Some Aspects on Solving Transportation Problem

TL;DR

This paper explores a specialized class of transportation problems with structured cost matrices, extending classical methods like Hungarian algorithm and Kőnig-Egerváry theorem to weighted versions, offering new solution approaches.

Contribution

It introduces a weighted Hungarian method and generalizes the Kőnig-Egerváry theorem for solving structured transportation problems with convex cost functions.

Findings

Optimality of North West corner solution extends to convex cost functions.

Weighted Hungarian method effectively solves the structured transportation problem.

Revisits and generalizes assignment problem solutions.

Abstract

In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices of these transportation problems are of special structure. We observe that the optimality of North West corner solution holds for the general problem where cost component is replaced by a convex function. We revisit assignment problem and present a weighted version of K$\ddot{o}$nig-Egerv$\acute{a}$ry theorem and Hungarian method. The weighted Hungarian method proposed in the paper can be used for solving transportation problem.