Dominance-based linear formulation for the Anchor-Robust Project Scheduling Problem

TL;DR

This paper introduces a dominance-based mixed-integer programming formulation for the NP-hard Anchor-Robust Project Scheduling Problem, improving solution tightness and analyzing polynomial cases under uncertainty.

Contribution

It develops a new dominance-based MIP formulation applicable to various uncertainty sets, including budgeted uncertainty, and explores the problem's combinatorial structure.

Findings

The formulation is tighter than previous models.

Polynomial cases under budgeted uncertainty are characterized.

Numerical experiments show improved performance on complex instances.

Abstract

In project scheduling under processing times uncertainty, the Anchor-Robust Project Scheduling Problem is to find a baseline schedule of bounded makespan and a max-weight subset of jobs whose starting times are guaranteed. The problem was proven NP-hard even for budgeted uncertainty. In the present work we design mixed-integer programming (MIP) formulations that are valid for a variety of uncertainty sets encompassing budgeted uncertainty. A new dominance among solutions is proposed, resulting into an MIP formulation. We further study the combinatorial structure of the problem. Non-trivial polynomial cases under budgeted uncertainty are exhibited, where the dominance-based formulation yields a polyhedral characterization of integer solutions. In more general cases, the dominance-based formulation is shown to be tighter than all previously known formulations. In numerical experiments we investigate how the formulation performs on instances around the polynomial cases, for both budgeted uncertainty sets and more elaborate uncertainty sets involving several budgets.