# An Integrated Model for the Harvest, Storage, and Distribution of Perishable Crops
## 4 Case Study
### Computational Experiments and Managerial Insights--Operational Level  
At the operational level, the two companies must make 4 types of decisions, which are listed below:  
* harvesting decisions: if and how much to harvest;
* inventory decisions: amount of product of each age to store;
* shipping decisions: amount of product of each age to ship to the main customer and spot customers;
* routing decisions: routes to reach the different DCs.  
With the aim to support the two suppliers operationally, we have proposed a framework, which is schematized in Figure 5.  
It suggests the best decisions to maximize the overall profit and verifies if horizontal collaboration is convenient or not, once a daily fee \(\omega\) has been fixed.  
Given a well defined time horizon, the first step is to solve Model \(M_{SS}\) separately for the two suppliers. The harvesting, inventory and shipping decisions, output of \(M_{SS}\) are inserted into the solution of the overall problem.  
At the second step, Model \(M_{CR}\) is solved. It receives the shipping decisions as input and returns the collaborative routes and their relative cost.  
At the third step, the profitability of the collaboration for both suppliers is checked. If yes, the routing decisions resulting from the \(M_{CR}\) model are inserted into the solution. Otherwise, the collaboration is not implemented and autonomous routing decisions, output of the respective models \(M_{SS}\), are inserted into the overall solution.  
We have solved separately \(M_{SS}\) for \(C_{1}\) and \(C_{2}\), on the ten instances generated for each company, and considering only one week as time horizon. Then, we have solved \(M_{CR}\) on the ten datasets, obtained by randomly combining the ten instances generated for each company. We have considered the three different scenarios in Table 14, in terms of fee that  
Figure 4: Average profit variation for the two suppliers, by varying the fee.  
\(C_{2}\) pays to \(C_{1}\) for having the distribution service. The computational time was not longer than 2 min in all cases.  
In Table 15, we show the results of our computational experience at the operational level. The profit in case of autonomous distribution is compared with the three scenarios of collaborative distribution. As expected, the collaboration brings benefits for both suppliers according to all 3 scenarios. The first two scenarios favor the second and the first supplier, respectively. While the third scenario allows the maximization of the benefits for both the companies, with an average increase in overall profit of 18.32%. Observe that under the third scenario, collaboration is implemented on average in 94% of the days, which means that it is almost always profitable for both companies. This percentage drops to 51% and 44%, respectively, if we refer to the first two scenarios.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Scenario** & \(\mathbf{\omega}\) \\  & **[EUR/Day]** \\ \hline \(Sc1\)—\(C_{1}\) has less bargaining power than \(C_{2}\) & 100.00 \\ \(Sc2\)—\(C_{1}\) has greater bargaining power than \(C_{2}\) & 500.00 \\ \(Sc3\)—\(C_{1}\) and \(C_{2}\) have the same bargaining power & 310.00 \\ \hline \hline \end{tabular}
\end{table}
Table 14: The three different scenarios for the operational level.  
Figure 5: Framework for the operational level.  
Next, we briefly report the benefits that collaboration can bring to the environment. We refer to carbon dioxide (CO\({}_{2}\)) emissions, whose conversion factor is estimated at 2.63 kg/L, as in [38]. In Figure 6, the amount of CO\({}_{2}\) emissions (kg) in the case of absence of collaboration between the two suppliers is compared with the 3 collaborative scenarios. Basically, the collaboration leads to a significant reduction in CO\({}_{2}\) emissions in all cases. In particular, in the third scenario there is an average reduction of over 31%, which is one more reason to prefer collaborative routing.