We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main phases that are iteratively repeated until an optimal basic feasible solution is reached. In the first "inside" phase, the algorithm progressively improves upon a given basic solution by increasing the value of several non-basic variables with negative reduced cost. This phase typically outputs a non-basic feasible solution interior to the constraints set polytope. The second "out" phase moves in the opposite direction by iteratively setting to zero several variables until a new improved basic feasible solution is reached. Extensive computational tests show that the proposed approach strongly outperforms all versions of network and linear programming algorithms available in the commercial solvers Cplex and Gurobi and other exact algorithms available in the literature.

翻译：我们针对网络优化中的典型问题——运输问题，提出了一种新颖的精确算法。该算法命名为“迭代内外法”（Iterated Inside Out），以基础可行解为输入，通过循环执行两个主要阶段直至达到最优基础可行解。在首个“内推”阶段，算法通过提升多个负检验数的非基变量取值，逐步改进当前基础解，通常输出位于约束集多胞体内部的非基础可行解。随后“外推”阶段反向操作，通过迭代将若干变量归零直至生成新的改进型基础可行解。大量计算实验表明，本算法在性能上显著优于商业求解器Cplex与Gurobi内置的各类网络及线性规划算法版本，以及文献中现有的其他精确算法。