Reliability evaluation for a multi-commodity multi-state distribution network under transportation emission consideration

This study, from the perspective of environmental effect, presents a novel reliability evaluation of a multi-commodity multi-state distribution network (MMDN) with consideration of transportation emission, in which a node stands for a supplier, a distribution center or a market, an arc represents a carrier offering transportation service along that arc, and multiple types of commodities are simultaneously transported from several sources to the destination. Due to the existence of unpredictable events, the available capacity of each arc should be multi-state, thus, network reliability under transportation emission consideration, defined as the probability that a specific amount of multiple types of commodities can be successfully distributed from several sources to the destination while the carbon emissions generated by all vehicles are within a limit, can serve as a valuable reference to assess the ability of an MMDN to complete the delivery task with limited environmental impact. An algorithm, using minimal paths vectors (MPVs), is proposed to evaluate the indicator, and the solution steps are explicated through an example network. Additionally, a case study is explored to indicate the practicality of the new reliability index and calculation method.