Worst Method Research Articles

Closed-form solutions of consistency ratio in best worst method minmax optimization model: max of edge error matrix and minmax edge error determinant methods

The Best Worst Method (BWM), a reduced version of the AHP, is a recent multi-criteria decision-making tool based on pairwise comparisons with reference to the best and worst criteria. Consistency Ratio (CR) measurement for the rating quality and prioritizations is still a controversial topic. Firstly, the computation for the current CR of BWM must rely on a software optimization solver to find the optimal values, and the solver may not always guarantee the exact optimal solutions, especially if the computational cost settings are not large enough for higher number of criteria. Secondly, much effort to evaluate optimization algorithms is needed to find the best solutions with the least computational resources due to diverse solvers possibly leading to different results with different performances. Thirdly, optimization programming code is not trivial to be implemented for general BWM users. To address these issues, this paper presents the closed-form solutions, Max of Edge Error Matrix (MEEM) (Eq. (44) of Theorem 4) and Minmax Edge Error Determinant (MEED) (Algorithm 1), to replace the BWM optimization models to directly calculate the CR values. Two simulations have been performed with a basic laptop using a single process. One simulation of twenty thousand random pairs of vectors took 26.34 h to perform to verify that the approximate results are higher than or very close to the exact closed-form values of both methods when high computational cost is allocated for the solver to increase the precision. Another simulation of one million random pairs of vectors only took 1.27 h to perform to verify that the MEED and MEEM methods always produce the same results for the number of criteria up to nine. The computational time for the exact results is dramatically reduced when the solver is not needed. The advantages of the proposed solutions include the following: the software to solve the optimization model to obtain CR is unnecessary, and the proposed calculation is extremely efficient to obtain the exact accuracy. The two-step optimization model can preserve the fixed Minmax Edge Error to find the weights which add up to one, which is the condition to determine if the model reaches exact optimal solutions. As the CR optimization model produces multiple versions of weights, which are recommended not to be used, the new method does not need to compute the unnecessary weight values to get the Minmax Edge Error. With the provision of equations leading to closed forms, users can understand the properties of CR in much clearer perspectives. Due to the computational efficiency and explainability, the proposed closed forms can replace the CR optimization model to compute CR efficiently and accurately for all diverse applications using BWM.

Evaluation of sustainable energy systems in smart cities using a Multi-Expert Pythagorean fuzzy BWM & TOPSIS methodology

Smart cities are technological settlements using the collected data to utilize resources and services effectively by combining information and communication technologies with various tools connected to the internet of things network. Sustainable energy systems in smart cities are systems can be evaluated by using multiple criteria decision making methods or methodologies based on several vague/imprecise evaluation criteria. In this paper, sustainable energy systems in smart cities are evaluated by interval-valued Pythagorean fuzzy (IVPF) sets with an integrated optimization based multi-expert fuzzy Best Worst Method (BWM) and TOPSIS methodology that can better handle uncertainty and vagueness in experts’ linguistic assessments than existing methodologies. The considered criteria are weighted by multi-expert IVPF Best Worst Method, which has become a popular weighting method in recent years. Later, the energy alternatives for a real case study are prioritized by multi-expert IVPF TOPSIS method. In the analysis, the most important criterion is found as Environmental sustainability (C1) with the defuzzified weight of 0.218 while the other weights are as initial investment (C2) with 0.196, operating expenses (C3) with 0.163, technical feasibility (C4) with 0.154, social acceptability (C5) with 0.140, and scalability (C6) with 0.129. The obtained results indicate that “Investing in advanced technologies” in a smart city with relative degree of closeness (RDC) value of 0.798, has been determined as the best alternative among the considered five alternatives. It is closely followed by “Developing a transportation system” with the RDC value of 0.681. Sensitivity analysis shows that the ranking results are quite robust and reliable. The comparative analysis with crisp BWM and TOPSIS methodology is applied to check the validity of the proposed methodology.

