A note: An improved upper bound for the online inventory problem with bounded storage and order costs

This work gives an improved competitive analysis for an online inventory problem with bounded storage and order costs proposed by Larsen and Wohlk (2010). We improve the upper bound of the competitive ratio from (2+1k)Mmto less than 45(2+1k)Mm,where k, M and m are parameters of the given problem. The key idea is to use linear-fractional programming and primal-dual analysis methods to find the upper bound of a central inequality.