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Machine configuration is a crucial strategic decision in designing a flow shop system (FSS) and directly affects its performance. This involves selecting device suppliers and determining the number of machines to be configured. This study addresses a bi-objective optimization problem for an FSS that considers repair actions and aims to determine the most suitable machine configuration that balances the production reliability and purchase cost. A nondominated sorting genetic algorithm II (NSGA-II) is used to determine all the Pareto solutions. The technique for order preference by similarity to an ideal solution is then used to identify a compromise alternative. It is necessary to assess the production reliability of any machine configuration identified by the NSGA-II. The FSS under the machine configuration is modeled as a multistate flow shop network, and Absorbing Markov Chain and Recursive Sum of Disjoint Products are integrated into the NSGA-II for reliability evaluation. The experimental results of solar cell manufacturing demonstrate the applicability of the proposed hybrid method and validate the efficiency of the NSGA-II compared with an improved strength Pareto evolutionary algorithm. [ABSTRACT FROM AUTHOR]

Network reliability, named multistate stochastic cloud/edge-based network (MCEN) reliability afterwards, is defined as the probability that demands can be satisfied for an MCEN. It can be regarded as a performance indicator of the MCEN to measure the service capability. The concept of existing algorithms is to produce all of minimal system-state vectors for calculating MCEN reliability. However, such concept cannot response MCEN reliability in time when the MCEN scale becomes complicated in the Industry 4.0 environment. For providing MCEN reliability for decision making immediately, an architecture of a deep neural network (DNN) is developed to propose a prediction model for MCEN reliability such that MCEN capability with varied data can be learned promptly. To train the reliability prediction model, MCEN information is transformed to the suitable format, and the related information for DNN setting, including the determination of related functions, are defined with appropriate hyperparameters by using Bayesian Optimization. An illustrative case and a practical case of Amazon Web Service are provided to demonstrate the prediction model for MCEN reliability to show the availability and the efficiency. [ABSTRACT FROM AUTHOR]

A stochastic flow network composed of multistate arcs can be utilized to describe several practical systems such as computer networks, where transmission time taken for sending data to a sink is an important index. Determining a path with minimum transmission time is known as the quickest path problem (QPP). All algorithms addressing the QPP assume that the determined minimal paths (MPs) are disjoint. Further, for the general case of intersectional MPs, if a congestion phenomenon occurs during the transmission process, these algorithms will lead to an incorrect outcome. Moreover, in practical scenarios, as a budget limit is considered, spare routing is applied to consolidate the system. The objective is to develop an algorithm based on Monte Carlo simulations (MCSs) for evaluating the system reliability while considering the congestion phenomenon. The system reliability is the probability that a specific amount of data can be transmitted successfully through multiple MPs under both time and budget constraints. Furthermore, spare routing to increase the system reliability is established in advance to specify the main and spare MPs. Experiments validate the evaluation of system reliability based on MCSs. The credibility and efficiency of the proposed algorithm are also discussed. [ABSTRACT FROM AUTHOR]

Searching for minimal path vectors (MPVs) is an important topic in solving network related problems, especially for the evaluation of network reliability. One of the popular approaches, namely the three-stage method (TSM), is influenced deeply on the efficiency of searching for minimal path vectors in multi-state networks (MSN). TSM consists of three stages, i.e., searching for all minimal path sets, searching for all MPVs, and calculating union probability on MPVs. After reviewing previous works in the literaure, this paper proposes a more efficient method based on cyclic check on the candidates of MPVs, which can do an efficient searching for MPVs in MSNs and even reduce the three-step approach to two-step approach. Benchmarking with the well-known algorithms are made in this paper, and more complicated networks are also examined for verification of the proposed method. [ABSTRACT FROM AUTHOR]