Fuzzy best–worst method–based approach for warehouse location selection and a case study in Izmir

PurposeThe study aims to propose a decision-support system to determine the location of a regional disaster logistics warehouse. Emphasizing the importance of disaster logistics, it considers the criteria to be evaluated for warehouse location selection. It is aimed to determine a warehouse location that will serve the disaster victims most efficiently in case of a disaster by making an application for the province of Izmir, where a massive earthquake hit in 2020.Design/methodology/approachThe paper proposes a fuzzy best–worst method to evaluate the alternative locations for the warehouse. The method considers the linguistic evaluations of the decision-makers and provides an advantage in terms of comparison consistency. The alternatives were identified through interviews and discussions with a group of experts in the fields of humanitarian aid and disaster relief operations. The group consists of academics and a vice-governor, who had worked in Izmir. The results of a previously conducted questionnaire were also used in determining these locations.FindingsIt is shown how the method will be applied to this problem, and the most effective location for the disaster logistics warehouse in Izmir has been determined.Originality/valueThis study contributes to disaster preparedness and brings a solution to the organization of the logistics services in Izmir.

The use of continuous visual aid in the Best–Worst Method: an experiment with organic farmers in Paraguay

The use of continuous visual aid in the Best–Worst Method: an experiment with organic farmers in Paraguay

Risk analysis of offshore rocket launch propellant filling system under data and knowledge scarcities

To improve the reliability of offshore launch propellant filling systems and mitigate potential hazards in the case of data and knowledge scarcity, a weighted Failure Mode and Effect Analysis (weighted-FMEA) methodology is proposed. A detailed hazard identification framework is proposed to identify potential failure modes of the systems. The Best Worst Method and a comparative matrix is then combined to unify the differences between systems and components. Subsequently, the grey theory is used to mitigate the subjectivity/uncertainty of experts’ judgment. Critical failures and corresponding preventive actions are recommended based on the analysis results. The superiority of the proposed model is confirmed by a comparison analysis with existing methods. Overall, the proposed weighted-FMEA model helps to prevent accidents and ensures the safe operation of offshore propellant-filling systems.

Better decisions with less cognitive load: The Parsimonious BWM

Despite its recent introduction in literature, the Best–Worst Method (BWM) is among the most well-known and applied methods in Multicriteria Decision-Making. The method can be used to elicit the relative importance (weight) of the criteria as well as to get the priorities of the alternatives on the criteria at hand. In this paper, we will present an extension of the method, namely, the parsimonious Best–Worst-Method (P-BWM) permitting to apply the BWM to get the priorities of the alternatives in case they are in a large number. At first, the Decision-Maker (DM) is asked to give a rating to the alternatives under consideration; after, the classical BWM is applied to a set of reference alternatives to get their priorities used to compute, then, the priorities of all the alternatives under consideration. We propose also a procedure to select reference alternatives, possibly in cooperation with the DM, providing a well-distributed coverage of the rating range. The new proposal requires the DM a fewer number of pairwise comparisons than the original BWM. Another contribution of the paper is related to the comparison between BWM, P-BWM, the Analytic Hierarchy Process (AHP), and the parsimonious AHP in terms of the amount of preference information provided by the DM in each method to apply it. In addition to the standard approach, we propose one alternative way of inferring the priority vectors in BWM and P-BWM based on the barycenter of the space of alternatives priorities compatible with the preferences given by the DM. Finally, an experiment with university students has been conducted to test the new proposal. Results of the experiments show that P-BWM performs better than BWM in terms of capability to represent the DM’s preferences and the difference between the results of the two methods is significant from the statistical point of view. The new proposal will permit to use the potentialities of the BWM to get the alternatives’ priorities in real-world decision-making problems where a large number of alternatives must be taken into account.

A novel multi-criteria conflict evidence combination method and its application to pattern recognition

