Benchmarking Quantum and Hybrid Annealing on Refinery Turnaround Scheduling A Rigorous Assessment against Constraint Programming and Mixed-Integer Formulations

Overview

This deposition provides the theoretical framework, mathematical formulations, and benchmarking protocol for the Refinery Turnaround Activity Scheduling Problem with Spatial Hazards (RTASP-SH). The research formally evaluates the performance of Superconducting Quantum Annealing (D-Wave QPU), Hybrid Classical-Quantum Solvers (D-Wave Leap CQM), and state-of-the-art classical Constraint Programming (Google OR-Tools CP-SAT) under strict semantic symmetry.

A central contribution of this work is addressing prevalent methodological deficiencies in quantum optimization literature—specifically asymmetric constraint modeling (e.g., omitting hard cumulative resource limits in QUBO/Ising models while retaining them in classical baselines) and the conflation of model compilation latency with computational execution time.

Core Scientific Contributions

• Formal Problem Characterization (RTASP-SH): An industrial extension of the strongly $\mathcal{NP}$-hard Resource-Constrained Project Scheduling Problem (RCPSP), incorporating renewable cumulative resources and pairwise disjunctive spatial hazards (e.g., co-located hot work and explosive hydrocarbon atmospheres).

• Graph-Theoretic Sanitization: Algorithmic preprocessing pipeline establishing provable minimum/maximum makespan horizons ($H_{\min} = \text{CPM}(V, E_0)$, $H_{\max} = \sum d_i$), computing transitive reductions $\text{TR}(E_0)$ to eliminate topological redundancies, and filtering out pseudo-disjunctive spatial conflicts between transitively reachable nodes via the reachability closure $\text{TC}(E_0)$.

• Semantically Symmetrical Dual Formulations:

  • Constraint Programming (CP-SAT): Native non-preemptive interval variables utilizing Lazy Clause Generation (LCG), global energetic reasoning (Cumulative), and disjunctive propagation (NoOverlap).

  • Time-Indexed Constrained Quadratic Model (CQM): Exact binary time-indexed representation enforcing execution uniqueness, makespan bounding on DAG sink tasks $\mathcal{T}_{\text{sink}}$, discrete-time cumulative capacity constraints, and time-step disjunctive spatial conflicts.

• Analytical Proof of Physical QPU Limitations (Proposition 1): Mathematical demonstration of why binary slack variable expansions for cumulative constraints induce quadratic coupling coefficients $J_{ij} \propto \lambda C_r^2$. This dynamic range expansion forces the coupling ratio below the physical Intrinsic Control Error ($\sigma_{\text{ICE}} \approx 10^{-2} J_{\max}$) and DAC resolution limits of physical flux qubits, proving that un-decomposed pure QPU annealing fails to yield feasible ground states.

• Slack-Free Hybrid Decomposition (LNS-MWIS): A decomposition-based Large Neighborhood Search (LNS) paradigm where the classical CP-SAT master problem manages global temporal constraints and cumulative resource ceilings, delegating congested, conflict-free Maximum Weight Independent Set (MWIS) subproblems to the quantum annealer without introducing slack variables.

Methodological Protocol and Metrics

To support reproducible benchmarking, the artifacts define rigorous evaluation criteria:

• Feasibility Ratio ($R_{\text{feas}}$): Strict verification of 100% compliance across cumulative and disjunctive constraints across all generated samples.

• Time-to-Target (TTT): Exact wall-clock solving trajectories required to reach certified bounds within 2% of $H_{\min}$.

• Overhead Separation: Granular profiling separating Python SDK instantiation/graph construction time from actual QPU/hybrid cloud solver execution time.

Citation & Metadata

@article{usai2026benchmarking,
  title     = {Benchmarking Quantum and Hybrid Annealing on Refinery Turnaround Scheduling: A Rigorous Assessment against Constraint Programming and Mixed-Integer Formulations},
  author    = {Usai, Luigi},
  year      = {2026},
  doi       = {10.5281/zenodo.XXXXXXX},
  publisher = {Zenodo},
  note      = {ORCID: 0009-0003-3001-717X}
}

Keywords: Quantum Annealing, D-Wave CQM, Turnaround Scheduling, RCPSP, CP-SAT, Constraint Programming, Maximum Weight Independent Set, Intrinsic Control Error, Operations Research, Mathematical Optimization.