Global Sensitivity Analysis for the Linear Assignment Problem

TL;DR

This paper investigates how much individual assignment weights in a linear assignment problem can be perturbed without altering the optimal solution, providing bounds, algorithms, and practical applications to prevent assignment churning.

Contribution

It extends existing perturbation results to all assignment weights and offers algorithms and practical methods for stability analysis in assignment problems.

Findings

Derived bounds for perturbations in all assignment weights

Developed algorithms to compute these bounds

Applied bounds to prevent assignment churning in multi-vehicle guidance

Abstract

In this paper, the following question is addressed: given a linear assignment problem, how much can the all of the individual assignment weights be perturbed without changing the optimal assignment? The extension of results involving perturbations in just one edge or one row/column are presented. Algorithms for the derivation of these bounds are provided. We also show how these bounds may be used to prevent assignment churning in a multi-vehicle guidance scenario.