In recent years, the Dempster–Shafer Theory (DST) has been widely applied in areas such as target classification and multi-modal fusion due to its advantages in uncertain reasoning. However, in DST, when there exists highly conflicts between Sources of Evidence (SoEs), it often leads to counterintuitive fusion results, thereby affecting the performance of the final fused decision-making. To eliminate the potential impact of highly conflicts during the fusion process, this paper primarily focuses on modifying the SoEs themselves to achieve the discounting fusion. Currently, existing literature has proposed numerous discounting fusion methods to address highly conflict fusion. However, in these discounting strategies, the determination of discounting factors is typically based on a single criterion. Considering that a single indicator cannot comprehensively and accurately assess the reliability of each evidence source, this paper introduces a novel conflict evidence combination method based on a multi-criteria evaluation strategy. In this method, the Best and Worst Method (BWM) is initially used to prioritize the best SoE, determining the solution points for each criterion and subsequently selecting the ideal solution. Then, combining the selected criteria: distance, relative entropy, and divergence metrics, reliability calculation is performed based on the Stable Preference Order Theory for Ideal Solution (SPOTIS), which achieves a stable preference order strategy towards the ideal solutions. Finally, leveraging the discounting fusion method in DST, modification and fusion of the original highly conflict SoEs are achieved. Through extensive experiments, the effectiveness and practicality of the proposed method in this paper have been validated.

Exploring the Challenges of Industry 4.0 Adoption in the FMCG Sector: Implications for Resilient Supply Chain in Emerging Economy

Background: Fast-moving consumer goods (FMCG) supply chains are experiencing various challenges due to the interactions between consumers and decision-makers during physical distribution, manufacturing, wholesale and retail. One possible strategy to address these challenges for smoothing the supply chain (SC) and logistics operations is to adopt Industry 4.0 (I4.0) based technologies in the FMCG business processes. In this regard, digitalization and automation of the FMCG supply chain can be strengthened by the alluring properties of I4.0 technologies. Methods: This study identified nine significant challenges through a literature review and expert validation. Later, the challenges were evaluated using a novel multicriteria decision-making (MCDM) framework, the Bayesian best worst method (BWM). Results: The findings indicated that “requirement for substantial investment and resources”, “incompatible technological infrastructure” and “poorly structured value chain” are the most significant challenges to implementing I4.0 in the FMCG industry. Conclusions: The study is expected to significantly contribute to improving the FMCG supply chain’s resilience, sustainability, visibility, traceability and responsiveness. Additionally, the research can provide industrial practitioners valuable insights into implementing I4.0 in FMCG and similar sectors and thus promote SC sustainability and resilience in those industries.

Analyzing the Shelter Site Selection Criteria for Disaster Preparedness Using Best–Worst Method under Interval Type-2 Fuzzy Sets

Shelters are vital for affected people after a disaster because of the accommodation, safety, and security. In this paper, we analyze the shelter site selection criteria for disaster preparedness applying the best–worst method under interval type-2 fuzzy sets. The proposed approach utilizes the advantages of fewer pairwise comparisons with the best–worst method and better reflection of uncertainty with interval type-2 fuzzy sets. For this reason, the criteria are determined based on a literature review and the opinion of nine disaster experts. The experts have worked as disaster officers in a variety of locations, including Sivrice (Elazığ), Pazarcık, and Elbistan (Kahramanmaras) and Syrian refugee camps such as Nizip container city. In this step, 6 main criteria and 25 sub-criteria are evaluated using the proposed approach. According to the nine experts’ opinions, the most important main criterion is determined as proximity. Distribution center capacity, adequate distribution logistics personnel, available electricity, distance to settlement, and landslides and flooding are also determined as the five most important sub-criteria. For disaster preparedness, responsible organizations and managers should consider these important criteria for temporary shelter site selection.

A decision framework of offshore photovoltaic power station site selection based on Pythagorean fuzzy ELECTRE-III method

Offshore photovoltaic power stations (OPVPS) greatly help solve energy problems and land resource scarcity. A crucial phase of the OPVPS project lifecycle is site selection. To select the optimal location of OPVPS with many difficulties such as the uncertainty of the environment, the compensating relationships among criteria, and the different attributes of the alternatives, this paper proposed a fuzzy multi-criteria decision-making framework based on Pythagorean fuzzy Elimination et Choix Traduisant la Realité-III (ELECTRE-III) method. First, the comprehensive criteria system for siting OPVPS was constructed, which included veto and evaluation criteria. Second, the Pythagorean fuzzy set was used to express the uncertain evaluation of experts. Third, considering the actual situation that experts had different experiences and abilities, this paper proposed a novel expert weighting method. Fourth, entropy weighting method, best–worst method, and combination weighting of game theory were introduced to calculate the criteria weights. Fifth, considering the compensation between criteria, ELECTRE-III was used for ranking. Finally, to verify the applicability and robustness of the proposed framework, a China case study was conducted; the results showed that Haizhou Bay is the best alternative.

