### State-of-the-Art Review  
Given the identified research gaps and the context of Industry 5.0, the research question for this study is the following: In a dynamic production environment with heterogeneous storage, how can data-driven inventory management strategies and decision-making frameworks be designed to simultaneously mitigate shortage risk, minimize holding costs, and promote sustainability? This research questions can be separated into three components of inventory management: sustainable inventory management; data-driven inventory management; multiobjective inventory management.  
Recent advancements in inventory management have underscored the importance of incorporating components of sustainability and environment impact. [PERSON] et al. [26] provide a review on sustainable inventory management. The authors show that the majority of the articles analysed have their environmental focus on reducing, mostly resorting to approaches of either simulation or exact programming methods. [PERSON] and [PERSON] [27] propose a bi-objective robust optimization focused on carbon emissions and total system cost, by changing routing decisions. [PERSON] and [PERSON] [28] optimize a single-objective problem, which weighs different costs, including greenhouse gas emissions, and considers cold storage on a trans-shipment problem. [PERSON] et al. [29] minimize a single objective comprised of weighed factors that include CO\({}_{2}\) emissions and holding costs, by optimizing a set of binary routing variables and order quantities. [PERSON] et al. [30] present an optimal replenishment strategy, focused on a single-objective optimization with environmental emissions reduction and holding cost as components of their objective.  
With the surge of big data, an increasing number of optimization strategies with a data-driven component have appeared. This trend has also been seen in inventory management. [PERSON] and [PERSON] [31] focus their work on safety stock under causal demand forecast. A single objective is optimized which includes holding and shortage costs, by balancing inventory levels and satisfied demands. The aforementioned work by [PERSON] and [PERSON] [27] is focused on robust optimization, which captures the multi-period uncertain production demand.  
Many publications on inventory management consider multiple objectives. To simplify the designation, as the definition is not consensual, in this work, an optimization with two objectives is classified as bi-objective optimization; three or more objectives are considered many-objective optimization--the main difference being that representation of the Pareto front is possible (with sufficient clarity) for only two objectives. The previously stated work by [PERSON] and [PERSON] [27] is an example of a bi-objective optimization approach, but there are additional instances. [PERSON] et al. [32] present a bi-objective inventory control system, focused on minimizing the cost of inventory and carbon emissions. [PERSON] and [PERSON] [33] present a many-objective approach to inventory optimization, considering three objectives, total inventory cost, average inventory level, frequency of inventory shortage, by changing the reorder point and order quantity.  
Besides the publications described here, additional state-of-the-art research was considered. Table 1 shows the classification of all articles considered in terms of how many objectives there were, what the decision variables were, what the objectives were, what storage types were considered and whether or not the work featured any data-driven components. These publications are compared with the proposed approach in the following subsection.