Mathematical properties of EOQ models with special cost structure

An existence-uniqueness theorem is proved about a minimum cost order for a class of inventory models whose holding costs grow according to a stock level power law. The outcomes of a previous work of two of the authors are then extended to different environments: i.e. when the holding costs change during time generalizing the Weiss model, or with invariable holding costs but adopting a backordering strategy. Application cases are provided assuming several functional behaviors of demand versus the stock level