Path Matters: Industrial Data Meet Quantum Optimization

Real-world optimization problems must undergo a series of transformations before becoming solvable on current quantum hardware. Even for a fixed problem, the number of possible transformation paths -- from industry-relevant formulations through binary constrained linear programs (BILPs), to quadratic unconstrained binary optimization (QUBO), and finally to a hardware-executable representation -- is remarkably large. Each step introduces free parameters, such as Lagrange multipliers, encoding strategies, slack variables, rounding schemes or algorithmic choices -- making brute-force exploration of all paths intractable. In this work, we benchmark a representative subset of these transformation paths using a real-world industrial production planning problem with industry data: the optimization of work allocation in a press shop producing vehicle parts. We focus on QUBO reformulations and algorithmic parameters for both quantum annealing (QA) and the Linear Ramp Quantum Approximate Optimization Algorithm (LR-QAOA). Our goal is to identify a reduced set of effective configurations applicable to similar industrial settings. Our results show that QA on D-Wave hardware consistently produces near-optimal solutions, whereas LR-QAOA on IBM quantum devices struggles to reach comparable performance. Hence, the choice of hardware and solver strategy significantly impacts performance. The problem formulation and especially the penalization strategy determine the solution quality. Most importantly, mathematically-defined penalization strategies are equally successful as hand-picked penalty factors, paving the way for automated QUBO formulation. Moreover, we observe a strong correlation between simulated and quantum annealing performance metrics, offering a scalable proxy for predicting QA behavior on larger problem instances.