Value iteration can find the optimal replenishment policy for a perishable inventory problem, but is computationally demanding due to the large state spaces that are required to represent the age profile of stock. The parallel processing capabilities of modern GPUs can reduce the wall time required to run value iteration by updating many states simultaneously. The adoption of GPU-accelerated approaches has been limited in operational research relative to other fields like machine learning, in which new software frameworks have made GPU programming widely accessible. We used the Python library JAX to implement value iteration and simulators of the underlying Markov decision processes in a high-level API, and relied on this library's function transformations and compiler to efficiently utilize GPU hardware. Our method can extend use of value iteration to settings that were previously considered infeasible or impractical. We demonstrate this on example scenarios from three recent studies which include problems with over 16 million states and additional problem features, such as substitution between products, that increase computational complexity. We compare the performance of the optimal replenishment policies to heuristic policies, fitted using simulation optimization in JAX which allowed the parallel evaluation of multiple candidate policy parameters on thousands of simulated years. The heuristic policies gave a maximum optimality gap of 2.49%. Our general approach may be applicable to a wide range of problems in operational research that would benefit from large-scale parallel computation on consumer-grade GPU hardware.

利用GPU加速技术运行价值迭代算法可以节省时间和计算资源，我们使用Python库JAX实现了该算法的高级API，并依靠该库的函数转换和编译器来高效地利用GPU硬件。通过将该算法应用于实际场景，我们的研究表明这种方法的普惠性，可以在消费级GPU上进行大规模并行计算，适用于一系列运营研究中需要处理的大规模问题。

GPU加速的价值迭代与模拟，在保质期库存控制中实现更远更快的前进