A distribution free newsboy problem under shortage-level constraints

Since order quantity has only been decided at a spot selling time in the classical newsboy problem, both the purchase timing and the time-variant variance of the forecast demand are neglected. When the buyer purchases seasonal commodity by changing his pre-planned schedule for more purchase discount, it is necessary for the buyer to forecast the demand of spot selling time, which may increase the variance of the demand. This paper deals simultaneously with optimal purchase timing and order quantity under a specified shortage-level limit in a distribution free newsboy problem. Besides, a numerical example is used to illustrate the largest amount called Expected Value of Additional Information, which decision-maker will be willing to pay for the knowledge of the normal distribution. Furthermore, the effects of parameters and economical meanings are also included. The resultant outcomes could apply to some cases in futures commodity contracts.