Prioritizing institutional pressures, green supply chain management practices for corporate sustainable performance using best worst method

The emerging institutional concerns regarding the environmental crisis over the past decades have promoted the implementation of green initiatives within the supply chain, aiming to reduce environmental harm while maintaining efficiency. This study employed the BWM from a double perspective, aiming to identify and rank institutional pressures for GSCM practice implementation and the importance of these practices for sustainable performance in the Moroccan manufacturing industry. The study used purposive sampling to identify respondents with supply chain management expertise. A survey was distributed to 124 potential respondents, resulting in 55 responses. Data collection occurred between April and August 2022, with an effective response rate of approximately 38%. The results indicate that institutional pressure increases the likelihood of firms improving their GSCM activities. Normative pressures are found to be the main influencing factor for businesses to implement GSCM practices, while mimetic pressures are the least important. However, certain GSCM practices, such as GP, ECO-D, and IEM, remain among the top three most affected by isomorphic pressures. The study also highlights the importance of certain GSCM practices, such as IEM, GP, and ECO-D, for firms' sustainable performance. Economic outcomes are perceived as the experts' priority, followed by environmental and social performance. This research provides a theoretical and practical foundation for decision-makers seeking to identify the pressures affecting the implementation of GSCM practices along with the activities that most likely contribute to improving various aspects of sustainable performance.

Analisis Manajemen Rantai Pasok dengan Metode Supply Chain Operation Reference PT Fourmi Asha Sejahtera

In an era of economic development, business competition demands the acquisition of as many consumers as possible. This naturally requires a sound strategy in order to gain a competitive edge over rivals. The aim of this research is to evaluate the supply chain performance of Multi-level Marketing (MLM) companies by measuring SCM performance. SCM performance measurement is carried out using the SCOR model with the weights for each level divided equally and processing the actual data for each performance metric. After processing the data there are 7 SCOR performance metrics. Based on the results of data processing, the actual values are then normalized using the De Boer Snorm to obtain SCOR performance metric measurement values. The results obtained were a total score of 72.2 which is included in the good category, these results indicate that there is still a need to evaluate and improve performance

Advancing Urban Healthcare Equity Analysis: Integrating Public Participation GIS with Fuzzy Best–Worst Decision-Making

This study provides an innovative collaborative spatial decision support system (SDSS) that aims to ensure an equitable spatial distribution of healthcare services. Evaluating the equality of access to health services across different geographical areas is important, as it requires the analysis of various criteria such as the proximity of health centres and hospitals (HCHs), the quality of services offered, connectivity to primary roads, the availability of public transportation hubs, and the density and distribution patterns of HCHs. This purpose is accomplished via the use of geographic information systems (GIS) and multi-criteria decision analysis (MCDA) methods. The proposed model includes the weights of the criteria, which are determined through the ordered weighted average (OWA) and evaluated based on their ORness, which ranges from 0 to 1. Furthermore, this model is improved by the best–worst fuzzy method (F-BWM). This approach produces a spatial map that clearly shows the equity of healthcare systems in urban environments. The findings show that the maximum score observed in this study was 0.38% (with an ORness value of 1), whilst the minimum score recorded was 0.28%. In the most severe scenario (ORness = 0), over 70% of the region shows different degrees of fairness, ranging from moderate to suitable and very suitable conditions. Governments and health authorities can use this information strategically to allocate resources and address inequities in access to healthcare facilities.

