Two Stage Optimization with Recourse and Revocation

TL;DR

This paper introduces a new two-stage optimization model allowing decision revocation, making it more realistic for practical applications, and develops approximation algorithms for related cover and facility location problems.

Contribution

It proposes a novel two-stage optimization with recourse and revocation model and provides LP rounding schemes and approximation algorithms for specific problems.

Findings

LP rounding scheme effective for cover problems

Approximation algorithms extend to facility location problem

Model enhances realism in two-stage optimization scenarios

Abstract

Two-stage optimization with recourse model is an important and widely used model, which has been studied extensively these years. In this article, we will look at a new variant of it, called the two-stage optimization with recourse and revocation model. This new model differs from the traditional one in that one is allowed to revoke some of his earlier decisions and withdraw part of the earlier costs, which is not unlikely in many real applications, and is therefore considered to be more realistic under many situations. We will adopt several approaches to study this model. In fact, we will develop an LP rounding scheme for some cover problems and show that they can be solved using this scheme and an adaptation of the rounding approach for the deterministic counterpart, provided the polynomial scenario assumption. Stochastic uncapacitated facility location problem will also be studied to show that the approximation algorithm that worked for the two-stage with recourse model worked for this model as well. In addition, we will use other methods to study the model.