The Distribution-Free Newsboy Problem with Resalable Returns

Abstract

We study the case of a catalogue/internet mail order retailer selling seasonal productsand receiving large numbers of commercial returns. Returned products arriving beforethe end of the selling season can be resold if there is sufficient demand. A single orderis placed before the season starts. Excess inventory at the end of the season is salvagedand all demands not met directly are lost. Since little historical information is available,it is impossible to determine the shape of the distribution of demand. Therefore, weanalyze the distribution-free newsboy problem with returns, in which only the mean andvariance of demand are assumed to be known. We derive a simple closed-form expressionfor the distribution-free order quantity, which we compare to the optimal order quantities whengross demand is assumed to be normal, lognormal or uniform. We find that the distribution-freeorder rule performs well in most realistic cases.

Keywords: inventory, distribution-free newsboy problem, product returns

JEL Classification: M, M11, R4, C61