Xiu-Zhen Xu's research while affiliated with Chongqing University of Posts and Telecommunications and other places

Multistate flow networks (MFNs) and their reliability problem have been studied extensively. However, most of the research on MFN reliability assumes that flow into and out of any arc is equal. In practical applications, flow may experience loss during transmission such that flow into and out of an arc may not be equal. Thus, this article concentrates on the reliability of an MFN with flow loss effect, defined as the probability that the sink node can receive a flow of at least d units when the flow experiences loss without replenishment during transmission. Using minimal paths, a simple method is put forth to compute this reliability index, and the solution procedure is illustrated via a simple network example. Finally, computational experiments are provided to investigate the impact of flow loss on network reliability.

This paper proposes a new reliability assessment for a distribution network with carbon emission constraint where a node represents a supplier, a distribution center, or a market, and an arc connecting a pair of nodes represents a carrier. The available capacity of each carrier (e.g., number of vehicles) is stochastic due to unexpected events. In this sense, such a distribution network is considered to be a stochastic-flow distribution network (SFDN). In addition, transportation emissions that have direct hazardous effects on environment and human health are becoming the major concern in the process of commodity distribution. Thus, SFDN reliability with carbon emission constraint, defined as the probability that the network can successfully deliver a specified quantity of goods from the source to the destination with the total transportation emissions no more than a given limitation, is taken as a key performance indicator for distribution activity. Grounded on minimal paths (MPs), an algorithm is proposed to calculate the new indicator. A simple example is provided to illustrate the procedure, and then, a real fruit distribution network is adopted to demonstrate the utility of the proposed algorithm.

This paper models a logistics network as a multi-distribution multi-state flow network (MFN) in which each arc has a random capacity characterized by more than one probability distribution under different budget allocations. An optimization model is constructed to minimize the total budget required for the network to achieve a given reliability level. By integrating a novel budget vector method with the well-known binary search method, an effective and efficient algorithm is developed to solve the optimization model, together with analyses on the computational complexity. A practical implementation on a simple network is presented to illustrate the proposed method, and the computational efficiency is explored via numerical examples. Finally, a real case study is provided to showcase the application of the proposed model and method.

The reliability and cost integrated performance measure R(d,b) of a multi-state flow network, defined as the probability of sending a flow of d units from the source to the sink with the total transmission cost no more than b, can be computed by means of (d, b)-minimal paths ((d, b)-MPs). The existing methods search for (d, b)-MPs by solving a large Diophantine system or several Diophantine subsystems that are shown to be NP-hard, then the computational efforts are prohibitive. This paper proposes a new search method for (d, b)-MPs, and major contributions include: (1) a correlation between (d, b)-MPs and minimum cost circulations is established, enabling the solution of (d, b)-MPs to be accomplished via minimum cost circulations; (2) a distinctive method merging the well-known capacity scaling algorithm and a decomposition technique is presented to find (d, b)-MPs. In contrast to the existing methods, the presented algorithm seeks for (d, b)-MPs without depending upon the solutions of Diophantine system and generating any duplicate (d, b)-MPs. An illustration of the proposed algorithm is presented, and computational results indicate the advantage of our algorithm over the existing methods.

Reliability and delivery cost are two crucial indicators to show whether a distribution network is in the stable and high-quality operation. This paper develops a (d, b)-minimal path ((d, b)-MP) based algorithm to compute the reliability R(d,b) of a stochastic distribution network as the probability that a prescribed demand d can be successfully delivered from the source to the destination subject to the constraint that the total delivery cost is not above b. Specifically, this paper focuses two aspects to facilitate the solution of (d, b)-MPs. Firstly, by transforming a large Diophantine system into several small Diophantine systems, a modified model is constructed to promote the efficiency of searching for (d, b)-MP candidates and narrow the scope of duplicate (d, b)-MPs. Secondly, a novel technique is devised to identify all duplicate (d, b)-MPs, and its efficiency advantage is theoretically proven. Finally, it is demonstrated through numerical experiments that the developed algorithm compares favorably with the existing ones in the literature, and a case study is provided to display the application of the algorithm.

Most of modern technological networks that can perform their tasks with various distinctive levels of efficiency are multistate networks, and reliability is a fundamental attribute for their safe operation and optimal improvement. For a multistate network, the two-terminal reliability at demand level d, defined as the probability that the network capacity is greater than or equal to a demand of d units, can be calculated in terms of multistate minimal paths, called d-minimal paths (d-MPs) for short. This paper presents an efficient algorithm to find all d-MPs for the multistate two-terminal reliability problem. To advance the solution efficiency of d-MPs, an improved model is developed by redefining capacity constraints of network components and minimal paths (MPs). Furthermore, an effective technique is proposed to remove duplicate d-MPs that are generated multiple times during solution. A simple example is provided to demonstrate the proposed algorithm step by step. In addition, through computational experiments conducted on benchmark networks, it is found that the proposed algorithm is more efficient.

Multi-state minimal paths, called d-minimal paths (d-MPs), are a popular tool for computing the reliability of multi-state flow networks. Most of the existing algorithms seek for d-MPs by solving an NP-hard Diophantine system in terms of the implicit enumeration method that is simple yet inefficient. This paper focuses on the development of a novel method for finding all d-MPs. By exploring the relationship between d-MPs and feasible circulations that are a well-known network flow problem, this paper proposes a distinctive method integrating the traditional max-flow algorithm and a partition technique to find all d-MPs. The developed method seeks for d-MPs by solving feasible circulations, rather than by solving an NP-hard Diophantine system; additionally, it neither requires MPs nor generates duplicate d-MPs during the solution process. Both theoretical and experimental results demonstrate the advantage of the developed method, and a real delivery network example is presented to illustrate its application.