# An Integrated Model for the Harvest, Storage, and Distribution of Perishable Crops
## 4 Case Study
### Computational Experiments and Managerial Insights--Tactical Level
#### 4.2.2 Collaboration between Suppliers  
Since suppliers \(C_{1}\) and \(C_{2}\) are geographically very close and share two customers, at the tactical level we have also explored the possibility of collaboration in the distribution of goods. In particular, we have solved \(M_{CR}\), using as input the output of \(M_{SS}\) in terms of amount to be shipped to each DC by each supplier at each period. This means that the decisions about harvesting and storage are fixed, while new solutions are possibile for the routing phase. Figure 2 shows a graphical example of horizontal collaboration between the two suppliers. Basically, \(C_{2}\) sends its goods to \(C_{1}\) incurring a routing cost for the round trip from its depot to that of the other supplier, which acts as a hub. At the hub, the goods are transferred from the \(C_{2}\) vehicle to the \(C_{1}\) fleet, which deals with the delivery of the agri-products to the DCs in exchange for a fee. We have solved \(M_{CR}\) on ten datasets, obtained by randomly combining the ten instances generated for the two companies, and under the most profitable parameter setting, according to the discussion made in the previous subsection. The only exception was that, the time limit was fixed to \(11\) h for the DCs of \(C_{1}\), which are not shared with \(C_{2}\), in order to guarantee the feasibility of the problem. We have supposed to implement the horizontal collaboration in any period of the time horizon. The mean computational time was around \(15\) s.  
In Figure 3, we show how the routing costs vary in the two cases of autonomous and collaborative distribution. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{2}{c}{**KPI**} & \multicolumn{3}{c}{\(\gamma\)} & \multicolumn{3}{c}{\(\delta\)} \\ \hline  & 2 & 3 & 4 & 5 & 6 & 7 \\ Revenue Main [EUR] & 81,140.74 & 81,611.02 & 81,650.38 & 80,820.37 & 79,846.40 & 79,279.38 \\ Reward Main [EUR] & 1368.48 & 1364.19 & 1,353.85 & 1338.96 & 1325.22 & 1315.94 \\ Revenue Spot [EUR] & 11,439.08 & 12,254.63 & 12,570.39 & 1356.62 & 14,414.08 & 14,699.79 \\ Inventory Cost [EUR] & 11,624.28 & 6360.80 & 4048.40 & 2588.84 & 1385.03 & 719.20 \\ Fuel Cost [EUR] & 19,081.74 & 19,081.74 & 19,081.74 & 19,081.74 & 19,081.74 & 19,081.74 \\ Driver Cost [EUR] & 5835.63 & 5855.63 & 5855.63 & 5835.63 & 5836.43 & 5835.63 \\ Production Cost [EUR] & 10,193.62 & 10,193.62 & 10,193.62 & 10,193.62 & 10,193.62 & 10,193.62 \\ Harvesting Cost [EUR] & 7200.00 & 10,800.00 & 14,400.00 & 18,000.00 & 21,600.00 & 25,200.00 \\ Number of trips [unit] & 41.70 & 41.70 & 41.70 & 41.70 & 41.70 & 41.70 \\ Average product age [day] & 2.05 & 1.57 & 1.36 & 1.23 & 1.13 & 1.08 \\ \hline Profit [EUR] & 40,013.02 & 42,955.04 & 42,015.23 & 40,022.14 & 37,486.49 & 34,264.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Average KPIs for the case of \(\delta=0.85\) (company \(C_{2}\)). Figure 3: Routing costs [EUR] in the cases of autonomous and collaborative distribution. Figure 2: Graphical example of horizontal collaboration between the two suppliers. As it can be noted, the implementation of the collaborative routing leads to an average reduction in fuel and driver costs of 31.56%, which corresponds to about 16,400 EUR. However, an important issue concerns the percentage of sharing of such saving between the two suppliers, which mainly depends on the amount of the fee that \(C_{2}\) pays to \(C_{1}\) for having the service. In Figure 4, we represent how the profit varies between the two suppliers, as the fee varies. If the service was performed free of charge by supplier \(C_{1}\), this latter would incur a loss of approximately 5600 EUR compared to non-collaboration, caused by the additional routing costs and the lack of reward from the main customer. Instead, \(C_{2}\) would have to bear the only costs to move to and from the \(C_{1}\) depot, therefore it would have a total saving of about 20,000 EUR. Looking at the graph, we can say that a fee of at least 140 EUR/day is required for supplier \(C_{1}\) to make profitable the collaboration with \(C_{2}\).