供应链微分博弈模型的高效有限元方法

In this project, by means of the control variable of the emission reduction intensity, we establish a differential game model for the green supply chain, which contains the gains from emission permits trading, learning by doing, and myopic and foresighted behaviors. Moreover, under the emission permits trading scheme, its equivalent Hamilton-Jacobi-Bellman system of partial differential equations is utilized to describe quantitatively the product pricing and emission reduction strategy, and the effects of the channel members’ myopic and foresighted behaviors as well as the learning by doing on the supply chain performance and the product pricing. For the Hamilton-Jacobi-Bellman system of partial differential equations in management science, we develop the stability and convergence of finite element methods, and especially probe superconvergence, Richardson extrapolation, iterated as well as the interpolation defect correction of finite element methods. In addition, on the basis of these finite element methods of higher efficiency, some reliable a posteriori error estimators are provided, such that adaptive and parallel algorithms can be constructed, which develops and enriches the theories and applications of the finite element methods of higher efficiency.

本项目将建立以减排强度为控制变量，含有生产商排放权交易的收益变量与干中学变量及近视与远视行为变量的绿色供应链微分博弈模型，并拟用等价的Hamilton-Jacobi-Bellman偏微分方程组来定量地刻画排放权交易机制下的产品定价及减排策略、渠道成员的近视与远视行为变量及干中学变量对供应链效益与产品定价的影响。发展管理问题中的Hamilton-Jacobi-Bellman方程组的有限元方法，建立算法的稳定性与收敛性等理论，给出相应问题有限元法的超收敛、Richardson 外推及迭代与插值校正等算法，并籍此构造出可靠的后验误差估计量，近而建立高效自适应算法与并行算法，发展和丰富高效自适应与并行有限元方法。

以减排强度为控制变量，建立了含有生产商排放权交易的收益变量与干中学变量及近视与远视行为变量的绿色供应链微分博弈模型，并用其等价的Hamilton-Jacobi-Bellman偏微分方程组来定量地刻画了排放权交易机制下的产品定价及减排策略、渠道成员的近视与远视行为变量及干中学变量对供应链效益与产品定价的影响。发展了管理问题中的Hamilton-Jacobi-Bellman方程组的有限元方法，建立了算法的稳定性与收敛性等理论，给出了相应问题有限元法的超收敛、Richardson 外推及迭代与插值校正等算法，并籍此构造出了可靠的后验误差估计量，近而建立了高效自适应算法与并行算法，发展和丰富了高效自适应与并行有限元方法。