methodology. This methodology is viewed from the perspective of the shipping line designing the inland transport chain while also taking the objectives of multiple other stakeholders into account. To that end, we develop a consensus model for a group Best-Worst Method (BWM) in order to aggregate the evaluations of the various stakeholders. The proposed method is applied to a real-life case study involving the Maersk shipping line, in which nine experts representing three different types of stakeholders assess six possible locations. After the evaluation, the market volume potential is identified as one of the most important criteria. Furthermore, a sensitivity analysis indicates that a varying influx of the container volume has no impact on the most desirable location.

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The Best-Worst Method (BWM) uses ratios of the relative importance of criteria in pairs based on the assessment done by decision-makers. When a decision-maker provides the pairwise comparisons in BWM, checking the acceptable inconsistency, to ensure the rationality of the assessments, is an important step. Although both the original and the extended versions of BWM have proposed several consistency measurements, there are some deficiencies, including: (i) the lack of a mechanism to provide immediate feedback to the decision-maker regarding the consistency of the pairwise comparisons being provided, (ii) the inability to consider the ordinal consistency into account, and (iii) the lack of consistency thresholds to determine the reliability of the results. To deal with these problems, this study starts by proposing a cardinal consistency measurement to provide immediate feedback, called the input-based consistency measurement, after which an ordinal consistency measurement is proposed to check the coherence of the order of the results (weights) against the order of the pairwise comparisons provided by the decision-maker. Finally, a method is proposed to balance cardinal consistency ratio under ordinal-consistent and ordinal-inconsistent conditions, to determine the thresholds for the proposed and the original consistency ratios.

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This communication examines the best–worst method for multi-criteria decision making from a more mathematical perspective. The central part of this manuscript is the introduction of a new metric into the framework of the best–worst method. This alternative metric does not change the original idea behind the best–worst method and yet it can be shown that it is not only mathematically more sound but also that it ultimately leads to an optimization problem which can be simply linearized and thus solved.

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