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首页> 外文期刊>Operations Research: The Journal of the Operations Research Society of America >Optimality Gap of Constant-Order Policies Decays Exponentially in the Lead Time for Lost Sales Models
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Optimality Gap of Constant-Order Policies Decays Exponentially in the Lead Time for Lost Sales Models

机译：丢失销售模型的提前期，定单策略的最优差距呈指数下降

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摘要

Inventory models with lost sales and large lead times have traditionally been considered intractable due to the curse of dimensionality. Recently, Goldberg and coauthors laid the foundations for a new approach to solving these models, by proving that as the lead time grows large, a simple constant-order policy is asymptotically optimal. However, the bounds proven there require the lead time to be very large before the constant-order policy becomes effective, in contrast to the good numerical performance demonstrated by Zipkin even for small lead time values. In this work, we prove that for the infinite-horizon variant of the same lost sales problem, the optimality gap of the same constant-order policy actually converges exponentially fast to zero, with the optimality gap decaying to zero at least as fast as the exponential rate of convergence of the expected waiting time in a related single-server queue to its steady-state value. We also derive simple and explicit bounds for the optimality gap, and demonstrate good numerical performance across a wide range of parameter values for the special case of exponentially distributed demand. Our main proof technique combines convexity arguments with ideas from queueing theory.
机译：传统上，由于维度的诅咒，销售损失和交货时间较长的库存模型难以解决。最近，Goldberg及其合作者通过证明随着交货时间的增加，简单的恒定阶策略在渐近最优性上奠定了解决这些模型的新方法的基础。但是，在那里证明的界限要求定常策略生效前的交货时间非常长，这与Zipkin展示的良好数值性能（即使对于较小的交货时间值）相反。在这项工作中，我们证明了对于相同的销售损失问题的无限水平变体，相同恒定订单策略的最优缺口实际上以指数方式迅速收敛至零，而最优缺口至少会与零一样快地衰减至零。相关单服务器队列中的预期等待时间与其稳态值的指数收敛速度。我们还推导了最优间隙的简单和显式边界，并针对指数分布需求的特殊情况在各种参数值上展示了良好的数值性能。我们的主要证明技术将凸论据与排队论的思想相结合。

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