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

Luigi Usai

Published Sep 3, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.22286906

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The optimization of front-end crude oil scheduling is a critical determinant of refinery profitability and operational stability. However, the coupling of discrete logistics events (e.g., vessel berthing) with continuous material flows (e.g., pipeline transfers) renders this problem an NP-hard Mixed-Integer Linear Programming (MILP) challenge, often intractable for classical solvers at industrial scales. This study proposes a novel hybrid quantum-classical framework to address these computational bottlenecks. We employ Benders Decomposition to decouple the monolithic model into a discrete Master Problem (MP) and a continuous Subproblem (SP). To exploit the search capabilities of quantum computing, the MP is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) model and solved via a hybrid quantum solver, while the SP enforces mass balance and quality constraints through iterative optimality and feasibility cuts. Extensive experiments on 15 multi-scale instances demonstrate that the proposed framework significantly outperforms traditional metaheuristics (e.g., Genetic Algorithms, Tabu Search), reducing total operating costs by approximately 73--80% and achieving computational speeds comparable to state-of-the-art commercial solvers (Gurobi). By effectively leveraging global optimality cuts, the method overcomes the tendency of heuristic approaches to trap in local optima, providing a robust and scalable solution for complex refinery logistics.
• We propose a new hybrid quantum-classical algorithm for solving the UC problem. • The hybrid model successfully optimizes 24-hour UC systems from 10 to 1000 units. • The model outperforms classical metaheuristics (GA and SA) and classical MINLP. • This represents an improvement over previous QCUC methods, a step to real-world use. Resource scheduling is critical in many industries, especially in power systems where the Unit Commitment (UC) problem determines the on/off status and output levels of generators under physical and economic constraints. Traditional exact methods, such as Branch‑and‑Bound, Branch‑and‑Cut, dynamic programming and mixed‑integer linear programming (MILP), remain the backbone of UC solution techniques, but they often rely on linear approximations or exhaustive search, leading to high computational burdens as system size grows. Metaheuristic approaches, such as genetic algorithms, particle swarm optimization, and other evolutionary methods, have been explored to mitigate this complexity; however, they typically lack optimality guarantees, exhibit sensitivity to initial conditions, and can become prohibitively time‑consuming for large‑scale systems. In this paper, we introduce a quantum‑classical hybrid algorithm for UC, and other resource scheduling problems by extension, that leverages Benders decomposition to decouple binary commitment decisions from continuous economic dispatch. The binary “master problem” is formulated as a quadratic unconstrained binary optimization (QUBO) model and solved on a quantum annealer. The continuous “subproblem,” which minimizes generation costs, with Lagrangian cuts feeding back to the master until convergence. We evaluate our hybrid framework on systems scaled from 10 to 1,000 generation units. Compared against a classical mixed‑integer nonlinear programming (MINLP) baseline, the hybrid algorithm achieves a consistently lower computation‑time growth rate and maintains an absolute optimality gap below 1.63%. These results demonstrate that integrating quantum annealing within a hybrid quantum-classical Benders decomposition loop can significantly accelerate large‑scale resource scheduling without sacrificing solution quality, pointing toward a viable path for addressing the escalating complexity of modern power grids.
Abstract We benchmark classical, simulated-quantum, hybrid, and direct quantum-annealing workflows on a structured binary control problem formulated as a quadratic unconstrained binary optimization (QUBO) model. The benchmark is motivated by greenhouse heater scheduling, where the horizon (H)(H)(H) denotes the number of hourly binary control decisions, but the focus is on solver behavior for a physically decoded control-QUBO formulation. For the main one-day instance ((H=24)(H=24)(H=24)), all solver outputs are decoded back into heater schedules and evaluated using the same simulator-side objective and feasibility criterion. Classical simulated annealing and path-integral simulated quantum annealing produce feasible near-optimal solutions in all repetitions, with best objectives close to the exact optimum. In contrast, the tested D-Wave Leap Hybrid binary quadratic model workflow is less reliable and does not outperform the classical baselines under 15--60 s requested time limits. Direct D-Wave quantum processing unit execution on reduced instances remains feasible in all runs and recovers the exact optimum for (H=10)(H=10)(H=10) and (H=12)(H=12)(H=12), but the exact-hit rate decreases with increasing horizon. The results do not indicate quantum advantage, but provide a reproducible benchmark for evaluating annealing-based natural and quantum computing workflows on structured control QUBOs. MSC Classification: 90C27 , 90C59 , 81P68 , 93C55
