Fully Distribution-Free Profit Maximization: The Inventory Management Case

We study profit maximization in inventory control problems where demands are unknown. Neither probabilistic distributions nor sets are available to characterize the unknown demand parameters. Therefore, we adopt an online optimization perspective for our analysis. The usual competitive ratio is not well defined for the problems we analyze; consequently, we introduce a new worst-case metric that is suitable. We consider two inventory management frameworks: (1) perishable products with lost sales and (2) durable products with backlogged demand. We consider both finite and infinite planning horizons. We design best-possible online procurement strategies for all cases.