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Estimation of Jointly Normally Distributed Demand for Cross-Selling Items in Inventory Systems with Lost Sales

机译：估计销售损失的库存系统中的交叉销售项目的共同正常分布式需求

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摘要

Demand estimation is often confronted with incomplete information of censored demand because of lost sales. Many estimators have been proposed to deal with lost sales when estimating the parameters of demand distribution. This study introduces the cross-selling effect into estimations, where two items are cross-sold because of the positive externality in a newsvendor-type inventory system. We propose an approach to estimate the parameters of a jointly normally distributed demand for two cross-selling items based on an iterative framework considering lost sales. Computational results based on more than two million numerical examples show that our estimator achieves high precision. Compared with the point estimations without lost sales, all the relative errors of the estimations of demand expectation, standard deviation, and correlation coefficient are no larger than 2% on average if the sample size is no smaller than 800. In particular, for demand expectation, the error is smaller than 1% if the comprehensive censoring level is no larger than four standard deviations (implying a 2 sigma-level of safety stock for each item), even if the sample size decreases to 50. This implies that the demand estimator should be competent in modern inventory systems that are rich in data.
机译：随着销售损失，需求估计往往面临着截查的需求的不完整信息。在估算需求分布参数时，已提出许多估算器来处理销售额。本研究介绍了跨销售效果进入估计，这两个物品由于新闻监督者型库存系统中的正外部性而被交叉。我们提出了一种基于考虑销售损失的迭代框架来估计两个跨销售项目的共同正常分布式需求的参数。基于超过200万个数字示例的计算结果表明，我们的估算器能够实现高精度。与销售损失的点估计相比，如果样品尺寸不小于800，则需求期望，标准偏差和相关系数的估计的所有相对误差都不大于2％。特别是对于需求期望如果综合审查水平不大于四个标准偏差（暗示每个项目的2秒钟级），则该误差小于1％，即使样本量减少到50，即使样品大小降至50。这意味着需求估算器应该有能力在丰富数据的现代库存系统中。

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  • 来源
    《Mathematical Problems in Engineering》 |2019年第16期|7219326.1-7219326.21|共21页
  • 作者

    Zhang Ren-Qian; Wang Qi-Qi; Zhang Yi-Ye; Zheng Hai-Tao; Hu Jie;

  • 作者单位

    Beihang Univ Sch Econ & Management Beijing 100083 Peoples R China;

    Beihang Univ Sch Econ & Management Beijing 100083 Peoples R China;

    Beihang Univ Sch Econ & Management Beijing 100083 Peoples R China;

    Beihang Univ Sch Econ & Management Beijing 100083 Peoples R China;

    Beihang Univ Sch Econ & Management Beijing 100083 Peoples R China;

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