To provide a risk-sharing mechanism that encourages a component supplier and a manufacturer to expand their production capacity of components and products, many researches on SCM suggested that it is better for the SC...To provide a risk-sharing mechanism that encourages a component supplier and a manufacturer to expand their production capacity of components and products, many researches on SCM suggested that it is better for the SC players to connect a long-term contract with flexible preconditions before doing the decision-making of production capacity. With considering of the uncertainty of demand and integrity problems between SC players, it is difficult to set reasonable preconditions. As a result, under-investment problems still occur frequently. In this paper, after we had discussed the decision-making of production capacity with the preconditions by analyzing the character of the players, we verified the under-investment problem of the supply chain. In order to clarify the optimum preconditions to alleviate the under-investment problem, we also analyzed the relations between preconditions and supply capacity of the whole supply chain. In the last part of this paper, we proposed a method of preconditions setting in such uncertain situations.展开更多
With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical wo...With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical work focusing on neural networks in solving interface problems.In this paper,we perform a convergence analysis of physics-informed neural networks(PINNs)for solving second-order elliptic interface problems.Specifically,we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump conditions.It is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples increases.Numerical experiments are provided to demonstrate our theoretical analysis.展开更多
文摘To provide a risk-sharing mechanism that encourages a component supplier and a manufacturer to expand their production capacity of components and products, many researches on SCM suggested that it is better for the SC players to connect a long-term contract with flexible preconditions before doing the decision-making of production capacity. With considering of the uncertainty of demand and integrity problems between SC players, it is difficult to set reasonable preconditions. As a result, under-investment problems still occur frequently. In this paper, after we had discussed the decision-making of production capacity with the preconditions by analyzing the character of the players, we verified the under-investment problem of the supply chain. In order to clarify the optimum preconditions to alleviate the under-investment problem, we also analyzed the relations between preconditions and supply capacity of the whole supply chain. In the last part of this paper, we proposed a method of preconditions setting in such uncertain situations.
基金the National Natural Science Foundation of China(Grant Nos.11771435,22073110 and 12171466).
文摘With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical work focusing on neural networks in solving interface problems.In this paper,we perform a convergence analysis of physics-informed neural networks(PINNs)for solving second-order elliptic interface problems.Specifically,we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump conditions.It is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples increases.Numerical experiments are provided to demonstrate our theoretical analysis.
