Abstract: This paper studies the decision-making problem of ordering and carrier capacity for an online sales enterprise with certain carrier capacities under uncertain demand. Based on the expected profit function of the online sales enterprise, a robust optimization model based on distribution-free is developed with the mean and variance as the only known demand distribution information. For the proposed model, the dual theory is used to transform it into tractable mathematical programming. The corresponding ordering and carrier capacity decisions are derived, and the sensitivity of relevant system parameters is analyzed. The effectiveness of the model in dealing with demand uncertainty is verified by numerical calculation. The results show that the optimal order quantity of the online sales enterprise increases while the increment of the optimal carrier capacity decreases with its original capacity. When the online sales enterprise has its own carrier capacity, the expected profit in different distribution is generally higher than that without capacity. In particular, a comparison of the robust decisions based on the proposed model with those obtained in normal or uniform distribution demonstrates that the difference between the expected profit derived from the robust decisions and the optimal expected profit when the demand distribution is known is relatively small, which indicates that the decisions derived from the proposed model have a good robustness.

Key words: online sales, carrier capacity, ordering decision, distribution-free, robust optimization

摘要： 针对一个拥有一定配送能力的在线销售企业，研究其在不确定需求下的订货和配送能力扩张决策问题。在构建在线销售企业的期望利润函数基础上，考虑仅知需求均值和方差信息，给出了基于自由分布的在线销售企业利润鲁棒优化模型。针对所建模型，采用对偶理论将其转化为易于求解的数学规划，给出了相应的订货和配送能力扩张策略，并对相关系统参数进行了灵敏度分析。最后，通过数值计算验证了所建模型在应对需求不确定性方面的有效性。结果表明：在线销售企业的最优订货量随自身原有配送能力的增加而增加，最优配送能力增量随自身原有配送能力的增加而降低。当在线销售企业自身拥有配送能力时，其在不同分布下得到的期望利润一般均高于无配送能力的情形。特别地，将基于文中模型的鲁棒策略与需求服从正态和均匀分布下得到的最优策略及期望利润进行比较分析发现，鲁棒策略下期望利润与已知需求分布时的最优期望利润相差较小，表明基于文中方法得到的策略具有良好的鲁棒性。

关键词: 在线销售, 配送能力, 订货决策, 自由分布, 鲁棒优化