Sensitivity Analysis for Bottleneck Assignment Problems

TL;DR

This paper extends sensitivity analysis in assignment problems by allowing simultaneous variations in all weights, focusing on the bottleneck assignment problem, and providing new algorithms and complexity discussions.

Contribution

It introduces a novel approach to sensitivity analysis for bottleneck assignment problems with methods for simultaneous weight perturbations.

Findings

Two methods for quantifying sensitivity are proposed.

Algorithms for each sensitivity measure are developed.

Complexity analysis and numerical examples are provided.

Abstract

In assignment problems, decision makers are often interested in not only the optimal assignment, but also the sensitivity of the optimal assignment to perturbations in the assignment weights. Typically, only perturbations to individual assignment weights are considered. We present a novel extension of the traditional sensitivity analysis by allowing for simultaneous variations in all assignment weights. Focusing on the bottleneck assignment problem, we provide two different methods of quantifying the sensitivity of the optimal assignment, and present algorithms for each. Numerical examples as well as a discussion of the complexity for all algorithms are provided.