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This paper aims to give a comprehensive review, summary, and discussion on inventory models that have appeared in the literature. During these past ten decades, no seminal paper reviewing the field of inventory lot sizing has even been published. This limitation has been identified in the literature by several researchers over the years, with the sheer volume of the number of published inventory lot sizing models acting as a factor which has limited a research endeavor to review the literature on inventory lot sizing models.

This article reviews research on inventory lot size models and provides a review of previously published literature review papers on inventory models. Based on this initial review, the literature extending current research practices on inventory modeling in supply chains and in sustainable practices is presented. Directions for expanding research in these two areas are examined in light of concerns expressed in the historical use of inventory models and in light of a new inventory research paradigm.

In our paper, we have adopted a novel strategy to overcome this limitation by focusing our review on a review of inventory lot sizing review papers.

By adopting the methodology of reviewing published inventory review papers, we can contribute a comprehensive review of the inventory lot sizing literature that serves to provide in one paper a consolidation of inventory research that can serve as a single source to keep researchers up to date with the research developments in inventory lot sizing models. We also identify gaps in the field which could stimulate new research agendas in the areas of supply chain management and sustainable inventory practices.