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Natural Sciences and Applied Technology

A Comparative Study of QAOA and Classical Metaheuristics for Inventory Optimization

Poonam Chaudhary, Pranav Singh, Sneha Kandacharam, Rajan Gupta

Published Sep 30, 2026• 0 citations
Publisher

Abstract

We investigate whether the Quantum Approximate Optimization Algorithm (QAOA) can compete with classical metaheuristics for multi-product, multi-location retail inventory optimization under demand uncertainty. We formulate the binary inventory decision problem as a Quadratic Unconstrained Binary Optimization (QUBO) model and benchmark QAOA (simulated via classical statevector simulation, $p=2$ layers) against Mixed-Integer Linear Programming (MILP), Simulated Annealing (SA), Genetic Algorithms (GA), and Tabu Search across problem sizes from $n=5$ to $n=200$ binary variables, using Walmart sales and Kaggle retail demand datasets. Our key finding is a \textbf{negative result}: while QAOA achieves a 2.3\% optimality gap and 97\% constraint satisfaction at small scales ($n \leq 20$), it is not competitive with classical metaheuristics at practical problem sizes. Classical heuristics---particularly SA and Tabu Search---consistently outperform QAOA on all instances tested and scale efficiently to $n=200$, whereas QAOA simulation becomes intractable beyond $n=30$ due to exponential memory requirements. We do not claim any quantum speedup. This comparative study provides important insights into the limitations of current QAOA implementations for supply chain problems, including the effects of penalty parameter scaling, barren plateaus in the optimization landscape, and circuit depth constraints. We additionally present an economic sensitivity analysis linking macroeconomic indicators to optimal inventory decisions and a rolling-horizon proof-of-concept for multi-period planning.

DOI
10.5281/zenodo.23000095

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We investigate whether the Quantum Approximate Optimization Algorithm (QAOA) can compete with classical metaheuristics for multi-product, multi-location retail inventory optimization under demand uncertainty. We formulate the binary inventory decision problem as a Quadratic Unconstrained Binary Optimization (QUBO) model and benchmark QAOA (simulated via classical statevector simulation, p=2p=2p=2 layers) against Mixed-Integer Linear Programming (MILP), Simulated Annealing (SA), Genetic Algorithms (GA), and Tabu Search across problem sizes from n=5n=5n=5 to n=200n=200n=200 binary variables, using Walmart sales and Kaggle retail demand datasets. Our key finding is a \textbf{negative result}: while QAOA achieves a 2.3% optimality gap and 97% constraint satisfaction at small scales (n≤20n \leq 20n≤20), it is not competitive with classical metaheuristics at practical problem sizes. Classical heuristics---particularly SA and Tabu Search---consistently outperform QAOA on all instances tested and scale efficiently to n=200n=200n=200, whereas QAOA simulation becomes intractable beyond n=30n=30n=30 due to exponential memory requirements. We do not claim any quantum speedup. This comparative study provides important insights into the limitations of current QAOA implementations for supply chain problems, including the effects of penalty parameter scaling, barren plateaus in the optimization landscape, and circuit depth constraints. We additionally present an economic sensitivity analysis linking macroeconomic indicators to optimal inventory decisions and a rolling-horizon proof-of-concept for multi-period planning.
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Managing inventory in large-scale supply chains necessitates quick, cost-effective decisions that adhere to constraints such as storage limits and variable demand. This paper describes a novel hybrid approach that uses both quantum and classical computers to tackle inventory problems structured as Quadratic Unconstrained Binary Optimization (QUBO). Each choice variable, such as restocking a product, is represented in binary form, with related costs and penalties built into the objective function. Business constraints are communicated indirectly using adjustable weights, allowing the model to remain unconstrained while discouraging unrealistic conclusions. Optimization is carried out using both classical methods like simulated annealing and quantum solvers such as D-Wave and QAOA, where a hybrid strategy selects the most viable solution. The results indicate that the hybrid system consistently produces lower total costs and better constraint compliance compared to individual solvers, especially for complex, high-dimensional datasets. To ensure secure, automated execution of these optimized decisions, a blockchain layer is introduced. Inventory actions—such as placing orders or updating stock—are carried out through smart contracts that provide tamper-proof, verifiable enforcement. By employing a lightweight Proof of Authority (PoA) mechanism, transaction validation remains fast while maintaining transparency across all nodes in the network. This integration of quantum optimization with blockchain automation enables a responsive and trustworthy framework for modern inventory management.
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The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles introduction to QAOA and its properties, focusing on its application to Quadratic and Polynomial Unconstrained Binary Optimization (QUBO and PUBO) problems. The tutorial begins by outlining variational quantum circuits and QUBO problems, focusing on their key properties and the encoding of problem constraints through quadratic penalty terms. Next, it explores the QAOA in detail, covering its Hamiltonian formulation, gate decomposition, and example applications, along with their implementation and performance results. This is followed by an analysis of the algorithm's energy landscape, where proofs are provided for its symmetry and periodicity, and where a resulting parameter space reduction is proposed. Finally, the tutorial extends these concepts to PUBO problems by generalizing the results to higher-order Hamiltonians and discussing the associated symmetries and circuit construction.