Impacts of Transportation Cost on Distribution-Free Newsboy Problems

A distribution-free newsboy problem (DFNP) has been launched for a vendor to decide a product’s stock quantity in a single-period inventory system to sustain its least maximum-expected profits when combating fierce and diverse market circumstances. Nowadays, impacts of transportation cost on determination of optimal inventory quantity have become attentive, where its influence on the DFNP has not been fully investigated. By borrowing an economic theory from transportation disciplines, in this paper the DFNP is tackled in consideration of the transportation cost formulated as a function of shipping quantity and modeled as a nonlinear regression form from UPS’s on-site shipping-rate data. An optimal solution of the order quantity is computed on the basis of Newton’s approach to ameliorating its complexity of computation. As a result of comparative studies, lower bounds of the maximal expected profit of our proposed methodologies surpass those of existing work. Finally, we extend the analysis to several practical inventory cases including fixed ordering cost, random yield, and a multiproduct condition.