Minimal Capacity Vectors Research Articles

Investigate exact reliability under limited time and space of a multistate online food delivery network

In recent years, especially during the outbreak of COVID-19, there have witnessed the emergence of online food delivery (OFD) services that allow customers to place orders via Internet-connected devices to obtain door-to-door delivered meals. In this service, on-time delivery to the right customer with high-quality fresh meals is deemed the primary factor. This paper investigates the reliability of OFD through its ability to meet customer needs in a specific context. During the delivery process, the courier receives the food at the store, packs it into a delivery box, and then delivers it to the customer. Note that, the delivery boxes are limited in space. Customers prefer having their orders delivered within a given time threshold. Thus, reliability is defined as the probability to complete non-integer and multiple orders under a limited time and space. Besides, the OFD system belongs to the gig economy, which allows couriers to select their shifts and working regions. Hence, the capacity of each region, which indicates the number of available couriers, is regarded as multistate. We, thus, construct the OFD system as a multistate online food delivery network (MOFN). Under the limitation of time and space, all feasible minimal capacity vectors are determined to compute the reliability. With the proposed investigation, managers can understand their MOFN’s ability to meet specific customer demands. Accordingly, they can make appropriate adjustments for better performance.

A multi-state network to evaluate network reliability with maximal and minimal capacity vectors by using recursive sum of disjoint products

This paper applies a multi-state network (MSN) model with multi-state capacity to evaluate network reliability with both maximal and minimal capacity vectors for real-life applications. To be specific, the proposed MSN model can be embedded in the practically related expert systems, especially in project networks, manufacturing, and supply chain. In the early works, the estimated network reliability with maximal and minimal capacity vectors and the exact value for the MSNs were measured based on an interval approach and inclusion and exclusion (IE) principle, respectively. Owing to the computational inefficiency, the early works are inappropriate to be integrated into practical expert systems. In this paper, a more efficient procedure based on the sum of disjoint products (SDP) principle calculates the exact network reliability. Additionally, a recursive function with simplified processes is developed to achieve the efficiency of reliability evaluation. By using a practical project network case with several numerical experiments, efficiency investigation reveals that the SDP-based procedure outperforms the IE-based approach in terms of efficiency under all the experiments. The proposed SDP-based procedure can achieve over 30 times (and reach up to 5,000 times) faster than the IE-based approach. That is, based on the proposed procedure, the reliability evaluation of practical applications such as project management can be implemented.

Network reliability evaluation for multi-state computing networks considering demand as the non-integer type

A multi-state computing network (MSCN) consists of multi-state edges such that the performance levels of the MSCN might differ. Network reliability is concerned with the probability that the predetermined demand from multiple sources can be successfully transmitted through the network. One of the major methods for efficiently calculating network reliability is to generate all minimal capacity vectors (MCVs), which represents the minimal capacity required for each edge. Every MCV is transformed from the flow vectors satisfying predetermined demands based on the minimal paths (MPs). In general, the amount flows were set as integers for flow vector generation in previous studies. In fact, the amount of data might be the non-integer type (such as 2.4Gbps) in the practical data transmission. An algorithm with a new approach for flow vector generation is developed to efficiently deal with demand as the non-integer type with any transmission unit such that the search spaces of the flows are stable. The experimental results of numerical examples and a practical case show that the proposed algorithm is more effective and efficient than the approaches in the literature.

Reliability Evaluation of Production System With In-Line Stockers

A reliability evaluation method is proposed for production systems by applying the capacitated-flow production network (CFPN) model. In particular, this article considers in-line stockers to monitor and to avoid blockage and starvation in the CFPN. First, the minimal capacity that all cells (group of machines) should provide to meet demand is generated. Second, status of stocker is monitored via the proposed “stocker volume check table” to calculate the volume usage of a stocker, and the stocker nonutilization is then obtained. Finally, the system reliability is derived in terms of the minimal capacity vector and stocker nonutilization. An important contribution of this article is to avoid complicated dependency calculation when multiple stockers are considered. A practical case of printed circuit board production is further studied to illustrate the applicability of the proposed method.

