## 7 Conclusions and Future Work  
In this paper, the Vehicle Routing Problem (VRP) with Pickup and Delivery (VRPPD) was addressed based on real-life perceptions. Three different VRPPD models have been developed based on Mixed Integer Linear Programming approaches. The first model is designed as a VRP with simultaneous pickup and delivery. The second one is modeled as a VRP with either simultaneous and/or separated pickup and delivery. The last one is modeled as a VRP with simultaneous and flexible delivery and pickup allowing both partial pickups and penalized losses. In addition, this study proposes a _proof of concept_ based on a rich benchmark. The data adopted in this work were provided by a poultry company in Tunisia, called CHAHIA. The developed models have been compared against each other using multiple state-of-the-art key performance indicators. Based on the presented richness in term of modeling, interesting perspectives could be considered in the future, such as matching operational issues with tactical planning elements in order to make the models more dynamic and robust facing various demand scenarios. Finally, various heuristics could be proposed in order to solve large instances and enable quicker convergence towards the optimum. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**n**} & \multirow{2}{*}{**m**} & \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Instances**} & \multicolumn{3}{c}{**MILP1**} & \multicolumn{3}{c}{**MILP2**} & \multicolumn{3}{c}{**MILP3**} \\ \cline{3-11}  & & & & **OF (TND)** & **CPU (Sec)** & **Nodes** & **OF (TND)** & **CPU (Sec)** & **Nodes** & **OF (TND)** & **CPU (Sec)** & **Nodes** \\ \hline \multirow{4}{*}{15} & 2 & S & Inst52.001 & 5.380 & 24,453.7 & 12,171,800 & - & - & - & 5.060 & 1110.6 & 654,979 \\ \cline{2-11}  & - & B & Inst52.001 & 5.5510 & 29,199.2 & 16,852,192 & - & - & - & 5.060 & 437 & 2,448,044 \\ \cline{2-11}  & 3 & S & Inst53.003 & 5.060 & 2714.4 & 1,311,100 & - & - & - & 5.060 & 2548.8 & 835,035 \\ \cline{2-11}  & 2 & S & Inst18.2001 & 3.630 & 4959.2 & 1,834,815 & - & - & - & - & - & - \\ \cline{2-11}  & - & B & Inst18.2002 & - & - & - & - & - & - & 3.630 & 4475.7 & 1,830,280 \\ \cline{2-11}  & 3 & S & Inst18.3003 & 3.630 & 9512.2 & 3,381,239 & - & - & - & - & - & - \\ \cline{2-11}  & - & B & Inst18.3004 & - & - & - & - & - & - & 3.630 & 6081.3 & 1,780,109 \\ \hline \multirow{4}{*}{20} & 2 & S & Inst20.2001 & 3.580 & 916.1 & 254,457 & - & - & - & - & - & - \\ \cline{2-11}  & - & B & Inst20.2002 & - & - & - & - & - & - & - & - & - \\ \cline{2-11}  & 3 & S & Inst20.3003 & 3.580 & 4472.9 & 893,970 & - & - & - & 3.580 & 4208.4 & 1,128,435 \\ \cline{2-11}  & - & B & Inst20.3004 & - & - & - & - & - & - & - & - & - \\ \hline \multirow{4}{*}{25} & 2 & S & Inst232.201 & 4.290 & 4396.2 & 851,800 & - & - & - & - & - & - \\ \cline{2-11}  & - & B & Inst23.2002 & - & - & - & - & - & - & 4.290 & 26,413.7 & 3,834,209 \\ \cline{2-11}  & 3 & S & Inst23.3003 & - & - & - & - & - & - & - & - & - \\ \cline{2-11}  & - & B & Inst23.3004 & - & - & - & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: High demand and customers number instances. **Author Contributions:** Conceptualization, A.L. and R.M. ; methodology, A.L. ; validation, R.L. and A.-A. ; experimentation (coding and data collection): A.L. ; writing--review and editing, A.L. ; project administration, A.L. and M.N. ; funding acquisition, A.L. All authors have read and agreed to the published version of the manuscript. **Funding:** Deanship of Scientific Research at Prince Sattam bin Abdulaziz University. Research project No. 2020/01/13222. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data is available on demand from the corresponding author. **Acknowledgments:** This project was supported by the Deanship of Scientific Research at Prince Sattam bin Abdulaziz University through the research project No. 2020/01/13222.