A class of random algorithms for inventory cycle offsetting

The inventory cycle offsetting problem (ICP) is a strongly NP‐complete problem. We study this problem from the view of probability theory, and rigorously analyse the performance of a specific random algorithm for this problem; furthermore, we present a 'local search' algorithm, and a 'modified local search' algorithm, which give much better results (the 'modified local search' gives better results than plain 'local search'), and lead to good solutions to certain practical instances of ICP, as we demonstrate with some numerical data. The regime where the random algorithm is rigorously proved to work is when the number of items is large, while the time horizon and unit volumes are not too large. Under such natural hypotheses, the law of large numbers, and various quantitative refinements (such as Bernstein's inequality) come into play, and we use these results to show that there always exist good solutions, not merely that good solutions holds with high probability.