A Hybrid Group Multi-Criteria Approach Based on SAW, TOPSIS, VIKOR, and COPRAS Methods for Complex IoT Selection Problems

The growth of Internet of Things (IoT) systems is driven by their potential to improve efficiency, enhance decision-making, and create new business opportunities across various domains. In this paper, the main selection problems in IoT-type systems, criteria used in multi-criteria evaluation, and multi-criteria methods used for solving IoT selection problems are identified. Then, a Hybrid Group Multi-Criteria Approach for solving selection problems in IoT-type systems is proposed. The approach contains the Best Worst Method (BWM) weighting method, multi-criteria Simple Additive Weighting (SAW), Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), and Complex Proportional Assessment Method (COPRAS), and a method that combines the solutions obtained using the four considered multi-criteria methods to obtain a single solution. The SAW, TOPSIS, VIKOR, and COPRAS methods were analyzed in relation to their advantages, disadvantages, inputs, outputs, measurement scale, type of normalization, aggregation method, parameters, complexity of implementation, and interactivity. An application of the Hybrid Group Multi-Criteria Approach for IoT platform selection and a comparison between the SAW, TOPSIS, VIKOR, and COPRAS solutions and the solution of the proposed approach is realized. A Spearman correlation analysis is presented.

Select a winning Lean Six Sigma 4.0 project: Best Worst Method based decision making approach

Manufacturers are adopting Lean Six Sigma4.0 (LSS4.0) to improve their operations. However, poor project selection results in substantial losses. The aim of this study is to provide a framework for LSS4.0 project selection in an industrial context using the Best-Worst-Method (BWM)-based ‘multi-criteria decision making’ (MCDM) technique. First, 25 project selection criteria were pre-selected using a literature review and expert opinions. All criteria were then grouped into six different dimensions, closely related to the LSS4.0 principles, based on expert opinion and similarity with literature findings. To finalize the selection, a rigorous evaluation is undertaken using corrected item-total correlation (CIMTC) and importance index analysis methods, resulting in a final set of 22 project selection criteria, prioritized using BWM. The practical applicability of this method is demonstrated by a case study in a Moroccan manufacturing context. Operational and technical feasibility, strategic orientation, finance and business development emerged as top priorities. This research can help senior managers make informed choices about projects and recognize potential in uncertain scenarios.

Correction to: Data‑driven prioritization of performance variables for flexible manufacturing systems: revealing key metrics with the best–worst method

Correction to: Data‑driven prioritization of performance variables for flexible manufacturing systems: revealing key metrics with the best–worst method

Research on the Safety Evaluation Method for Quayside Container Cranes Based on the Best–Worst Method–Pythagorean Fuzzy VIKOR Approach

In the port domain, quayside container cranes are an indispensable component of maritime freight transport. These cranes are not only costly but also associated with safety accidents that often result in casualties and property loss, severely impacting port operations and the surrounding environment. Given their complex operational environment, rapid technological updates, high dependency on human factors, and the challenges of maintenance and inspection, the safety of quayside container cranes is a significant concern for port enterprises and managers. This paper, based on the operational modes and structural characteristics of the cranes, divides them into five main systems and identifies twenty-eight safety evaluation indicators, covering a comprehensive range of risk factors from equipment integrity to operator behavior, as well as environmental factors. However, numerous pain points exist in the safety risk evaluation process of quayside container cranes, such as fuzziness, uncertainty, and complex multi-criteria decision-making (MCDM) environments. These issues make traditional safety evaluation methods inadequate in accurately reflecting the actual safety conditions. Therefore, this paper proposes a safety evaluation method for quayside container cranes based on the Best–Worst Method (BWM) and Pythagorean hesitant fuzzy VIKOR. This method effectively overcomes the uncertainties and fuzziness of traditional safety evaluation methods by integrating the decision maker’s preference information from the BWM and the fuzzy handling capability of Pythagorean hesitant fuzzy sets, enhancing the accuracy and reliability of the evaluation results. A case study was conducted on a quayside container crane at a specific port. Through empirical analysis, the feasibility of the proposed method was validated. Overall, the safety evaluation method for quayside container cranes based on the BWM and Pythagorean hesitant fuzzy VIKOR proposed in this paper enriches the theoretical research on the safety risk assessment of quayside container cranes and offers a new approach and tool for port enterprises and managers in practice.

