Taxicab distance based best-worst method for multi-criteria decision-making: An analytical approach

Mathematics > Optimization and Control [Submitted on 26 Aug 2024 (v1), last revised 18 Jun 2026 (this version, v3)] Title:Taxicab distance based best-worst method for multi-criteria decision-making: An analytical approach View PDFAbstract:The best-worst method is a well-known distance based multi-criteria decision-making method used for computing the weights of decision criteria. This article provides a comprehensive analytical examination of the taxicab distance based model of the method, with the objectives of investigating the uniqueness of these solutions, and performing a rigorous consistency analysis. To achieve this, an optimal modification based optimization problem, equivalent to the original one, is first formulated. This reformulated problem is then solved analytically, and the optimal weight sets are derived from its solutions. Contrary to the prevailing understanding derived from numerical experiments with the taxicab model, our analytical framework proves that the model can, in fact, lead to multiple optimal weight sets, and we formally establish the conditions for this occurrence. A mixed-integer linear programming model is then employed to compute the consistency index. A decision-maker-aided selection strategy is also proposed for addressing non-uniqueness of optimal weight sets. In addition, threshold values of the consistency ratio to assess the admissibility of given preferences are also established. This framework provides a solid mathematical foundation that enhances the understanding of the model and eliminates the requirement for optimization software. By significantly improving the model's computational efficiency, it enables implementation in large-scale, dynamic real-world applications such as electricity market bidding strategies and portfolio rebalancing under market volatility. The effectiveness of the proposed framework is demonstrated through numerical examples, and its practical applicability is illustrated via a smartphone selection problem. Submission history From: Harshit Ratandhara [view email][v1] Mon, 26 Aug 2024 17:47:24 UTC (221 KB) [v2] Fri, 4 Apr 2025 06:44:11 UTC (225 KB) [v3] Thu, 18 Jun 2026 05:47:20 UTC (135 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.