EOQ when holding costs grow with the stock level: well-posedness and solutions

An existence-uniqueness theorem is proved about a minimum costorder for a class of inventory models whose holding costs grow, following a power law,with the stock level. The theorem requires to perform a check of convergence of someimproper integrals, and constitutes the article's main theoretical contribution to thesubject. As application, several cases of demand are considered as functions of thestock level