Recently, taking more than one means of transportation to work or to deliver goods has become common for citizens in big cities or logistics companies. A transport system that contains various transport means is called a multimodal transport system. In each route, there is carrier: airline, railway or bus company who has contracted to carry passengers with a specific schedule. As each carrier may have other customers, the number of passengers that it can serve is stochastic. Hence, this study formulates a stochastic multimodal transport network (SMTN) to model a multimodal transport system. The transfer time and fee are necessary when changing the means of transportation. This study proposes a complete algorithm to evaluate the reliability of the SMTN that is the probability that the requested number of passengers can be sent successfully from the origin to the destination under time and budget constraints. Since time and budget are the passengers considered most before traveling, the reliability in this study evaluates the SMTN regarding meeting travel demand and passengers' requirements simultaneously. A case study of a travel agent is presented to demonstrate the solution procedure. [ABSTRACT FROM AUTHOR]

In this paper, a modern computer network, cloud-based network, which comprises internet of things (IoT), edge servers, and cloud servers for data transmission, is investigated and evaluated. A cloud-based network is modeled as a graph having a set of nodes and a set of links. Each link represents a transmission route, and each node represents a device, such as an IoT device, edge server, and cloud server. In practical, a transmission route comprises several physical lines or virtual channels. Each physical line (virtual channel) may provide a capacity or may fail to imply several and stochastic states. Such a cloud-based network is called a stochastic flow cloud-based network (SCN) herein. System reliability for an SCN is then evaluated. It is defined as the probability of the data being successfully transmitted through the SCN under edge server capacity and budget constraints. The SCN is modeled firstly in order to elucidate the flow relationship among the whole system; capacity limitation of the edge servers and costs of data transmission/process are also considered. Subsequently, we conclude an algorithm to evaluate system reliability. Supervisors can manage the SCN based on system reliability which presents the system capability with capacity and budget consideration. [ABSTRACT FROM AUTHOR]

Network reliability is famous for its problem solving ability in several real-life applications. However, due to its NP-hard nature (Ball in IEEE Trans Reliab 35(3):230–238, 1986), researchers are devoted to the improvement of computational efficiency in various approaches. Although flow in networks depicts its combination properties, only few of them are useful in the calculation of network reliability. In some point of views, we call it mining in flow data. This paper presents techniques of how to efficiently do the flow data mining tasks. A skill based on backtrack and maximal flow is illustrated with examples and benchmarks. The results show that the proposed approach is valuable in the calculation of network reliability. [ABSTRACT FROM AUTHOR]

Correlation can seriously degrade reliability and capacity due to the simultaneous failure of multiple components, which lowers the probability that a system can execute its required functions with acceptable levels of confidence. The high cost of fault in time-critical systems necessitates methods to explicitly consider the influence of correlation on reliability. This paper constructs a network-structured model, namely time-constrained multi-state network (TCMSN), to investigate the capacity of a computer network. In the TCMSN, the physical lines comprising the edges of the computer network experience correlated faults. Our approach quantifies the probability that d units of data can be sent from source to sink in no more than T units of time. This probability that the computer network delivers a specified level of data before the deadline is referred to as the system reliability. Experimental results indicate that the negative influence of correlation on reliability could be significant, especially when the data amount is close to network bandwidth and the time constraint is tight. The modeling approach will subsequently promote design and optimization studies to mitigate the vulnerability of networks to correlated faults. [ABSTRACT FROM AUTHOR]

Amidst the rising global recognition of sustainability and the United Nations' sustainable development goals, enhancing the sustainability of the supply chain while properly distributing orders has become a key point. In contrast to the previous research, this research involves supplier sustainability in reliability evaluation and proposes a new algorithm for computing reliability. In the constructed supply chain network, a node represents a supplier, assembly plant, or customer, and an arc connecting the nodes. For each arc, it has a carrier whose available carrying capacity for demand transmission. The capacity of each carrier, represented by the available delivery containers, should not be deterministic as they may be partially reserved by other customers. Under these conditions, such a supply chain network is regarded as a stochastic supply chain network (SSCN). The reliability for an SSCN is defined as the probability that the SSCN can successfully transport a specific amount of goods to a customer under supplier sustainability level, supplier production capacity, and budget. Reliability is also regarded as a performance indicator for supply chain capability when managers makes decisions under supplier sustainability consideration. [ABSTRACT FROM AUTHOR]

