The beautiful art of rearranging matrices
本文综述了将多种不确定性优化问题转化为矩阵重排问题的方法，并介绍了一种简单迭代算法（重排算法）来近似求解，适用于装配线排班、多路划分、金融依赖不确定性边界计算、不可分物品公平分配等场景。
Abstract In this paper we review several optimization problems under uncertainty that can be represented as the problem of finding the optimal rearrangement of a matrix. By rearrangement we mean a permutation of the order of the elements in each column of the matrix, such that each column turns out to be oppositely ordered to the sum of the others. A simple heuristic iterative procedure called the Rearrangement Algorithm has been designed to find rearranged matrices so that the vector of their rowsums is minimal in the so-called Schur order, a notion connected to convex stochastic dominance, and to provide approximations to the solutions of various challenging problems with uncertainty scenarios. By changing the initial design of the matrix, or by introducing a family of matrices to be rearranged simultaneously, or by rearranging the columns in a prescribed way or in blocks, the Rearrangement Algorithm can be adapted to deal with several applications in a variety of fields including: the assembly line crew scheduling problem with uncertain labour times, the multi-way partitioning problem, the computation of dependence uncertainty bounds in finance, the fair allocation of indivisible items, and the estimation of a joint distribution subject to statistical uncertainty.