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 G. Mingari Scarpello, D. Ritelli, EOQ when holding costs grow with the stock level: well-posedness and solutions, Advanced Modeling and Optimization, 10 (2) (2008) 233-240. are then extended to different environments: i.e. when the holding costs change during time generalizing a model available in H.J. Weiss, Economic Order Quantity Models with Nonlinear Holding Costs, European Journal of Operational Research 9 (1) (1982) 56-60., or with invariable holding costs but adopting a backordering strategy. Application cases are provided assuming several functional behaviors of demand versus the stock level