Minimal Capacity Vectors Research Articles

A Novel Reliability Evaluation Technique for Stochastic-Flow Manufacturing Networks With Multiple Production Lines

This paper presents a novel technique to measure the performance of a stochastic-flow manufacturing network (SMN) which violates the so-called flow conservation law due to the failure rates of stations. We address the mission reliability, the probability of demand satisfaction, as a performance indicator for the SMN while considering both the stochastic capacities and the multiple production lines. First, we construct a manufacturing system as an SMN through a graphical transformation, and decompose the transformed SMN into several paths for further analysis. Subsequently, two algorithms for different scenarios are designed to generate all minimal capacity vectors that stations should provide to satisfy the given demand. The first scenario is for the SMN with identical production lines in parallel. The second scenario is for distinct production lines with common stations in the SMN. We derive the mission reliability in terms of minimal capacity vectors by applying the recursive sum of disjoint products (RSDP) algorithm. A decision making issue is also discussed to decide a reliable production strategy.

Graphical-based reliability evaluation of multiple distinct production lines

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.

Stochastic computer network with multiple terminals under total accuracy rate

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.

Stochastic Flow Network Reliability with Tolerable Error Rate

Service-level agreements for data transmission often define criteria such as availability, delay, and loss. Internet service providers and enterprise customers are increasingly focusing on tolerable error rate during transmission. Focusing on a stochastic flow network (SFN), this study extends reliability evaluation to considering tolerable error rate, in which network reliability is the probability that demand can be satisfied. In such an SFN, each component (branch or node) has several capacities and a transmission error rate. Network reliability can be regarded as a performance index for assessing the SFN. We propose an efficient algorithm based on minimal paths to find all minimal capacity vectors that allow the network to transmit d units of data under tolerable error rate E. Network reliability is computed in terms of such vectors by the recursive sum of disjoint products algorithm. The proposed algorithm is tested for a benchmark network and the National Science Foundation Network. The computational complexity of the proposed algorithm is analyzed as well.

Reliability-based performance indicator for a manufacturing network with multiple production lines in parallel

This paper addresses the system reliability evaluation for a manufacturing system with multiple production lines in parallel, where the system reliability is the possibility that a manufacturing system can satisfy demand. In the manufacturing system, the capacity of each machine is stochastic (i.e., multi-state) due to failure, partial failure, or maintenance. Thus, the manufacturing system can be constructed as a manufacturing network in terms of stochastic-flow network model. With considering reworking actions, we propose a graphical-based methodology to transform the manufacturing system into a manufacturing network. Thereafter, the manufacturing network is decomposed into general manufacturing paths and reworking paths. A simple algorithm is subsequently developed to generate the minimal capacity vectors that machines should provide to satisfy demand. The system reliability is derived in terms of such capacity vectors afterwards.

A stochastic node-failure network with individual tolerable error rate at multiple sinks

Many enterprises consider several criteria during data transmission such as availability, delay, loss, and out-of-order packets from the service level agreements (SLAs) point of view. Hence internet service providers and customers are gradually focusing on tolerable error rate in transmission process. The internet service provider should provide the specific demand and keep a certain transmission error rate by their SLAs to each customer. This paper is mainly to evaluate the system reliability that the demand can be fulfilled under the tolerable error rate at all sinks by addressing a stochastic node-failure network (SNFN), in which each component (edge or node) has several capacities and a transmission error rate. An efficient algorithm is first proposed to generate all lower boundary points, the minimal capacity vectors satisfying demand and tolerable error rate for all sinks. Then the system reliability can be computed in terms of such points by applying recursive sum of disjoint products. A benchmark network and a practical network in the United States are demonstrated to illustrate the utility of the proposed algorithm. The computational complexity of the proposed algorithm is also analyzed.

Reliability evaluation subject to assured accuracy rate and time for stochastic unreliable-node computer networks

In many real-life networks such as computer networks, branches and nodes have multi-state capacity, lead time, and accuracy rate. The network with unreliable nodes is more complex to evaluate the reliability because node failure results in the disabled of adjacent branches. Such a network is named a stochastic unreliable-node computer network (SUNCN). Under the strict assumption that each component (branch and node) has a deterministic capacity, the quickest path (QP) problem is to find a path sending a specific amount of data with minimum transmission time. The accuracy rate is a critical index to measure the performance of a computer network because some packets are damaged or lost due to voltage instability, magnetic field effects, lightning, etc. Subject to both assured accuracy rate and time constraints, this paper extends the QP problem to discuss the system reliability of an SUNCN. An efficient algorithm based on a graphic technique is proposed to find the minimal capacity vector meeting such constraints. System reliability, the probability to send a specific amount of data through multiple minimal paths subject to both assured accuracy rate and time constraints, can subsequently be computed.

