在线补货与订单履行
Online Order Fulfillment with Replenishment
AI总结：
本文研究了补货与订单履行对系统性能的影响，提出了一种前瞻在线算法，通过比较补货与履行的优化价值，揭示了在不同情况下哪种策略对利润影响更大。
摘要：
在现代电子商务和服务运营中，企业必须共同管理库存补货和实时订单履行，以在需求不确定性下最大化利润。尽管每个组成部分在孤立状态下已被广泛研究，但它们的相互作用仍处于探索阶段。本文探讨了一个基本的运营问题：补货和履行中哪一个因素对整体系统性能影响更大？我们将系统建模为一个单地点的在线订单履行问题，其中存在销售损失和随机客户到达，每个都提供异质奖励。补货遵循基库存或恒定订单策略，而实时履行决策则通过在线算法进行。我们的核心性能指标是每个补货周期的预期平均利润，评估所有这些策略和算法的组合。我们的主要理论结果表明，当补货周期较长时，在线履行的累积遗憾保持与相应单周期问题相同量级，即使在重复补货的情况下，揭示了一种遗憾稳定性现象。这种现象也扩展到多地点设置。我们进一步开发了一个基于遗憾的框架，定量比较改进补货与改进履行的价值，并且我们刻画了在优化补货比优化在线履行算法（反之亦然）产生更大收入影响的制度。受某些例子中短视算法表现不佳的启发，我们引入了一种新的前瞻在线算法，预测未来的补货和需求。数值实验验证了该算法优于短视基线。总体而言，我们的结果为库存补货策略影响更大以及反之亦然的情况提供了理论和管理见解。
英文摘要：
In modern e-commerce and service operations, firms jointly manage inventory replenishment and real-time order fulfillment under demand uncertainty. We study their interaction in a single-resource lost-sales system with heterogeneous rewards, positive lead times, and replenishment cycles of length $T$. A central difficulty is that low regret in one fulfillment cycle need not imply a small profit gap under repeated replenishment, since fulfillment decisions change inventory and, under base-stock replenishment, subsequent orders. We consider base-stock and constant-order replenishment and compare online fulfillment with a myopic offline benchmark that knows current-cycle demand but not future demand. We give conditions under which $O(T^α)$ one-cycle regret yields an $O(T^α)$ upper bound on the expected average profit gap, uniformly over all finite horizons $N$. For base stock, the bound remains valid when the online and offline targets are optimized separately. For constant orders, a uniform quadratic count-loss bound gives an unrestricted two-sided comparison between separately optimized systems. For the cycle-restarted Bayes Selector, the finite-horizon bounds are $O(1)$. The optimized long-run constant-order profit gap is also $O(1)$. We use these results to compare optimized base stock with greedy fulfillment against optimized constant order with the Bayes Selector and decompose the profit difference into replenishment and fulfillment components. A representative finite-horizon simulation shows that the ranking of the two policy combinations can change with cycle length. We also extend the transfer analysis to multiple resources. Under single-resource base-stock replenishment, a mean-LP quota policy has uniform $O(\sqrt T)$ regret against full-information benchmark.
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