Inverse Quadratic Transportation Problem

TL;DR

This paper introduces inverse quadratic transportation problems under $L_1$ and $L_ abla$ norms, combining quadratic programming and inverse optimization techniques to extend transportation problem models.

Contribution

It presents the inverse quadratic transportation problem formulations under $L_1$ and $L_ abla$ norms, utilizing duality and optimal value concepts.

Findings

Formulated inverse quadratic transportation problems under $L_1$ and $L_ abla$ norms.

Applied duality and optimal value methods to derive inverse models.

Extended quadratic programming and inverse optimization to transportation problems.

Abstract

Many research has been conducted about quadratic programming and inverse optimization. In this paper we present the combination aspect of these subjects, applying on transportation problem. First, we obtain the inverse form of quadratic tranportation problem under $L_1$ norm by using duality as well as introducing the optimal value. Then, we do the same process for inverse quadratic transportation problem (IQTP) under $L_\infty$ norm.