The distribution-free newsboy problem under the worst-case and best-case scenarios

• We present new foundations for analyzing the distribution-free newsboy problem.
• Some reductions to the standard newsboy problem are revealed.
• Tools for seeking solutions under different demand knowledge scenarios are identified.
• The demand distribution is characterized by its support, mean and variance.
• Extensions to other stochastic inventory problems are indicated.

New theoretical foundations for analyzing the newsboy problem under incomplete information about the probability distribution of random demand are presented. Firstly, we reveal that the distribution-free newsboy problem under the worst-case and best-case demand scenarios actually reduces to the standard newsboy problem with demand distributions that bound the allowable distributions in the sense of increasing concave order. Secondly, we provide a theoretical tool for seeking the best-case and worst-case order quantities when merely the support and the first k moments of the demand are known. Using this tool we derive closed form formulas for such quantities in the case of known support, mean and variance, i.e. k = 2. Consequently, we generalize all results presented so far in literature for the worst-case and best-case scenarios, and present some new ones. Extensions of our findings to the cases of the known mode of a unimodal demand distribution, the known median, and to other stochastic inventory problems are indicated.