A fuzzy BWM and MARCOS integrated framework with Heronian function for evaluating cryptocurrency exchanges: a case study of Türkiye

Crypto assets have become increasingly popular in recent years due to their many advantages, such as low transaction costs and investment opportunities. The performance of crypto exchanges is an essential factor in developing crypto assets. Therefore, it is necessary to take adequate measures regarding the reliability, speed, user-friendliness, regulation, and supervision of crypto exchanges. However, each measure to be taken creates extra costs for businesses. Studies are needed to determine the factors that most affect the performance of crypto exchanges. This study develops an integrated framework, i.e., fuzzy best–worst method with the Heronian function—the fuzzy measurement of alternatives and ranking according to compromise solution with the Heronian function (FBWM’H–FMARCOS’H), to evaluate cryptocurrency exchanges. In this framework, the fuzzy best–worst method (FBWM) is used to decide the criteria’s importance, fuzzy measurement of alternatives and ranking according to compromise solution (FMARCOS) is used to prioritize the alternatives, and the Heronian function is used to aggregate the results. Integrating a modified FBWM and FMARCOS with Heronian functions is particularly appealing for group decision-making under vagueness. Through case studies, some well-known cryptocurrency exchanges operating in Türkiye are assessed based on seven critical factors in the cryptocurrency exchange evaluation process. The main contribution of this study is generating new priority strategies to increase the performance of crypto exchanges with a novel decision-making methodology. “Perception of security,” “reputation,” and “commission rate” are found as the foremost factors in choosing an appropriate cryptocurrency exchange for investment. Further, the best score is achieved by Coinbase, followed by Binance. The solidity and flexibility of the methodology are also supported by sensitivity and comparative analyses. The findings may pave the way for investors to take appropriate actions without incurring high costs.

Supplier Selection in Downstream Oil and Gas and Petrochemicals with the Fuzzy BWM and Gray COCOSO Methods Considering Sustainability Criteria and Uncertainty Conditions

A project always needs the participation of suppliers to provide the goods and services needed by the project. As the size of the project increases, the need to use suppliers also increases. Choosing the appropriate suppliers for the project is always a difficult task, and considering different criteria along with the existence of multiple alternatives always increases the difficulty and complexity of the supplier selection problem. This study deals with the supplier selection problem, which is one of the important issues in projects and organizations in the downstream field of oil, gas, and petrochemicals. The purpose of this paper was to investigate and improve the supplier selection procedure in this field by considering real-world uncertain conditions. To this end, the fuzzy set theory and gray numbers were taken into account. In the present study, the criteria were first determined by expert judgment; then, the fuzzy best–worst method (FBWM) was exploited to rank the criteria; finally, the suppliers were prioritized and ranked by using the gray COCOSO method The results showed that the highest and the lowest weights were obtained for the “price” and “attention to environmental issues” criteria, respectively. Also, the selected supplier was a supplier with a high score in all criteria. One of the practical benefits of this research is to provide a solution to speed up, facilitate, and improve the process of selecting suppliers for companies in the downstream field of oil, gas, and petrochemicals.

Supplier selection among manufacturing companies based on their MSME partners’ supply chain finance adoption capability using BWM and VIKOR

PurposeThe purpose of this paper is to identify and prioritise supply chain finance (SCF) adoption enablers and develop a novel comprehensive framework to select supplier firms based on their SCF adoption capability.Design/methodology/approachThe study deploys a three-phase method to identify and prioritise SCF adoption enablers, followed by developing a model to select suppliers according to their SCF adoption capability. An extensive literature review, followed by a Delphi approach-based expert interview, has been used to finalise the enablers. Using the Best Worst Method and the VIsekriterijumsko KOmpromisno Rangiranje technique, a supplier selection model has been developed in the context of a case company.FindingsThe financial health and technological advancement variables received the top priority, followed by collaborative efficiency, whereas the human resources and organisational variables received the slightest significance. A supplier selection framework has also been developed by using the adoption capability of these factors by the supplier partners. In this study’s model, Supplier 4 exhibited better SCF adoption capability and received the top priority.Research limitations/implicationsManufacturing supply chains in a developing country are the scope of the current study. Extensive future studies are required to derive a global consensus.Practical implicationsThe proposed framework of this study can be used to select supplier firms based on their SCF adoption capability. Policymakers can emphasise the most critical enablers of SCF adoption to assist small supplier firms to be a part of the advanced global supply chains.Originality/valueThe current study established a novel comprehensive framework for supplier selection based on the Supply Chain Finance adoption capability of MSME supplier firms.