Abstract: It is found that the newsboy has loss of disgust and loss of probability aversion characteristics. In the paper, the Newsboy model with loss aversion and probabilistic loss aversion under shortage cost is studied. Using stochastic profit distribution functions and ranking functions when order quantity is less than maximum loss equivalent and order quantity is greater than maximum loss equivalent, its prospect value function is derived, and the nature of prospect value is revealed. The results show that the prospect value function is a continuous and non differentiable convex function, in which non differentiable points is in maximum loss equivalent; and Newsboy models with loss aversion or risk neutral are its special case. The analysis shows that:under the optimal order quantity being less than the maximum loss equivalent, the optimal order quantity increases with the increase of the degree on the extreme gain and unfavorable results. Under the optimal order quantity being greater than the maximum loss equivalent, the optimal order quantity increases with the increase of the degree on the extreme gain, and the optimal order quantity reduces with the degree on the extreme unfavorable results. The numerical results show that the optimal order quantity increases with the increase of the sensitivity of non extreme gain and non extreme loss. With the increase of the loss aversion coefficient, the optimal order quantity decreases. This study is helpful to understand the impact of the behavioral characteristics of newsboy on decision making.

Key words: newsvendor problem, prospect theory, loss aversion, probability loss aversion