In last decades, air transportation plays an important role in global economy. Several scholars have studied optimizing air transportation system or proposed reliability evaluation algorithms from airline management viewpoints. This work evaluates the reliability of an air transportation system from the perspective of travel agency instead. An air transportation system can be modeled as a multi-state air transportation network (MATN) wherein each node represents an airport and each arc denotes a flight carrying passengers between a pair of airports from scheduled departure time to scheduled arrival time. Significantly, this study focuses on investigating the reliability of multiple travel demands. Therefore, the reliability of an MATN is defined as the probability that a set of demands can be carried successfully under constraints of time and number of stopovers. This study employs the concept of minimal paths in reliability evaluation. Subsequently, a searching procedure is added to the proposed algorithm. In addition, an illustrative example and a case study are utilized to demonstrate the proposed algorithm and discuss the implications of reliability evaluation for the management of travel agency. [ABSTRACT FROM AUTHOR]

In an intermodal logistics network, there is a carrier along each route whose capacity (number of available containers) is stochastic because the containers may be occupied by other customers. Hence this paper focuses on single commodity in a stochastic intermodal logistics network (SILN) with cargo terminals, transit stations, and routes. In particular, commodities may rot or be spoilt during delivery due to traffic accidents, collisions, natural disasters, weather, etc., and thus the intact commodities may not satisfy the market demand. The arrival time at the cargo terminal should be in the time window which is the interval between the earliest and latest acceptable arrival times. The delivery time depends on the number of containers and type of vehicle. So we propose an algorithm to evaluate the network reliability, the probability that the SILN can successfully deliver sufficient amount of commodity to meet market demand under the time and delivery spoilage constraints. Finally, a practical case of starting motor distribution between Taiwan and China is presented to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Background: This study examined the association between methylenetetrahydrofolate reductase ( MTHFR) polymorphisms and survival of patients with colorectal cancer (CRC) treated with 5-fluorouracil (5-FU)-based chemotherapy in Taiwan. Methods: We genotyped MTHFR polymorphisms C677T (rs1801133) and A1298C (rs1801131) for 498 CRC patients treated with 5-FU-based chemotherapy after receiving surgery. Survival analyses on MTHFR polymorphisms were performed using log-rank test and Kaplan-Meier curve. Cox proportional hazards models were used to calculate the hazard ratios (HRs) and 95% confidence intervals (CIs) for the association between MTHFR genotypes and survival. Results: Overall survival (OS) was significantly longer in CRC patients with MTHFR 677 CT+TT genotypes compared with those with 677 CC genotype (HR 0.77; 95% CI 0.60-0.98). Although the MTHFR A1298C polymorphism was not associated with OS in CRC, this polymorphism was associated with significantly shorter OS in rectal cancer. Among rectal cancer patients, OS was shorter for patients with AC+CC genotypes than for those with the AA genotype (HR 1.95; 95% CI 1.35-2.83). In haplotype analysis, better OS was found for colon cancer patients carrying the MTHFR 677T-1298A haplotype (HR 0.73; 95% CI 0.55-0.97), but worse survival was linked to rectal cancer patients carrying the MTHFR 677C-1298C haplotype (HR 1.53; 95% CI 1.08-2.18). Conclusions: Our findings suggest that MTHFR genotypes provide prognostic information for CRC patients treated with 5-FU-based chemotherapy. [ABSTRACT FROM AUTHOR]

