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研究了具损失厌恶和损失概率厌恶行为的考虑缺货成本报童模型。利用订购量小于和大于最大损失等量订购量时的随机利润分布函数以及随机获利和损失的排名函数,获得了报童的前景值函数,分析了报童的前景值函数性质。结果表明:前景值函数为订货量的连续不可微凹函数,不可微点位于最大损失等量订购量处;而且仅具损失厌恶或仅具风险中性的报童模型是本模型的特例。解析分析表明:当最优订购量小于最大损失等量订购量时,最优订购量随极端获利和不利结果重视程度的提高而增加;当最优订购量大于最大损失等量订购量时,最优订购量随极端获利结果重视程度的提高而增加,最优订购量随极端不利结果重视程度的提高而减少。数值结果表明:最优订购量随非极端获利和非极端损失结果敏感度的提高而增加;最优订购量随损失厌恶系数的提高而减少。
The newsboy model with out-of-stock cost is studied with loss aversion and loss probability abhorrence. Using the random profit distribution function and the ranking function of random profit and loss when order quantity is less than or greater than the maximum order loss quantity, the foreground function of newsboy is obtained, and the nature of foreground function of newsboy is analyzed. The results show that the foreground value function is a continuous non-differentiable concave function of the order quantity, and the non-differentiable point is located at the order of the largest loss equivalent order quantity. And only the newsboy model with loss aversion or only risk neutrality is a special case of this model. The analytical analysis shows that when the optimal order quantity is less than the maximum loss order quantity, the optimal order quantity increases with the increase of the extreme profit and unfavorable result; when the optimal order quantity is more than the order of the largest loss equivalent quantity, The optimal order quantity increases with the degree of attention paid to the outcome of the extreme profit, and the optimal order quantity decreases with the increase of the degree of extreme unfavorable result. The numerical results show that the optimal order quantity increases with the increase of the sensitivity of non-extreme profitability and non-extreme loss results. The optimal order quantity decreases with the increase of loss aversion coefficient.