System Reliability Assessment of a Fast Retransmit Through ${k}$ Separate Minimal Paths Under the Latency

A fast retransmit, which reduces the sender’s waiting time before retransmitting a lost segment, is applied to guarantee data integrity with no data loss in transmission. Based on fast retransmit, many application protocols have been enhanced and evolved to ensure quality of service and reduce data transmission time. One of application protocols is the multipath transmission control protocol which is catholically applied in modern computer networks. Communication lines used in this kind of network have different states, namely, failure, partial failure, and maintenance. Therefore, a computer network with a fast retransmit can be classified as stochastic and is called a stochastic-flow computer network with a fast retransmit (SCNFR). This paper assesses the system reliability of SCNFR for the successful transmission of demand d through ${k}$ ( ${k} \,\, >1$ ) separate minimal paths ( ${k}$ SMiP) under the latency. An algorithm is proposed to find all minimal capacity vectors (MCVs) that satisfy the demand and latency. Then, the system reliability is computed based on all MCVs. We adopt two practical cases of the pan-European research and education network and the Taiwan academic network to explore the effectiveness of the algorithm. The results show that the system reliability can be classified as decision reference while the manager decides the better ${k}$ SMiP with higher system reliability.

System reliability for a multi-state distribution network with multiple terminals under stocks

To achieve the most efficiency in supply chain management, the capability of distribution networks is a key point for the entire supply chain. Stocks are critical for enhancing the efficiency of satisfying the demand of retailers in the distribution network. A configuration of a distribution network is consisted of routes and nodes. Each route connects a pair of nodes and each node is denoted as a supplier, a distribution center, or a retailer. For each route, it has a carrier whose available capacity for demand transmission is multi state. Hence, a distribution network is also regarded as a multi state network and such a network is named as a multi state distribution network (MDN) in here. The propose of this paper is to evaluate the system reliability which is defined as the probability that the MDN can meet all retailers’ demand under stocks. In practical, all retailers’ demand should be satisfied by stocks in the distribution centers (DCs) firstly. Therefore flow assignment in MDN model is mainly clarified by the relationship between the demand of retailers, stocks on DCs, and suppliers. The concept of minimal capacity vectors (MCVs) is then proposed and an algorithm is developed to obtaining MCVs for evaluating system reliability.

A novel minimal cut-based algorithm to find all minimal capacity vectors for multi-state flow networks

Real systems, such as computer systems, can be modeled as network topologies with vertices and edges. Owing to equipment failures and maintenance requirements, the capacities of edges have several states. Such systems are regarded as multi-state flow networks (MSFN). System reliability of an MSFN is the probability that the required flow (i.e., demand) can successfully be sent from the source to the sink. By adopting a minimal path (MP) approach, system reliability can be computed in terms of all minimal capacity vectors meeting the demand d. A minimal capacity vector is called a d-MP. Although several algorithms have been presented in the literature for finding all d-MP, improving efficiency in the search for all d-MP is always a challenge. A group approach with both the concepts of minimal cut and MP is developed in this study, narrowing the search range of feasible flow vectors. An algorithm based on the group approach is then proposed to improve the efficiency of the d-MP search. According to the structure of the proposed algorithm, parallel computing can be implemented with significant improvement in the efficiency of the d-MP generation, where the proposed algorithm is compared with previous ones based on three benchmarks, in terms of CPU time.

Reliability evaluation of a multistate flight network under time and stopover constraints

Abstract From the management perspective, network reliability is a crucial indicator to evaluate the service performance of many real-life networks. This research, therefore, focused on investigating network reliability in the airline industry and proposed an algorithm of evaluating flight network reliability of a multistate flight network (MSFN) considering the time and the number of stopovers. An MSFN is composed of nodes and arcs, in which each node denotes an airport and each arc represents a flight which connects a pair of nodes at fixed departure and arrival time. Flight network reliability is defined as the probability of successfully carrying a certain number of passengers from the origin to the final destination under the constraints of time and the number of stopovers. We first model the flight system into an MSFN and then generate all minimal capacity vectors that can satisfy demand under the time and stopovers constraints. Significantly, this study developed a searching method instead of giving all minimal flightpaths in advance and computed flight network reliability efficiently based on all the minimal capacity vectors. A case study from Ho Chi Minh City to Taipei is presented to demonstrate the solution procedure. The findings from this study are convinced to contribute equivalent information to policymakers and airlines executives for their strategic decision-making regarding flight network and thereby contribute to advancement towards sustainability.

