# An Integrated Model for the Harvest, Storage, and Distribution of Perishable Crops
## 4 Case Study  
With the aim to prove the usefulness and efficiency of the above introduced and explained optimization models, we consider a real-life case study. Two agricultural companies, located in the Southern Italy, deal with planting, growing, harvesting and distributing perishable crops to the same main contract customer, which has several distribution centers scattered throughout Italy, and they can also exploit the more profitable opportunities offered by spot customers. We refer to the two companies as \(C_{1}\) and \(C_{2}\), respectively. \(C_{1}\) deals with broccoli, while \(C_{2}\) with artichokes. At the beginning of the season, the main customer decides the planting plan of the two supplier companies, in terms of scheduling and quantities, in order to have a balanced amount of goods along the harvesting/distribution season, which usually lasts from December to April. The main customer has seven DCs, which must be periodically supplied. \(C_{1}\) and \(C_{2}\) supply, respectively, five and four DCs, and they share two of them. A fleet of two vehicles with load capacity of 10,000 kg each is owned by \(C_{1}\), while \(C_{2}\) uses only one vehicle with load capacity of 4000 kg for the distribution of the agricultural products. Currently, the two companies have inefficiencies regarding the coordination of the harvesting, storage and routing activities. These three steps of the supply chain are characterized by conflicting objectives, then an integrated approach is desiderable. Once mature, each agricultural product can be harvested within a certain time interval. Therefore, two first fundamental decisions are: how much to harvest at each time period and how often. Once harvested, each product unit can be stored taking into account the limited capacity of the inventory, or immediately sent (as fresh product) to the customers, based on their demand. The inventory capacity of \(C_{1}\) and \(C_{2}\) is 30,000 kg and 10,000 kg, respectively. The harvested products are perishable, that is, they are subject to deterioration of their physical state and to the reduction of value perceived by customers, over time. Therefore, they can be stored for a time period not longer than 4 days, based on the contractual agreements. Selling price varies with product age. The main customer recognizes a unit reward to the two suppliers, on the basis of the guaranteed service level, as follows:  
\[\beta^{C_{1}}(\theta,\delta)=\left\{ \begin{array}{ll}0.010\;\text{EUR/kg},& \text{for }\theta=9\;\text{h},\delta=0.85\\ 0.005\;\text{EUR/kg},&\text{for }\theta=10\;\text{h},\delta=0.85\\ 0\;\text{EUR/kg},&\text{for }\theta=11\;\text{h},\delta=0.85\\ \end{array} \right\}\]  
\[\beta^{C_{2}}(\theta,\delta)=\left\{ \begin{array}{ll}0\;\text{EUR/kg},&\text {for }\theta=10\;\text{h},\delta=0.75\\ 0.015\;\text{EUR/kg},&\text{for }\theta=10\;\text{h},\delta=0.85\\ \end{array} \right\}\]  
We have used Model \(M_{SS}\) for supporting \(C_{1}\) and \(C_{2}\) at the tactical and operational level. At the tactical level, in fact, the two companies are willing to determine the most profitable combination between the harvesting frequency and the quality of service guaranteed to the main customer. These are fundamental choices because impact all other decisions. At operational level, they need to be helped by a decision-support system in order to organize in an integrated manner their harvesting, inventory, and routing activities, and maximize profit, on a daily base. Considering that \(C_{1}\) and \(C_{2}\) share a part of their customers, we have also explored the possibility of horizontal collaboration for what concerns the distribution activities. We have applied Model \(M_{CR}\), which deals with the routing activities, but receives as input the quantities to be shipped from the solution of \(M_{SS}\). The type of collaboration explored in this paper is such that \(C_{2}\) sends the agricultural products to \(C_{1}\), which takes care of the distribution to customers in exchange for a fee.