## 4 Materials and Methods  
This research was conducted within an SC of chestnuts considering supply, production and distribution operations. The proposed case study regards a firm that processes and supplies fresh and cooked chestnuts to a firm producing seasonal sweets and operating within qclarge international distribution. After being receive, the fruits are delivered either to (i) distributors or (ii) to multinational firms belonging to the seasonal sweets and cakes sector. The retailer is registered to the EU with a Protected Geographic Indication. For this reason, some restrictions regarding specific selection parameters (fruits size and weight) impose additional manual selection/calibrating process on fruits. The SC operations begin with the supply of fresh fruit from the growers to the company. Then, the fruit is selected and dried. The processor pack and deliver the fruit to the sweets' producers or serve their local distribution channels (supermarkets and shops) after shelling, drying and cooking within two parallel ovens. The ovens, propelled by wood pellets, work for 8 h a day. Based on the processes described, the configuration of the SC includes two types of customers: the multinational cakes industries, and the local clients made of small shops and supermarkets. The firm produces three main varieties of chestnuts: (i) cooked, (ii) fresh and (iii) dried, where the first two account for more than 77% of the orders. Around 65% of these orders regards fresh ones, while the remaining 35% are cooked ones. The production process decreases the weight to about one-third for fresh fruits and two-thirds for cooked fruits. Cooked fruits and fresh fruits are packaged in bags of 5 kg and 10 kg, respectively. Each pallet of cooked/fresh fruits contains 30 and 20 bags, as reported in Table 3, which also sums up the volumes of fruits processed during the harvesting season. Figure 1 gives the synoptic of the processing and distribution tasks, with the relative material flows for cooked and fresh fruits. \begin{table}
\begin{tabular}{c c c} \hline \hline
**SC Phase** & **Material Flow** & \\ \hline Receiving & & 895.4 tons \\ Quality selection (\% scrapes) & & 10\% \\  & Cooked & Fresh \\ Treatment & 676 tons & 138 tons \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material flow in the observed chestnut SC. From Figure 1, we can see that after the supply of the fresh fruits from local growers, during the selection phase the fruits are separated based on their dimension and weight. The receiving and stocking process is organized into bulky wood silos. In this phase, a first selection of fruits is carried out based on size and destination. The firm can (i) package the fruits for the main multinational firms, or (ii) make additional shelling, cooking, and packaging processes to serve national distribution centres. The VCOR modelling was developed based on the processing and distribution of chestnuts for the first six customers (in terms of volume), composed of three multinational firms and three national distributors, which together accounted for 70% of fresh and 55% of the cooked fruits processed, respectively. Value Chain ConfigurationThis SC can be intended as a three-tiered configuration, in which the firm receives products from the suppliers, then it processes and store them for the distribution phase. The VCOR configuration of the SC proposed by [7], provides the supplier with the fulfill block, and the customer with the acquire block. Table 4 gives the VCOR configuration and the quantities processed at each block. In this table, the modules Acquire, Build, and Fullfill of the VCOR model are involved in the acquiring of the fruits, and in their processing/delivering to the final customers. Figure 1: The chestnuts supply chain operations.