Competitive analysis of interrelated price online inventory problems with demands

This paper investigates the interrelated price online inventory problems in which decisions as to when and how much to replenish must be made in an online fashion to meet some demand even without concrete knowledge of future prices. The objective of the decision maker is to minimize the total cost with the demands met. Two different types of demand are considered carefully, which are linearly related demand to price and exponentially related demand to price. In this paper, the prices are online with only the price range variation known in advance, which are interrelated with the preceding price. Two models of price correlations are investigated. Namely an exponential model and a logarithmic model. The corresponding algorithms of the problems are developed and the competitive ratio of the algorithms are also derived by the solutions of linear programming.