Competitive algorithms for the on-line inventory problem

An on-line inventory problem is proposed and studied by our team differing from the traditional version of the problem, in which probability distributions for sales are supposed to know to the decision-maker, the on-line inventory problem of concern is due to the uncertainty where decision-makers only know the upper bound and lower bound of the daily demand for a particular product. The objective of game is to decide how many products should be prepared everyday so that the competitive ratio, which shows how close the on-line algorithm's performance to that of the relevant off-line optimal algorithm, can be minimized. First, a simplified on-line inventory problem model is formulated. Then, a competitive algorithm for general version of the problem, namely the general harmonic algorithm is presented. Furthermore the competitive ratio is proved to be the best one if decision-makers choose a fixed quantity product for any sequence of quantities from buyers. Finally, some other variants are also investigated and relevant competitive algorithms are developed.