A Coupled Newsvendor Benchmark for QAOA: Budget-Constrained Multi-Item Formulations, Depth Effects, Scaling, and Optimizer Sensitivity

This study develops a budget-constrained multi-item newsvendor benchmark for analysing the Quantum Approximate Optimization Algorithm (QAOA) on an inventory problem with explicit combinatorial coupling. The single-item closed-form newsvendor model is used only as a calibration benchmark, whereas the main formulation links multiple order decisions through a shared resource constraint. After binary expansion, the problem is expressed as a quadratic unconstrained binary optimization model and mapped to an Ising Hamiltonian with non-trivial pairwise interactions. QAOA is implemented in Qiskit 0.46.0 using COBYLA and SPSA under a reproducible multi-start protocol, and evaluated across depths p ∈ {1, 2, 3, 4, 6} and instance sizes from 4 to 16 qubits. Performance is assessed against exact enumeration or mixed-integer linear programming baselines using objective gap, feasible-sample mass, optimizer variability, and runtime. On the calibration benchmark, the QAOA mode recovers the classical optimum. On a representative 12-qubit coupled benchmark, increasing depth reduces the objective gap from 23.58% at p = 1 to 1.63% at p = 6. The study provides a reproducible benchmark for evaluating low-depth QAOA on coupled inventory optimization problems with direct economic interpretation.