Reliability evaluation of a computer network in cloud computing environment subject to maintenance budget

This paper measures the performance of a computer network in the cloud computing environment. To retain a good quality of service (QOS), the computer network is required to preserve a sufficient capacity level so that it can send d units of data from the source (a cloud computing center) to the sink (a set of clients) through multiple paths within time T. Thus, the maintenance action should be taken when the computer network falls to a specific state so that it cannot provide sufficient capacity to satisfy demand d. Given the maintenance budget B and time constraint T, we evaluate the probability that d units of data can be sent from the source to the sink, where the probability is referred to as the system reliability. A branch-and-bound approach including an adjusting procedure is proposed to obtain all minimal capacity vectors satisfying d, B, and T. Subsequently, the corresponding system reliability can be derived in terms of such vectors by applying the recursive sum of disjoint products algorithm.

Reliability evaluation for a manufacturing network with multiple production lines

This paper focuses on performance evaluation of a manufacturing system with multiple production lines based on the network-analysis perspective. Due to failure, partial failure, or maintenance, the capacity of each machine is stochastic (i.e., multi-state). Hence, the manufacturing system can be constructed as a stochastic-flow network, named manufacturing network herein. This paper intends to measure the probability that the manufacturing network can satisfy customers’ orders. Such a probability is referred to as the system reliability. A graphical representation is first proposed to transform a manufacturing system into a manufacturing network. Thereafter, we decompose the manufacturing network into general processing paths and reworking paths. Three algorithms are subsequently developed for different scenarios and multiple production lines to generate the minimal capacity vectors that machines should provide to satisfy demand. The system reliability can be derived in terms of such capacity vectors afterwards.

Reliability evaluation for a waste-reduction parallel-line manufacturing system

Reworking in a manufacturing system is usually an environment-friendly way to eliminate waste during producing. This paper develops a performance evaluation procedure for the parallel-line manufacturing system with different station failure rates. Considering reworking actions, we propose a graphical-based methodology to model the manufacturing system as a stochastic-flow network. First, a transformation technique is utilized to build the manufacturing system as a manufacturing network. Second, a simple algorithm integrating decomposition technique is proposed to generate the minimal capacity vectors that stations should provide to satisfy the given demand. We evaluate the probability that the manufacturing network can meet the demand in terms of the minimal capacity vectors, where the probability is referred to as the system reliability. A footwear manufacturing system is utilized to demonstrate the performance evaluation procedure. A further decision making issue is discussed based on the derived system reliability for achieving higher demand satisfaction and less waste.

Estimated system reliability of a cloud computing network subject to maintenance budget

This paper proposes an estimation method to evaluate the capability of a cloud computing network. To keep a good quality of service, maintenance actions are necessary when the CCN falls to a specific state such that it cannot afford enough capacity to meet d units of data. Another crucial factor to consider is the transmission time for sending data from the cloud to the client. Given the maintenance budget B and within time T, we estimate the system reliability that is defined as the probability that d units of data can be sent from the cloud to the client under both B and T. Several disjoint minimal paths are utilized to send data simultaneously such that the transmission time is decreased. To estimate the system reliability, a bounding approach is proposed to generate two sets of capacity vectors, UB-MPs and LB-MPs, where a UB-MP is the minimal capacity vector satisfying d and T while an LB-MP is the minimal capacity vector satisfying d, B, and T. Subsequently, the upper and lower bounds of system reliability can be computed in terms of such vectors by applying the recursive sum of disjoint products algorithm.

RELIABILITY EVALUATION OF A MANUFACTURING NETWORK WITH REWORKING ACTION

This paper focuses on performance evaluation of a manufacturing system from the network analysis perspective. Due to failure, partial failure, or maintenance, the capacity of each machine is stochastic (i.e., multistate). Hence, a manufacturing system can be constructed as a stochastic-flow network, named manufacturing network herein. Considering reworking action and failure rates of machines, this paper assesses the probability that the manufacturing network can satisfy demand. Such a probability is defined as the system reliability. First, a graphical technique is proposed to decompose the manufacturing network into one general processing path and one reworking path. Subsequently, two algorithms are utilized for different network models to generate the minimal capacity vector of machines that guarantee that the manufacturing network is able to produce sufficient products fulfilling the demand. The system reliability of the manufacturing network is derived in terms of such a capacity vector afterward.