In recent years, the system maintenance service has been transitioning from the resource-based contract (RBC) approach towards a new outcome-based contract (OBC) approach, enabling better profits for the service provider and lower cost and risk equilibrium for the service buyer. Prior studies usually focus on a single criterion as a service outcome for a complex and repairable system. This paper proposes a novel risk equilibrium OBC model with a given multi-outcome in maintenance service. The proposed model solves the multi-criteria obligation problem in a complex repairable system maintenance service to achieve three objectives: searching for a dominant risk equilibrium and inner cost, attaining the system's expected outcome, and controlling the multi-outcome and risk equilibrium. The proposed model can apply to disparate maintenance policies comprising various preventive and corrective maintenance methods. Furthermore, the proposed model presents a comparative mechanism to different contract types by game-theoretical analysis, which leads to a first-best solution and avoids moral hazard problems. The case study shows that the proposed OBC model forms a game-theoretical equilibrium for both parties, ensuring the risk equilibrium with the optimal cost. [ABSTRACT FROM AUTHOR]

In many real-time networks such as computer networks, each arc has stochastic capacity, lead time, and accuracy rate. Such a network is named a multi-state computer network (MSCN). Under the strict assumption that the capacity of each arc is deterministic, the quickest path (QP) problem is to find a path that sends a specific amount of data with minimum transmission time. From the viewpoint of internet quality, the transmission accuracy rate is one of critical performance indicators to assess internet network for system administrators and customers. Under both assured accuracy rate and time constraint, this paper extends the QP problem to discuss the flow assignment for a MSCN. An efficient algorithm is proposed to find the minimal capacity vector meeting such requirements. The system reliability, the probability to send $$d$$ units of data through multiple minimal paths under both assured accuracy rate and time constraint, can subsequently be computed. Furthermore, two routing schemes with spare minimal paths are adopted to reinforce the system reliability. The enhanced system reliability according to the routing scheme is calculated as well. The computational complexity in both the worst case and average case are analyzed. [ABSTRACT FROM AUTHOR]

This paper focuses on developing a network model to evaluate supply-chain reliability for the brittle commodity logistics, in which the network is composed of branches and vertices. A vertex denotes a supplier, a transfer center, or a customer and a branch connecting a pair of vertices denotes a carrier. In the brittle commodity logistics network, each supplier has limited production capacity and the production cost is counted in terms of the number of the provided goods. Moreover, the delivery capacity (e.g. number of containers) provided by any carrier is multistate because the partial capacities may be reserved for other customers, and the delivery cost is counted in terms of the consumed delivery capacity. In the brittle commodity delivery, the goods may be damaged by natural disasters, traffic accidents, collisions, and so on, such that the intact goods can not satisfy the customer demand. Hence the delivery damage should be considered while evaluating the performance of a logistics network. This paper proposes the supply-chain reliability, which is defined as the probability of the network to successfully deliver goods to the customer with the delivery damage, limited production capacity, and budget considerations, to be a performance index. In terms of minimal paths, an algorithm is developed to evaluate the supply-chain reliability. A practical case of flat glass logistics is employed to discuss the management implications of the supply-chain reliability. [ABSTRACT FROM AUTHOR]

To maintain a reliable computer network is now a challenge in our daily business operations especially when the transmission budget is limited. A computer network usually consists of transmission lines and transmission facilities, both of which may suffer failure, partial failure, or be in maintenance. Such a computer network is called a stochastic-flow network, since both kinds of resources are stochastic in nature. The problem of double resource optimization for a robust computer network subject to a transmission budget (DROCNTB) is to search for the exact minimum double-resource assignments under transmission-budget constraint such that the computer network keeps survived even under both kinds of failures. This paper develops an efficient algorithm to search for the exact optimal assignment for the DROCNTB problem. Several benchmark examples are explored and compared. The results show that the proposed algorithm is very efficient. [ABSTRACT FROM AUTHOR]

