Optimal Transportation Solution with Least-Looping Stepping-Stone-based ASM (LS-ASM)

Abstract

The Least-Looping Stepping-Stone-based ASM (LS-ASM) method is a transportation problem-solving approach aimed at achieving an optimal solution more efficiently than the classical method. It begins with row and column reductions to simplify the cost matrix, followed by stepwise allocation based on selecting the most advantageous cells, and then uses the formation of closed loops to evaluate cost changes and identify potential improvements to the current solution. Through this systematic process, LS-ASM is able to minimize the number of iterations required, using cost change values for optimality checks to ensure that the final allocation structure consistently meets source capacities and destination demands, ultimately resulting in a stable, directed, and optimal solution for minimizing distribution costs.