This paper considers the impact of consumer environmental awareness (CEA), retailer’s fairness concern, and government subsidies on the two echelon supply chain with one manufacturer and one retailer. The manufacturer produces green products with carbon emission reduction. The government provides two types of alternative subsidies: a fixed subsidy (referred to as an F-type subsidy) or a discount subsidy (referred to as a D-type subsidy) to encourage the manufacturer to produce a product with a high carbon emission reduction rate. We aim to provide optimal solutions to the manufacturer and the retailer with regard to the retailer’s fairness concern and government subsidies; thus we discuss four decision scenarios: the benchmark model without the fairness concern and subsidy, the model with the retailer’s fairness concern, the model with fairness concern and the F-type subsidy, and the model with fairness concern and the D-type subsidy. We provide explicit solutions and numerical examples of the optimal carbon emission reduction rate, wholesale price, and retail price. Our study has four main findings: firstly, high consumer environmental awareness will benefit both the manufacturer and the retailer in the above four scenarios; secondly, the fairness concern and subsidy have a counter effect on the optimal strategies (the subsidy could alleviate the negative influence caused by retailer’s fairness concern); thirdly, the government could subsidize the retailer when there is unfairness in the supply chain so that the manufacturer could produce a product with lower carbon emission; finally, using the subsidy related to the environmental quality will be more helpful for improving environment quality, especially when the government has a budget constraint.

Spiking neural P systems are a new candidate in spiking neural network models. By using neuron division and budding, such systems can generate/produce exponential working space in linear computational steps, thus provide a way to solve computational hard problems in feasible (linear or polynomial) time with a “time-space trade-off” strategy. In this work, a new mechanism called neuron dissolution is introduced, by which redundant neurons produced during the computation can be removed. As applications, uniform solutions to two NP-hard problems: SAT problem and Subset Sum problem are constructed in linear time, working in a deterministic way. The neuron dissolution strategy is used to eliminate invalid solutions, and all answers to these two problems are encoded as indices of output neurons. Our results improve the one obtained in Science China Information Sciences, 2011, 1596-1607 by Pan et al.

Apriori algorithm, as a typical frequent itemsets mining method, can help researchers and practitioners discover implicit associations from large amounts of data. In this work, a fast Apriori algorithm, called ECTPPI-Apriori, for processing large datasets, is proposed, which is based on an evolution-communication tissue-like P system with promoters and inhibitors. The structure of the ECTPPI-Apriori algorithm is tissue-like and the evolution rules of the algorithm are object rewriting rules. The time complexity of ECTPPI-Apriori is substantially improved from that of the conventional Apriori algorithms. The results give some hints to improve conventional algorithms by using membrane computing models.

In this paper we propose a new graph based P system. The main feature of graph P system is that membrane compartments spread on edges as well as on vertices. These two kinds of compartments are topologically connected with certain communication rules. A new neural computing technique is proposed to solve cluster splitting into finding the equilibrium of Hopfield neural networks. Then we use the new graph P systems to obtain stable status of the neural networks. An example is presented to show the computing efficiency of the new P system with comparison with classical genetic algorithms.