Variational Inequality

Variational Inequality Given a subset $K$ of the Euclidean $n$-dimensional space $\mathbb{R}^{n}$ and a mapping $F: K \rightarrow \mathbb{R}^{n}$, the variational inequality, denoted $\text{VI}(K, F)$, is to find a vector $x \in K$ such that $$ (y-x)^{T} F(x) \geq 0, \quad \forall……

Reinforcement Learning and Optimal Control

Exact Dynamic Programming Deterministic Dynamic Programming A deterministic DP problem involves a discrete-time dynamic system of the form $$ x_{k+1} = f_k(x_k, u_k), \quad k = 0, 1, \dots, N-1 $$ where $k$ is the time index $x_k$ is the state of……

Inventory Pooling Under Heavy-Tailed Demand

发表于 Management Science, 2016. DOI: http://doi.org/10.1287/mnsc.2015.2204. Keywords: inventory management; inventory pooling; demand uncertainty; heavy-tailed distributions Area of review: operations management This paper considers a classic multilocation newsvendor setting following Eppen (1979), where the demand distribution is heavy tailed rather than……

Transshipment Between Overconfident Newsvendors

发表在 Production and operations management, 2021. DOI: https://doi.org/10.1111/poms.13424. Key words: overconfidence; transshipment; behavioral operations management; managerial bias 这篇文章研究了过度自信这一行为对带转运的报童模……

Inverse of the sum of matrices

如果 $A, B$ 都是正定矩阵,那么: $$ (A + B)^{-1} = A^{-1}-A^{-1}(A^{-1} + B^{-1})^{-1}A^{-1} $$ 根据 $A^{-1}B^{-1}=(BA)^{-1}$ 可以得到: $$ (A + B)^{-1} = A^{-1} (A^{-1} + B^{-1})^{-1} B^{-1} $$……