This paper studies the reliability evaluation of a stochastic manufacturing system with multiple production lines in parallel. Multiple repairs and different failure rates, never simultaneously addressed in earlier works, are taken into account. First, a revised graphical methodology integrating transformation and decomposition is utilized to construct the stochastic manufacturing system as a multi-state manufacturing network (MSMN). In particular, a 'predecessor-set' technique is proposed to deal with multiple repairs. An algorithm is proposed to generate the lowest capacity vectors (LCVs) that stations should provide to satisfy the workloads. Subsequently, the system reliability of the MSMN, which is defined as the probability of demand satisfaction, is calculated in terms of the LCVs. A real case of a printed circuit board manufacturing system is utilized to demonstrate how the system reliability can be evaluated. A further decision making issue is addressed based on the derived system reliability. [ABSTRACT FROM AUTHOR]

From the viewpoint of service level agreements, the transmission accuracy rate is one of critical performance indicators to assess internet quality for system managers and customers. Under the assumption that each arc's capacity is deterministic, the quickest path problem is to find a path sending a specific of data such that the transmission time is minimized. However, in many real-life networks such as computer networks, each arc has stochastic capacity, lead time and accuracy rate. Such a network is named a multi-state computer network. Under both assured accuracy rate and time constraints, we extend the quickest path problem to compute the probability that d units of data can be sent through multiple minimal paths simultaneously. Such a probability named system reliability is a performance indicator to provide to managers for understanding the ability of system and improvement. An efficient algorithm is proposed to evaluate the system reliability in terms of the approach of minimal paths. [ABSTRACT FROM AUTHOR]

With the development of information technology, the cloud computing system (CCS) has become a new paradigm for the business and clients. The system supervisor has to guarantee the CCS keeps a good quality of service (QoS) to satisfy the clients' requirements. The maintenance action is thus necessary when the CCS falls to a specific state such that it cannot afford enough capacity to meet demand d. In order to measure the service level of a CCS, this paper constructs a network model and proposes a key performance indicator (KPI), where the KPI is utilized to evaluate the probability that the demand can be satisfied under both transmission time and maintenance budget constraints. A method to derive the interval estimation for the KPI is developed. The system supervisor can conduct the sensitive analysis to improve/investigate the most important part in a large CCS afterwards. [ABSTRACT FROM AUTHOR]

This paper proposes a graphical-based methodology to evaluate the performance of a manufacturing system in terms of network model. We focus on a manufacturing system which consists of multiple distinct production lines. A transformation technique is developed to build the manufacturing system as a manufacturing network. In such a manufacturing network, the capacity of each machine is multistate due to failure, partial failure, or maintenance. Thus, this manufacturing network is also regarded as a multistate network. We evaluate the probability that the manufacturing network can meet a given demand, where the probability is referred to as the system reliability. A simple algorithm integrating decomposition technique is proposed to generate the minimal capacity vectors that machines should provide to eventually satisfy demand. The system reliability is derived in terms of such capacity vectors afterwards. A practical application in the context of IC card manufacturing system is utilized to demonstrate the performance evaluation procedure. [ABSTRACT FROM AUTHOR]

From the viewpoint of service level agreements, data transmission accuracy is one of the critical performances for assessing Internet by service providers and enterprise customers. The stochastic computer network (SCN), in which each edge has several capacities and the accuracy rate, has multiple terminals. This paper is aimed mainly to evaluate the system reliability for an SCN, where system reliability is the probability that the demand can be fulfilled under the total accuracy rate. A minimal capacity vector allows the system to transmit demand to each terminal under the total accuracy rate. This study proposes an efficient algorithm to find all minimal capacity vectors by minimal paths. The system reliability can then be computed in terms of all minimal capacity vectors by the recursive sum of disjoint products (RSDP) algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm to evaluate estimated and exact system reliabilities for a computer network in the cloud computing environment. From the quality of service (QOS) viewpoint, the computer network should be maintained when falling to a specific state such that it cannot afford enough capacity to satisfy demand. Moreover, the transmission time should be concerned as well. Thus, the data can be sent through several disjoint minimal paths simultaneously to shorten the transmission time. Under the maintenance budget B and time constraint T, we evaluate the system reliability that d units of data can be sent from the cloud to the client through multiple paths. Two procedures are integrated in the proposed algorithm-an estimation procedure for estimated system reliability and an adjusting procedure utilizing the branch-and-bound approach for exact system reliability. Subsequently, the estimated system reliability with lower bound and upper bound, and exact system reliability are computed by applying the recursive sum of disjoint products (RSDP) algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with a stochastic-flow network in which each node and arc has a designated capacity, which will have different lower levels due to various partial and complete failures. We try to evaluate the probability that the maximum flow of the network is equal to the demand d without exceeding the budget B. Such a probability is treated as a performance index to measure the quality level of the network. A simple algorithm in terms of minimal cuts is first proposed to generate all upper boundary points for ( d, B), and then the probability that the maximal flow is less than or equal to d can be calculated in terms of such points. The upper boundary point for ( d, B) is a maximal vector, which represents the capacity of each component (arc or node), such that the maximum flow of the network under the budget B is d. The performance index can be calculated by repeating the proposed algorithm to obtain all upper boundary points for ( d−1, B). A computer simulation example is shown to illustrate the solution procedure. [ABSTRACT FROM AUTHOR]

