# An Integrated Model for the Harvest, Storage, and Distribution of Perishable Crops
## 4 Case Study
### Computational Experiments and Managerial Insights--Tactical Level  
#### 4.2.1 Single-Supplier Model  
At the tactical level, we have adopted \(M_{SS}\), with the aim to determine the most profitable combination of two important parameters: the harvesting frequency (i.e., number of harvesting days per week) and the quality of service guaranteed to the DCs. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\mathbf{C_{1}}\) & \(\mathbf{DC_{1}}\) & \(\mathbf{DC_{2}}\) & \(\mathbf{DC_{3}}\) & \(\mathbf{DC_{4}}\) & \(\mathbf{DC_{5}}\) \\ \hline \(C_{1}\) & 0 & 235 & 276 & 51 & 188 & 360 \\ \(DC_{1}\) & 235 & 0 & 113 & 222 & 406 & 152 \\ \(DC_{2}\) & 276 & 113 & 0 & 245 & 343 & 215 \\ \(DC_{3}\) & 51 & 222 & 245 & 0 & 226 & 344 \\ \(DC_{4}\) & 188 & 406 & 343 & 226 & 0 & 480 \\ \(DC_{5}\) & 360 & 152 & 215 & 344 & 480 & 0 \\ \hline \end{tabular}
\end{table} 
Table 6: Temporal distance between nodes [minute], referring to the first supplier. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(\mathbf{C_{2}}\) & \(\mathbf{DC_{1}}\) & \(\mathbf{DC_{2}}\) & \(\mathbf{DC_{3}}\) & \(\mathbf{DC_{4}}\) \\ \hline \(C_{2}\) & 0 & 512 & 739 & 604 & 691 \\ \(DC_{1}\) & 512 & 0 & 236 & 103 & 272 \\ \(DC_{2}\) & 739 & 236 & 0 & 145 & 161 \\ \(DC_{3}\) & 604 & 103 & 145 & 0 & 182 \\ \(DC_{4}\) & 691 & 272 & 161 & 182 & 0 \\ \hline \end{tabular}
\end{table} 
Table 7: Spatial distance between nodes [kilometer], referring to the second supplier. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \(\mathbf{C_{1}}\) & \(\mathbf{DC_{1}}\) & \(\mathbf{DC_{2}}\) & \(\mathbf{DC_{3}}\) & \(\mathbf{DC_{4}}\) \\ \hline \(C_{1}\) & 0 & 392 & 433 & 55 & 277 & 619 \\ \(DC_{1}\) & 392 & 0 & 152 & 367 & 696 & 236 \\ \(DC_{2}\) & 433 & 152 & 0 & 405 & 583 & 337 \\ \(DC_{3}\) & 55 & 367 & 405 & 0 & 362 & 592 \\ \(DC_{4}\) & 277 & 696 & 583 & 362 & 0 & 851 \\ \(DC_{5}\) & 619 & 236 & 337 & 592 & 851 & 0 \\ \hline \end{tabular}
\end{table} 
Table 5: Spatial distance between nodes [kilometer], referring to the first supplier. The choice of \(\gamma\) is quite critical in that, harvesting very frequently corresponds to increase the costs related to the renting of the specialized harvesting equipment, but it allows to ship fresh products quite often; on the other hand, harvesting only in a few days of the week entails greater use of the warehouse to stock up and delivery of products with an average higher age (i.e., lower market value). Six alternatives have been explored, namely \(\gamma\in\{2,\ldots,7\}\). Observe that \(\gamma=1\) is not feasible because \(\tau=4\) is not enough to ensure that DCs demand can be met every day. Moreover, we have determined the service level, which maximizes the profit. In this case, \(\theta\in\{9,10,11\}\) and \(\delta\in\{0.75,0.85\}\) have been explored for the two companies, respectively. Observe that the values to be contractually guaranteed are, respectively, \(\theta=11\) h and \(\delta=0.75\), but some rewards are ensured in order to encourage the decrease of \(\theta\) and the increase of \(\delta\). In Tables 9-11, we report the computational results of the experiments carried out on the 10 instances generated with reference to the first supplier. We highlight the average value of 10 key performance indicators (KPIs). The first eight KPIs characterize the objective funcion (2) of \(M_{SS}\). Moreover, we show the number of trips and the average age of the product shipped to the main customer and spot customers. First of all, we can say that the average profit, fixed \(\theta\), initially increases as the harvesting frequency increases until it reaches the peak when \(\gamma\in\{3,4\}\). Then, it starts to significantly decrease. The reasons behind this trend are multiple. As it can be noted, the increase in the harvesting frequency has two main effects: the revenue (main and spot) increases because the average age of the product delivered decreases, while storage costs decrease significantly. These two benefits are \"paid\" through the increase in harvesting costs.