Online Algorithms for the Newsvendor Problem with and without Censored Demands

The newsvendor problem describes the dilemma of a newspaper salesman—how many papers should he purchase each day to resell, when he doesn’t know the demand? We develop approaches for this well known problem in operations research, both for when the actual demand is known at the end of each day, and for when just the amount sold is known, i.e., the demand is

censored

. We present three results: (1) the first known algorithm with a bound on its worst-case performance for the censored demand newsvendor problem, (2) an algorithm with improved worst-case performance bounds for the regular newsvendor problem compared to previously known algorithms, and (3) more precise bounds on the performance of the two algorithms when they are seeded with an approximate “guess” on the optimal solution. In addition (4) we test the algorithms in a variety of simulated and real world conditions, and compare the results to those by previously known approaches. Our tests indicate that our algorithms perform comparably and often better than known approaches.