Exact and heuristic methods for Anchor-Robust and Adjustable-Robust RCPSP

TL;DR

This paper introduces anchored solutions for the RCPSP under uncertainty, proposing exact and heuristic methods to compute robust schedules with guaranteed starting times, improving robustness and efficiency.

Contribution

It develops a new anchored solutions framework for RCPSP, integrating and extending adjustable-robust approaches with novel graph models and reformulations.

Findings

Proposed MIP reformulations are efficient for benchmark instances.

Heuristics based on the graph model improve solution quality.

Anchored solutions enhance robustness in project scheduling under uncertainty.

Abstract

The concept of anchored solutions is proposed as a new robust optimization approach to the Resource-Constrained Project Scheduling Problem (RCPSP) under processing times uncertainty. The Anchor-Robust RCPSP is defined, to compute a baseline schedule with bounded makespan, sequencing decisions, and a max-size subset of jobs with guaranteed starting times, called anchored set. It is shown that the Adjustable-Robust RCPSP from the literature fits within the framework of anchored solutions. The Anchor-Robust RCPSP and the Adjustable-Robust RCPSP can benefit from each other to find both a worst-case makespan and a baseline schedule with an anchored set. A dedicated graph model for anchored solutions is proposed for budgeted uncertainty. Compact MIP reformulations are derived for both the Adjustable-Robust RCPSP and the Anchor-Robust RCPSP. Dedicated heuristics are designed based on the graph model. For both problems, the efficiency of the proposed MIP reformulations and heuristic approaches is assessed through numerical experiments on benchmark instances.