Reliability with finite buffer size for a multistate manufacturing system with parallel production lines

This study examines system reliability for a manufacturing system with parallel production lines by creating a model of a multistate manufacturing system (MMS). System reliability is defined as the probability of demand satisfaction, which reflects the probability that the current capacity state of the MMS can successfully process a given demand. In particular, a buffer station with a finite size is taken into consideration to avoid blockage and starvation in the MMS. To the best of our knowledge, there is no existing research that considers a finite buffer size in a model of an MMS with parallel production lines. This study proceeds through the following phases. (i) In the model construction phase, the amount of input material, workload, and minimal capacity required by each workstation to satisfy a given demand level are studied by flow analysis; subsequently, a buffer usage matrix (BUM) is proposed to calculate buffer reliability. (ii) In the performance evaluation phase, system reliabilities with both infinite and finite buffer sizes are derived in terms of both minimal capacity vector and buffer reliability. (iii) In the case demonstration phase, two examples are utilized to illustrate the proposed method. Results of both examples show that the system reliability is overestimated with an infinite buffer size.

Data transmission reliability evaluation of a stochastic computer network through minimal paths with a retransmission mechanism

Multipath Transmission Control Protocol is a new networking protocol which can allow data transmission and retransmission across multiple minimal paths. It can reduce data transmission time and ensure data integrity. In computer networks, the capacity of each arc should be considered as stochastic because there are different situations such as failures, partial failures, and maintenance. This article focuses on a stochastic retransmission flow network to evaluate data transmission reliability that the data can be transmitted successfully through multiple minimal paths within transmission time threshold. We first propose an algorithm to generate all minimal capacity vectors satisfying both constraints and requirements and to obtain data transmission reliability. A numerical example and a large-scale case study of the Pan-European Research and Education Network are presented to illustrate the algorithm.

Reliability Evaluation of a Multi-state Network with Multiple Sinks under Individual Accuracy Rate Constraint

From the viewpoint of service level agreements (SLAs), Internet service providers and customers are gradually focusing on transmission accuracy. The Internet service provider should provide the specific bandwidth and individual accuracy rate requirement by their SLAs to each customer. This paper mainly evaluates the system reliability that a stochastic computer network can fulfill all requirements at all sinks. An efficient algorithm is proposed to generate the lower boundary points, minimal capacity vectors satisfying the demand and accuracy rate requirement for all sinks. The system reliability can be computed in terms of such points by applying recursive sum of disjoint products.

Demand satisfaction and decision-making for a PCB manufacturing system with production lines in parallel

This paper studies demand satisfaction and decision-making for a printed circuit board (PCB) manufacturing system. A performance indicator, the system reliability, is proposed to evaluate the demand satisfaction. In particular, two important characteristics, (i) multiple production lines in parallel and (ii) multiple repair actions, are considered in this study. The PCB manufacturing system is modelled as a stochastic-flow manufacturing network (SFMN) by the graphical transformation and decomposition techniques. Based on the network-structured SFMN, this paper develops an algorithm to generate all minimal capacity vectors that workstations should provide to satisfy a given demand. In terms of all minimal capacity vectors, the system reliability is derived. In addition, the reliable production policy is determined based on each single minimal capacity vector.

Reliability evaluation according to a routing scheme for multi-state computer networks under assured accuracy rate

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.

Decision making procedure of demand satisfaction and production policy for capacitated production systems

This paper develops a reliability-based decision making procedure for production systems to (i) evaluate the system reliability and (ii) determine the reliable production policy. The production system is represented as a capacitated production network (CPN) for system reliability evaluation, in which the system reliability is defined as the probability of demand satisfaction. The decision making to determine a reliable production policy is based on the derived system reliability. Two layouts are considered in this paper: the first layout is for the CPN with parallel lines; while the second layout is for the CPN with joint lines. Transformation and decomposition techniques are proposed to generate all minimal capacity vectors that workstations should provide to satisfy demand. In terms of the minimal capacity vectors, the system reliability is derived by applying the recursive sum of disjoint products (RSDP) algorithm. A case study in the context of footwear production system is utilized to demonstrate the decision making procedure.

Reliability assessment of a stochastic node-failure network with multiple sinks under tolerable error rate

Internet service providers and enterprise customers are increasingly focusing on the tolerable error rate during transmission. This has high significance especially in service-level agreements. This study concentrates on a stochastic node-failure network (SNFN) with multiple sinks, where each component (arc or node) has several possible capacities and a transmission error rate. Measuring the performance level for an SNFN is an important issue in the system-design and system diagnosis phases. This study evaluates the system reliability of a network, or the probability that the demand is fulfilled under the tolerable error rate. In terms of minimal paths, we propose an efficient algorithm to find all minimal capacity vectors, and then compute the system reliability in terms of all minimal capacity vectors using the recursive sum of disjoint products algorithm. Finally, we test the proposed algorithm for a benchmark network and two practical networks.

