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The United Nations' sustainable development goals have highlighted the significance of improving supply chain sustainability and ensuring the proper distribution of orders. This study proposes a novel framework involving Z-number, game theory, an indifference threshold-based attribute ratio analysis (ITARA), and a combined compromise solution method (CoCoSo) to evaluate the sustainability of suppliers and order allocations. To better reflect the decision makers' current choices for the sustainability of assessed suppliers and order allocations and enhance the comprehensiveness of decision-making, the importance parameter of the supplier is obtained through game theory objectively for transforming supplier performance into order allocation performance. The Z-numbers are involved in ITARA (so-called ZITARA) and CoCoSo (so-called ZCoCoSo) to overcome the issue of information uncertainty in the process of expert evaluation. ZITARA and ZCoCoSo are used to determine the objective weights of criteria and to rank the evaluated order allocations, respectively. A case study of a China company is then presented to demonstrate the usefulness of the proposed framework and to inform their decision-making process regarding which suppliers the orders should be assigned to. [ABSTRACT FROM AUTHOR]

A stochastic cold chain (SCC) is a common supply chain in real life that emphasizes the need for commodities to arrive fresh within time constraints. In previous research on supply chains, the time factor was regarded as a fixed number. However, the travel time is a stochastic factor due to traffic and weather conditions during the delivery. Therefore, this paper concentrates on the two multi-state factors simultaneously. Network reliability is one of the performance indexes used to assess the cold chain efficacy, defined as the probability that the flow of SCC can satisfy the demand within the delivery time threshold. The SCC with two multi-state factors is modeled as a stochastic cold chain network with multi-state travel time (SCCNMT). To calculate the network reliability of an SCCNMT, we will calculate the demand reliability and time reliability separately, treating them as independent events, and multiply the demand and time reliability to estimate the network reliability of the two multi-state factors. [ABSTRACT FROM AUTHOR]

In the container shipping industry, a company could have an advantage over its competitors while its liner container shipping system (LCSS) can successfully transport the requested demand. However, some uncertainties such as unstable sea state, terrible weather, sailor's negligence, and the condition of vessels would affect the number of slots on the vessel to place containers when shipping on different legs. Thus, that number should be regarded as stochastic. At the container terminal, containers are loaded from and unloaded to the vessel ship by the quay cranes. The number of available quay cranes at each terminal is also stochastic because of the reservation of other competitors. Therefore, this study proposes an algorithm that constructs an LCSS as a stochastic liner container shipping network (SLCSN) model to analyze the network reliability. Network reliability is defined as the probability that all vessels in the SLCSN can satisfy the demands within the time threshold. For an executive of the liner container shipping company, the network reliability can be utilized as the performance indicator to make an appropriate managerial decision. [ABSTRACT FROM AUTHOR]

Real-world systems, such as manufacturing or computer systems, can be modeled as multistate network (MSN) consisting of arcs with stochastic capacity. Network reliability for an MSN is described as the probability that the system can meet the demand. The network reliability for demand level d can be computed in terms of the minimal path (calledd-MP). However, efficiently calculating network reliability is challenging in large-scale networks. Deep learning approaches are rapidly advancing several areas of technology, with significant applications in image recognition, parameter adjustment, and autonomous driving. Hence, in this study, we adopt a deep neural network (DNN) model to predict network reliability for a given demand level. To train the DNN model, network information is first used as input data. Then, a DNN model is constructed, including the determination of related functions. Furthermore, Bayesian optimization (BO) is applied to determine related hyperparameters. A practical implementation using a bridge network demonstrates the feasibility of the DNN model. Finally, experiments involving two networks with more nodes and arcs indicate the computational efficiency of combining deep learning methods and the existing d-MP algorithm. [ABSTRACT FROM AUTHOR]