Calculation of minimal capacity vectors through k minimal paths under budget and time constraints

Abstract Reducing the transmission time is an important issue for a flow network to transmit a given amount of data from the source to the sink. The quickest path problem thus arises to find a single path with minimum transmission time. More specifically, the capacity of each arc is assumed to be deterministic. However, in many real-life networks such as computer networks and telecommunication networks, the capacity of each arc is stochastic due to failure, maintenance, etc. Hence, the minimum transmission time is not a fixed number. Such a network is named a stochastic-flow network. In order to reduce the transmission time, the network allows the data to be transmitted through k minimal paths simultaneously. Including the cost attribute, this paper evaluates the probability that d units of data can be transmitted under both time threshold T and budget B . Such a probability is called the system reliability. An efficient algorithm is proposed to generate all of lower boundary points for ( d , T , B ), the minimal capacity vectors satisfying the demand, time, and budget requirements. The system reliability can then be computed in terms of such points. Moreover, the optimal combination of k minimal paths with highest system reliability can be obtained.

On transmission time through k minimal paths of a capacitated-flow network

The quickest path problem is to minimize the transmission time for sending a specified amount of data through a single minimal path. Two deterministic attributes are involved herein; the capacity and the lead time. However, in many real-life networks such as computer systems, urban traffic systems, etc., the arc capacity should be multistate due to failure, maintenance, etc. Such a network is named a capacitated-flow network. The minimum transmission time is thus not a fixed number. This paper is mainly to evaluate system reliability that d units of data can be transmitted through k minimal paths under time constraint T. A simple algorithm is proposed to generate all minimal capacity vectors meeting the demand and time constraints. The system reliability is subsequently computed in terms of such vectors. The optimal k minimal paths with highest system reliability can further be derived.

System Reliability Evaluation for a Multistate Supply Chain Network With Failure Nodes Using Minimal Paths

This work devotes to the application of network methods for the reliability of a complex supply chain system, which is a set of several factories with supply-demand relationship. Two characters are considered in the proposed network: 1) nodes, and arcs all have multiple possible capacities, and may fail; and 2) the capacity weight varies with arcs, nodes, and types of commodity. The purpose of this paper is to study the systems reliability, in this case the possibility that a given quantity ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) of two types of commodities can be transmitted from the source factory to the destination factory simultaneously. Such a possibility can be treated as a performance index to measure the quality level of a supply chain network. The flow model is constructed by flow assignments, and capacity vectors. The ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) -MP, which represents the capacity of each arc/node, is a minimal capacity vector meeting the demand constraint. A simple algorithm in terms of minimal paths is first proposed to generate all ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> )-MP. The system reliability can then be calculated efficiently in terms of ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> )-MP. Time complexity of the proposed algorithm is also analyzed.

SYSTEM RELIABILITY OF A STOCHASTIC-FLOW NETWORK WITH NODES HAVING CAPACITY AND COST ATTRIBUTES

A stochastic-flow network in which nodes as well as arcs all have both capacity and cost attributes is studied. We evaluate the possibility that the maximum flow of the network is not less than a demand under the budget constraint. Such a possibility is in general called the system reliability. A minimal path, an order sequence of arcs &amp; nodes from the source to the sink without cycles, is used to assign the flow to each component (arc or node). Based on minimal paths, an efficient algorithm is proposed to generate all (d, C)-MPs that are the minimal capacity vectors meeting the demand d and the budget C. The system reliability can then be calculated in terms of all (d, C)-MPs.

Reliability of a Stochastic-Flow Network With Unreliable Branches &amp;amp; Nodes, Under Budget Constraints

System reliability evaluation for flow networks is an important issue in quality management. This paper concentrates on a stochastic-flow network in which nodes as well as branches have several possible capacities, and can fail. The possibility is evaluated that a given amount of messages can be transmitted through the stochastic-flow network under the budget constraint. Such a possibility, system reliability, is a performance index for a stochastic-flow network. A minimal path, an order sequence of nodes & branches from the source to the sink without cycles, is used to assign the flow to each component (branch or node). A lower boundary point for (d, C) is a minimal capacity vector, which enables the system to transmit d messages under the budget C. Based on minimal paths, an efficient algorithm is proposed to generate all lower boundary points for (d, C). The system reliability can then be calculated in terms of all lower boundary points for (d, C) by applying the inclusion-exclusion rule. Simulation shows that the implicit enumeration (step 1) of the proposed algorithm can be executed efficiently.