Network reliability is always a powerful index for measuring the performance of the multistate flow network (MFN) that is commonly used to model real-world applications. The multistate minimal cut (MC) vector is a special vector, and it is one of the most popular tools in evaluating the reliability of MFNs. Due to its importance, a novel multistate MC vectors problem is proposed by extending the traditional multistate MC vectors problem from a specific fixed flow to all different flows for more applications. To solve this novel problem, a new algorithm is proposed. The time complexity and demonstration of the proposed algorithm are analyzed, and examples are provided. An experiment is also conducted to compare the proposed multistate MC vectors algorithm and the multistate minimal path vectors algorithm (another important method of calculating MFN reliability).

Resources scarcity and environmental degradation have made sustainable resource utilization and environmental protection necessary worldwide. The development of the circular economy is considered an approach for more appropriate economic and environmental management. This work introduces a cooperative game network data envelopment analysis model for evaluating the implementation effect of recycling production systems from a closed loop and centralized control perspective. The factor efficiency analysis of the involved inputs and outputs is presented to provide guidance for the factor dominance of subsystem efficiencies. An application for assessing the circular economy of EU countries is provided to illustrate the validation of the proposed method. Our results show that the average performance of the production subsystem is superior to that of the recycling subsystem in EU countries. Furthermore, factor efficiency analysis reveals that the inefficient environmental treatment input is the culprit in worse performance of the recycling subsystem. A comparison of the proposed method with recent studies for circular economy performance evaluation is also included.

In this paper, a novel approach combining fuzzy data envelopment analysis (DEA) and the analytical hierarchical process (AHP) is proposed to rank units with multiple fuzzy criteria. The hybrid fuzzy DEA/AHP approach derives the AHP pairwise comparisons by fuzzy DEA and utilizes AHP to fully rank units. It shows that the proposed approach generates a logical ranking of units that has perfect compatibility with fuzzy DEA ranking and there is no any form of subjective analysis engaged within the methodology. A study on the facility layout design in manufacturing systems is provided to illustrate the superiority of the proposed approach and show the compatibility between the proposed approach and fuzzy DEA ranking.

Resources scarcity and environmental degradation have made sustainable resource utilization and environmental protection worldwide. A circular economy system considers economic production activities as closed-loop feedback cycles in which resources are used sustainably and cyclically. Improving the eco-efficiency of the circular economy system has both theoretical value and practical meaning. In this work, the efficiency measurement model of the circular economy system with imprecise data based on network data envelopment analysis is proposed. The two-level mathematical programming approach is employed for measuring the system and process efficiencies. The lower and upper bounds of the efficiencies scores are calculated by transformed conventional one-level linear programs so that the existing solution methods can be applied. The proposed method is applied to assess the circular economy system of EU countries. Our results show that most countries have large difference among fuzzy efficiencies between the production efficiency and recycling efficiency stages, which reveals the source that causes the low efficiency of the circular economy system.

Network data envelopment analysis (DEA) concerns using the DEA technique to measure the relative efficiency of a system, taking into account its internal structure. The results are more meaningful and informative than those obtained from the conventional DEA models. This work proposed a new network DEA model based on the fuzzy concept even though the inputs and outputs data are crisp numbers. The model is then extended to investigate the network DEA with fuzzy non-discretionary variables. An illustrative application assessing the impact of information technology (IT) on firm performance is included. The results reveal that modeling the IT budget as a fuzzy non-discretionary factor improves the system performance of firms in a banking industry.