Performance evaluation for the logistics system in case that capacity weight varies from arcs and types of commodity

Most of Taiwan high-technology companies establish their factories in China to enhance the logistics systems. In order to show and improve the company's competitive advantage, it is an important issue to measure the performance of the logistics system. Hence, we try to propose an index to evaluate the performance of the logistics system between China and Taiwan by constructing a two-commodity capacitated-flow network. In the proposed model, each arc has both the capacity and cost attributes. Each type of commodity consumes the capacity of each arc differently. That is, the capacity weight varies from the arcs and types of commodity. It is known that the system capacity is the maximum flow from the source to the sink for a single-commodity capacitated-flow network. However, the conventional performance indexes proposed for a single-commodity case are not suitable for a two-commodity case. Hence, we define the system capacity as a vector for a two-commodity capacitated-flow network. Then a performance index, the probability that the upper bound of the system capacity equals a given pattern under the budget constraint, is proposed to measure the performance of logistics systems. An efficient algorithm based on minimal cuts is presented to evaluate such a performance index.