Conclusions

This paper has discussed the key characteristic of inventory systems that have been addressed by researchers since the year 2001. It revealed, in general, that there has been an incremental effort for representing reality using the inventory modeling approach from a theoretical point of view, but with little attention to its potential applicability. As a result, we found that the gap between theory and practice is increasingly wide, and there is an urgent need for incorporating more empirical evidence and useful guidelines for practitioners in this important research field. This recall us the famous aphorism attributed to George E. P. Box “all models are wrong, but some are useful”, which highlights the importance of developing good enough models for real life applications instead of overrepresenting reality by increasing model complexity. Therefore, in general, we call for the incorporation of more empirical evidence into the modeling of inventory systems dealing with perishable products by critically evaluating the trade-off between applicability, simplicity, and level scientific technique. For a complete discussion of this three aspects on scientific modeling, we suggest [358].
Given the above concerns, it would be interesting to find out whether the same is happening for perishable products subjects to obsolescence (like electronics components and fashionable products), or even for non-perishable products. If the gap between theory and practice is also an increasingly growing phenomenon in the modeling of these types of products, then it is likely that one or more concepts within the inventory modeling framework have become “reified”. According to Lane, Koka [359], reification is problematic because it threatens the validity of studies using a theoretical framework. A particular concept or construct becomes taken for granted and researchers increasingly fail to specify the assumptions that justify its use. To the inventory modeling literature, this would means that some of the modeling characteristics commonly used to represent inventory systems are being included or adapted out of context in an increasing range of papers instead of being treated as a building modeling approach that need to be constantly refined and revised. The problem created by reification, thus, can only be addressed through a systematic assessment of the literature in which the diverse interpretations and applications of the construct are investigated along with its underlying assumptions. Toward this aim, we recommend consulting [359, 360] and the references cited therein.
The literature on inventory management also suggests additional ways in which the models included in our review may be improved to obtain more suitable inventory policies. For example, in most of these models, it is assumed that the deterioration rate of perishable products is constant over time. i.e., a constant fraction of the on-hand inventory is assumed to spoil over time. Although this modeling approach was originally proposed to accurately represent the deterioration nature of volatile liquids and radioactive substances, it has also been extensively used by researchers as an approximation to represent a great variety of perishable products such as fresh produce. We agree that this modeling approach is particularly useful when the spoilage of products comes from multiple sources. However, there are still situations in which modeling a time-varying deterioration rate may produce a better profitable inventory policy. Similarly, exploring other topics of the inventory management literature may be of great importance for extending the existing literature. Such topics include the analysis of multiple substitutes and/or complementary products, the study of different demand patterns and marketing strategies for boosting demand, the inclusion of fuzzy parameters and so on. Particularly, from all these, we consider that applying Game theory to supply chain inventory models would be of great benefit to promote an effective management, given the natural competitive restriction in which operates company all around the world. All these topics may be explored in future research.
As in previous review papers, we also found an overuse of deterministic inventory models when compared to stochastic. Nevertheless, a deeper analysis conducted in our review for deterministic inventory models has revealed that there is still too much research needed in this research stream. For example, in Section 4.2 we showed that most of the deterministic inventory models have assumed that the demand is constant, stock-dependent or price dependent. However, the interest for modeling other factors, such as the freshness or quality of products, the advertisement effort and the customer service level, has grown in recent years. As would be anticipated, the study of such important factors affecting the demand through the use of a stochastic inventory modeling approach is still in its infancy. Also, with regards to the concern of best capturing the deterioration nature of products for determining suitable inventory policies, we have identified in Section 4.2 various interesting modeling approach than can be further explored and evaluated in future research. And not only in a deterministic inventory modeling approach but in a stochastic setting.
Another finding comes from the fact that incorporating practical insights from different but related research fields can be very beneficial for developing the state of art of a particular research stream. Accordingly, based on our analysis, we identified for each topic discussed the few works that have been developed to guide such integrated approaches. For example, even though queueing theory has been studied extensively by many authors, as far as our analysis reveals, only few studies [335, 344-346] have been address to unify into the inventory modeling this important research streams.
Finally, throughout Section 4.2 of the present study, we also unveiled various covered topics in which future research efforts may take the lead. For example, since the call for research of previous literature reviews [15, 17] to address the existence of multiple items into the inventory modeling, an increasing volume of papers have included this aspect. However, our analysis showed that the effect of complementary and substitute products on lot-size determination is still a critical research stream where more research is needed. In particular, important new challenges are expected for food supply chains in which actors, more than in other context, need to collaborate in sharing information and deciding common lot sizing strategy policies in order not only to achieve an overall profitability but to achieve a sustainable development that minimizes food waste concerns. Creating new approaches for considering sustainability concerns into the lot sizing modeling is also, from our perspective, a promising research area.
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Tables
Table 1 Number of records provided by each of the keywords search used.