## 2 An Overview of Related Research  
In this paper, we develop a centralized multi-echelon inventory control model for purchasing pharmaceutical products from a manufacturer and distributing them among multiple foreign markets under deterministic and stochastic demand. In the context of supply chain management, the echelon represents the physical location where the products are located [17]. A multi-echelon system is characterized by the connection of inventory decisions from downstream locations and upstream locations, such as, different markets and central warehouses or manufacturers [23], for example. Multi-echelon inventory problems have been extensively studied for different applications. Nevertheless, most of the existing inventory models are not appropriate for pharmaceutical products. Pharmaceutical products are often more expensive than other products to purchase and distribute, while shortages cause a high cost related to wasted resources and preventable illness. Thus, inventory control of pharmaceutical products has to ensure high product availability, at the right time, at the right cost. Inadequate inventory management strategies in the pharmaceutical industry may have a significant impact on financial losses and people's health. Consequently, inventory management of pharmaceutical products is more critical than for other products [2]. Based on the above-mentioned, a \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Reference** & **Real-Life Problem** & **Conceptual** & **Mathematical** & **Real-World Settings** & **Software** \\
**Settings** & **Model** & **Model** & **Implementation/** & **Practical Validation** & **Solution** \\ \hline \hline \multirow{8}{*}{Current study} & \multirow{8}{*}{A real-life} & \multirow{8}{*}{The modern} & \multirow{8}{*}{Real-life data, collected over two years, are used for the validation of the proposed model and the solution procedure. The environment, and procedures are} \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._specific inventory model that reflects real-life problems is necessary for the control of pharmaceutical products, in order to maintain patients' health and reduce unnecessary costs. Depending on the country, the procurement and distribution of pharmaceutical products can be organized regionally or in commercial supply systems, existing parallel with public systems. According to [3], considering national and regional levels, private distribution companies offer cost-effective alternatives for delivering and storing medicines. From a supply chain network design point of view, a system can be either centralized or decentralized. The centralized system implies that all local warehouses deliver their demand information, like a forecasted demand, to a central warehouse or manufacturer. Aggregated demand, based on the received demand information, is used for the defining of the inventory control parameters in the central warehouse. When it comes to the decentralized system, local warehouses define inventory decisions independently. [PERSON] et al. [24] suggest the centralization approach for deterministic supply and stochastic demand. In this case, the centralization results in a lower expected cost without affecting the variance of the cost compared to a decentralization approach. [PERSON] and [PERSON] [25] state that centralized planning and control, characteristic for DRP, is beneficial under realistic situations of time-varying demand and replenishment time uncertainty. They examined performances of two common distribution planning and control systems, DRP and Order Point replenishment, within networks involving manufacturing, distribution and retail facilities. Results indicate that a centralized system performs best when demands vary through time and when there is significant uncertainty with respect to demand and replenishment times.