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：本文提出一种针对运输问题的新型精确算法，该问题是网络优化领域的典型问题之一。该算法名为"迭代内外法"，需输入一个基本可行解，通过反复执行两个主要阶段直至达到最优基本可行解。在第一阶段（"内"阶段），算法通过增加多个具有负检验数的非基变量值，逐步改进给定基解，通常输出一个位于约束集多胞体内部的非基可行解。第二阶段（"外"阶段）则反向推进，通过迭代将多个变量置零，直至获得新的改进基本可行解。广泛的计算测试表明，本文方法在性能上显著优于商业求解器Cplex和Gurobi提供的所有网络与线性规划算法版本，以及文献中现有的其他精确算法。