Abstract
Network reliability refers to the probability that a live connection exists between a source node and a sink node. Network structures are applied extensively in many real-world systems, such as computers, power transmission, and distribution systems. Therefore, reliability evaluation of a general network is very important. Network reliability can be adopted as an index of network quality to indicate the probability of successful on-time delivery. To estimate an adequate index for network quality, we search for all feasible combinations instead of a pre-defined MP set which appeared on literature. This study first considers the quick path problem within the multi-state flow network (MQPFN) which conveys only one type of commodity. It tries to locate all feasible solutions and evaluate the probability that d units of commodities can be sent from the source node to the sink node through MQPFN within T units of time. Commodities may be transmitted via single or multiple MPs, and solutions are not subject to disjointed MPs. This study contributed to develop a new algorithm which not only finds for all QPs to transmit commodities on time via a network, but also accurately evaluates the probability of successful delivery of the network. Secondly, transmission of multi-commodity is investigated. Delivery within the promised time frame is especially the most critical quality criterion for supply chain networks. However, little attention has been given to the performance evaluation of on-time delivery for multi-commodity networks. This paper presents a time-constrained multi-commodity multistate flow network (TMMN) which is characterized by (1) each arc employs two attributes, capacity and lead time; (2) the arc capacity is multistate; (3) different commodities consume the arc capacity differently and (4) the delivery has to be completed within the promised time frame. The proposed method is targeted towards the situation where multi-commodities are conveyed through all minimal paths (MPs) in a network, no matter the MPs are disjointed or not. This is the first study that develops a method to locate the most reliable routing in a TMMN and to estimate the network reliability as a performance index for on-time delivery of multi-commodity systems.