Fuzzy Gaussian mixture optimisation of the newsvendor problem: mixing fuzzy perception and randomness of customer demand
针对决策者同时面临统计数据和主观判断的需求信息，本文开发了一个模糊高斯混合模型，将概率输入与模糊权重结合，推导出最优订货策略，并允许放松需求分布的单模态假设和编码决策者的风险态度。
Motivated by the increasing exposition of decision makers to both statistical and judgemental based sources of demand information, we develop in this paper a fuzzy Gaussian Mixture Model (GMM) for the newsvendor permitting to mix probabilistic inputs with a subjective weight modelled as a fuzzy number. The developed framework can model for instance situations where sales are impacted by customers sensitive to online review feedback or expert opinions. It can also model situations where a marketing campaign leads to different stochastic alternatives for the demand with a fuzzy weight. Thanks to a tractable mathematical application of the fuzzy machinery on the newsvendor problem, we derived the optimal ordering strategy taking into account both probabilistic and fuzzy components of the demand. We show that the fuzzy GMM can be rewritten as a classical newsvendor problem with an associated density function involving these stochastic and fuzzy components of the demand. The developed model enables to relax the single modality of the demand distribution usually used in the newsvendor literature and to encode the risk attitude of the decision maker.