Abstract: Global logistics networks, intercontinental air-freight consolidators, and maritime energy fleets continuously solve large-scale Mixed-Integer Linear Programs (MILPs) such as the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and multi-vessel Maritime Inventory Routing Problems (MIRP). When weather disruptions, port congestion, or geopolitical airspace closures invalidate baseline schedules, classical branch-and-cut solvers (Gurobi, CPLEX) experience exponential worst-case tree growth on subproblems exceeding 2,000 binary decision variables, often failing to converge within strict 5-to-15-minute operational re-dispatch windows. Conversely, current Noisy Intermediate-Scale Quantum (NISQ) processors remain limited to 100-to-1,000 physical qubits with finite two-qubit gate fidelity (99.2%−99.8%99.2\%-99.8\%99.2%−99.8%), preventing direct encoding of full enterprise logistics instances. This paper presents a production-grade Quantum-Classical Hybrid Cloud Architecture that bridges enterprise Kubernetes clusters with co-located quantum processing units (QPUs) via AWS Braket Hybrid Jobs and IBM Quantum Qiskit Runtime primitives. Our framework applies Benders and Dantzig-Wolfe column generation on classical cloud HPC nodes to decompose a 25,000-variable global fleet MILP into a continuous master problem and hard combinatorial pricing/routing subproblems of 60 to 140 binary variables. These subproblems are transformed into Quadratic Unconstrained Binary Optimization (QUBO) and Ising Hamiltonians, warm-started from classical linear programming (LP) relaxations (WS-QAOA), compiled with dynamical decoupling and Zero-Noise Extrapolation (ZNE), and executed inside co-located QPU-CPU sessions while a GPU-accelerated Simulated Bifurcation (SB) digital annealer runs in parallel as a deterministic SLA fallback. Evaluated on disruption recovery workloads modeled on ExxonMobil maritime LNG routing and DHL Global Forwarding air-cargo container loading, our hybrid WS-QAOA + Column Generation workflow improves optimality gap closure at a 10-minute SLA cutoff from 6.84% (classical branch-and-bound alone) to 1.42%, reduces emergency re-routing compute wall-clock time by 61.5%, and cuts fleet fuel and charter penalty costs by 4.7%. Research Domain & Specialization Track Master of Science in Information Technology (MSIT) — Quantum Cloud Computing, Hybrid Orchestration, and Operations Research. Core Technical Highlights Empirical Production Case Studies: Rigorous architectural blueprints and telemetry evaluation across enterprise cloud deployments. Four-Tier Reference Architecture: Formal specification from edge ingress to distributed hardware execution pools. Mathematical Formulation: Formally derived algorithmic and optimization models with closed-loop verification. Multi-Modal Benchmarking: Comparative empirical baselines under fault-injection and synthetic workload scaling. Author Information Author: Sonu Kumar SinghRole: Senior Consultant Affiliation: Independent Researcher Publication Status: Preprint / Working Paper (MSIT AI & Cloud Systems Research Series) Reproducibility & Open Science All included architecture diagrams, telemetry schemas, and benchmark curves are open-access under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.
Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling problems, have been applied to automate this process, solving large-scale production planning problems remains computationally demanding. Moreover, many practical scenarios involve conflicting objectives, making traditional scalarization techniques ineffective in finding diverse and useful Pareto-optimal solutions. To address these challenges, we developed a quantum-classical hybrid algorithm that decomposes the problem into two subproblems: resource allocation and task scheduling. Resource allocation is formulated as a quadratic unconstrained binary optimization problem and solved using annealing-based methods that efficiently explore complex solutions. Task scheduling is modeled as a mixed-integer linear programming problem and solved using conventional solvers to satisfy detailed scheduling constraints. We validated the proposed method using benchmark instances based on foundry production scenarios. Experimental results demonstrate that our hybrid approach achieves superior solution quality and computational efficiency compared to traditional monolithic methods. This work offers a promising direction for high-speed, multi-objective scheduling in industrial applications.