Combinatorial two-stage minmax regret problems under interval uncertainty

TL;DR

This paper studies two-stage combinatorial optimization problems under interval uncertainty using minmax regret, analyzing properties and providing results for shortest path and selection problems.

Contribution

It introduces a framework for two-stage minmax regret problems with interval uncertainty and presents specific results for shortest path and selection problems.

Findings

Established general properties of the problem

Derived results for shortest path problem

Derived results for selection problem

Abstract

In this paper a class of combinatorial optimization problems is discussed. It is assumed that a feasible solution can be constructed in two stages. In the first stage the objective function costs are known while in the second stage they are uncertain and belong to an interval uncertainty set. In order to choose a solution, the minmax regret criterion is used. Some general properties of the problem are established and results for two particular problems, namely the shortest path and the selection problem, are shown.