  Motivated by the application of energy storage management in electricity
markets, this paper considers the problem of online linear programming with
inventory management constraints. Specifically, a decision maker should satisfy
some units of an asset as her demand, either form a market with time-varying
price or from her own inventory. The decision maker is presented a price in
slot-by-slot manner, and must immediately decide the purchased amount with the
current price to cover the demand or to store in inventory for covering the
future demand. The inventory has a limited capacity and its critical role is to
buy and store assets at low price and use the stored assets to cover the demand
at high price. The ultimate goal of the decision maker is to cover the demands
while minimizing the cost of buying assets from the market. We propose BatMan,
an online algorithm for simple inventory models, and BatManRate, an extended
version for the case with rate constraints. Both BatMan and BatManRate achieve
optimal competitive ratios, meaning that no other online algorithm can achieve
a better theoretical guarantee. To illustrate the results, we use the proposed
algorithms to design and evaluate energy procurement and storage management
strategies for data centers with a portfolio of energy sources including the
electric grid, local renewable generation, and energy storage systems.