Reliability of a production system with intersectional lines

This article addresses reliability evaluation for a production system with intersectional lines and multiple reworking actions, where the reliability is the probability of demand satisfaction. First, the production system is constructed as a capacitated-flow production network by the revised graphical transformation and decomposition techniques. Capacity analysis is implemented to determine the input flow of each workstation subsequently. Second, two algorithms, including a general algorithm, are proposed to generate all minimal capacity vectors that workstations should provide to satisfy demand. The reliability is derived in terms of such vectors accordingly. A real-world case of printed circuit board production system is utilized to demonstrate the performance evaluation procedure.

System reliability evaluation of a touch panel manufacturing system with defect rate and reworking

In recent years, portable consumer electronic products, such as cell phone, GPS, digital camera, tablet PC, and notebook are using touch panel as interface. With the demand of touch panel increases, performance assessment is essential for touch panel production. This paper develops a method to evaluate system reliability of a touch panel manufacturing system (TPMS) with defect rate of each workstation and takes reworking actions into account. The system reliability which evaluates the possibility of demand satisfaction can provide to managers with an understanding of the system capability and can indicate possible improvements. First, we construct a capacitated manufacturing network (CMN) for a TPMS. Second, a decomposition technique is developed to determine the input flow of each workstation based on the CMN. Finally, we generate the minimal capacity vectors that should be provided to satisfy the demand. The system reliability is subsequently evaluated in terms of the minimal capacity vectors. A further decision making issue is discussed to decide a reliable production strategy.

A novel model for a manufacturing system with joint production lines in terms of prior-set

A novel model integrating transformation and decomposition techniques is proposed to construct a manufacturing system with joint production lines as a multi-state manufacturing network (MMN). Reworking actions and different defect rates of workstations are both taken into account in the MMN model. The capacity analysis and performance evaluation are implemented accordingly. In particular, a technique in terms of ‘prior-set’ is developed to deal with multiple reworking actions. Subsequently, two simple algorithms are proposed to generate all minimal capacity vectors that workstations should provide to satisfy a given demand. In terms of such vectors, the probability of demand satisfaction can be derived. Such a probability is referred to as the system reliability, which is a performance indicator to state the capability of the MMN. According to each specific minimal capacity vector, the production manager may further determine a better strategy to produce products.

Stochastic computer network under accuracy rate constraint from QoS viewpoint

In the past, the main concerns for competitive enterprise environment of computer networks were data transmission delays and costs. However, from the viewpoint of quality of service (QoS), internet service providers and enterprise customers are increasingly focusing on data accuracy during transmission. This study extends a stochastic computer network (SCN) to evaluate the system reliability, where the system reliability is the probability that demand can be transmitted through the SCN under the total accuracy rate. In such an SCN, each arc has several capacities, and an accuracy rate. We can regard the system reliability as a measurable index for assessing the SCN performance. A lower boundary point for (d,K) is a minimal capacity vector, which allows the system to transmit demand d under the total accuracy rate K. Using the minimal paths, we propose an efficient algorithm to find all lower boundary points for (d,K). The system reliability can then be computed in terms of all lower boundary points for (d,K) by the recursive sum of disjoint products (RSDP) algorithm. Several numerical examples are demonstrated to illustrate the utility, efficiency, and effectiveness of the proposed algorithm.

Performance evaluation for a footwear manufacturing system with multiple production lines and different station failure rates

This paper develops a three-phase procedure to measure the performance of a highly value-added footwear manufacturing system taking reworking actions into account, in which the system consists of multiple production lines. We mainly address the system reliability as a performance indicator to evaluate the possibility of demand satisfaction. First, we construct the manufacturing system as a manufacturing network by graphical transformation and decomposition. Second, capability analysis is implemented to determine the input flow of each station based on the manufacturing network. Third, a simple algorithm is proposed to generate all minimal capacity vectors that stations should provide to satisfy the given demand. We evaluate the system reliability in terms of the minimal capacity vectors. A further decision making issue is discussed to decide a reliable production strategy. Whenever the system state changes, the proposed performance evaluation procedure can be implemented easily and flexibly.