# Optimizing Perishable Product Supply Chain Network Using Hybrid Metaheuristic Algorithms
## 3 Solution Algorithms
### Hmpga-Vns Algorithm
### Managerial Implications

The results of this study hold significant managerial implications, particularly for decision-makers and managers aiming to establish a supply chain for perishable products to meet the rapidly increasing market demand. Firstly, the models and solutions developed in this study can be utilized to construct a PPSCN, effectively connecting manufacturers, DCs, and retailers. This approach enables a comprehensive reduction in supply chain costs from a global perspective. Additionally, the proposed model can be applied to optimize objectives in other food industries. Furthermore, strategic planning of DCs, efficient inventory management, and effective route planning between DCs and retailers are vital in minimizing overall costs. During the planning process, decision-makers must carefully consider their specific circumstances, as any interconnection significantly impacts overall costs. The joint optimization of the PPSCN presents a significant challenge, and this study offers decision-makers a framework to consider all relevant factors when establishing a supply chain network for perishable products. Lastly, the sensitivity analysis conducted in this study emphasizes the importance of focusing on product shelf life and waste rate to reduce supply chain costs. For instance, significant benefits can be achieved by improving product packaging. Therefore, managers in the perishable product industry should prioritize making sustainable decisions, which contribute to both economic growth and environmental sustainability. ## 5 Conclusions, Limitations, and Future Works

In this paper, a LIRP for the multi-echelon, multi-product, multi-period PPSCN was proposed. The characteristics of perishable products were considered in regard to the integrated decision problem. To solve the NP-hard problem, two hybrid metaheuristic algorithms, HGA-VNS and HMPGA-VNS, were proposed. A new chromosome representation was introduced to cater to the unique problem structure. Further, the Taguchi experimental design method was employed to tune the algorithm parameters. After solving \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Change of** & \(-\)**40\%** & \(-\)**20\%** & **Base Case** & **20\%** & **40\%** \\ \hline Objective value & 12,354,318.19 & 15,789,639.54 & 19,452,555.80 & 23,154,377.17 & 27,177,165.7 \\ Sensitivity (\%) & \(-\)36.49 & \(-\)18.83 & 0 & 19.03 & 39.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Sensitivity analysis in demand. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Product Shelf** & **2** & **3** & **Base Case** & **5** & **6** \\
**Life** & & & & & \\ \hline Objective value & 19,966,103.27 & 19,645,136.10 & 19,452,555.80 & 19,263,866.00 & 19,176,329.51 \\ Sensitivity (\%) & 2.64 & 0.99 & 0 & \(-\)0.97 & \(-\)1.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sensitivity analysis in product shelf life. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Change of** & \(-\)**40\%** & \(-\)**20\%** & **Base Case** & **20\%** & **40\%** \\ \hline Objective value & 18,318,471.79 & 18,865,088.61 & 19,452,555.80 & 20,242,329.57 & 21,255,807.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Sensitivity analysis in product transportation loss rate. the suggested model by the proposed algorithms, the results revealed that HMPGA-VNS outperforms HGA-VNS, MPGA, and GA. Lastly, a sensitivity analysis was conducted on the key parameters of the model to validate its effectiveness. Managerial implications are valuable for practitioners and managers who are involved in establishing a supply chain for perishable products. This research, like other studies, has certain limitations that are described below:

* In terms of the absence of an official dataset, randomly generated data were employed to conduct an experimental analysis. This approach may not fully represent real-world scenarios. * Like many other metaheuristic algorithms, the proposed algorithms in this study often lack theoretical guarantees or bounds on their performance.