This special issue of the Annals of Operations Research is related to the Asia–Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM 2016), held during 24–26 August 2016, at the Hanyang University, Seoul, South Korea. It focuses on new international research in theoretical and related applications to solve quality management problems. Reliability and quality management are quite important in many practical stochastic systems, such as computer systems, logistic systems, production systems, and the like. Developing and applying operations research methods to measure the robustness and to solve the engineering problem of a stochastic system is indeed a crucial task, enabling the system manager to carry out improvements after measuring the stochastic system. [ABSTRACT FROM AUTHOR]

A manufacturing system with reworking actions is constructed as a stochastic-flow manufacturing networks (SFMN) because components (arcs and nodes) are with multi-state capacity. Network reliability is a useful indicator of the performance of an SFMN. It is defined as the probability that that a SFMN can satisfy a given demand. However, the network scale becomes complex in the environment of Industry 4.0 and big data context. The algorithm YKLIN (Lin and Chang in Computers & Industrial Engineering 63:1209–1219, 2012b) cannot calculate network reliability in time for those large cases. For responding network reliability immediately, this paper utilizes an architecture of a deep neural network (DNN) to propose a prediction model for network reliability evaluation. The proposed prediction model can estimate network reliability with a small error (root-mean-square error (RMSE) = 0.0022) in the numerical case. Furthermore, compared to the algorithm YKLIN, the computational time is significantly reduced for a large tile manufacturing system with 14 production lines. In detail, the algorithm YKLIN takes 56.78 s for evaluating network reliability of each data point, whereas the proposed model only takes 0.02 s. The proposed DNN model provides a feasible and efficient approach to achieve network reliability immediately for the real-world manufacturing system in the industry 4.0 environment. [ABSTRACT FROM AUTHOR]

Casualty rescue is always a critical issue in emergency departments when the buildings collapsing, bridges or roads damaged happen in the earthquakes. However, previous studies essentially considered such a problem by assuming fixed travel time for the ambulance. This paper aims to involve road failure during the earthquake by considering the stochastic durations for each road. The probability that the casualty can be successfully rescued to the casualty collection point (CCP) provides further medical treatment for the casualties. Such a probability is named network reliability which is defined as the probability that the number of casualties can be successfully transported to the CCP in a given rescue time. To evaluate the network reliability, the data transformation procedure is firstly developed to convert the road data into duration probability table, which addresses the travel time and corresponding probability of each road. Second, the multi-state rescue network is established, and an algorithm is constructed to obtain all upper bound vectors meeting the demand and time constraint. The network reliability can be computed by obtained upper bound vectors using the recursive sum disjoint product method. An example of a real earthquake disaster in Tainan City, Taiwan is adopted to demonstrate the practicality of the proposed algorithm. Finally, the experimental results with different number of ambulances and times can provide the commander decision recommendations for immediate emergency responses. [ABSTRACT FROM AUTHOR]