# Pallet Picking Strategy in Food Collecting Center
## 5 Methodology  
The design of the warehouse begins with the calculation of the travelled distances within each format. To do so, it is necessary to set and consider its main features. Before going to the description, the following list shows the notation used in the formula in the article:  
Figure 2: Flying-V, Fishbone, New Diagonal cross-aisle layouts. \(A\): width of the warehouse [m];  
\(B\): length of the warehouse [m];  
\(P\)/\(D\): pickup and deposit point [m\({}^{2}\)];  
\(L_{x}\): distance along the x axis between the \(P\)/\(D\) point and storage area [m];  
\(L_{y}\): distance along the y axis between the \(P\)/\(D\) point and storage area [m];  
\(N\): overall number of the items to be stocked in warehouse [unit]  
\(D\): width of the aisles [m];  
\(e_{l}\), \(e_{uv}\), \(e_{d}\): size of the selected item according length, width, and depth [m];  
\(V_{c}\): average travel speed of the forklift [km/h];  
\(t\): average time taken by the forklift for the material handling activities [h];  
\(I\): turnover index of the n-th item [#];  
\(\overline{P}\): average path required for the handling of the items stored in warehouse [m/unit];  
\(CF_{LPG}\), \(CF_{elc}\): average Carbon Footprint of the adopting forklift, equipped by electric ('ele' as subscript) or LPG ('LPG' as subscript) engine [kgCO\({}_{2}\)]. The method considers the following assumptions:  
* The number of the total items stored in warehouse is constant and the maximum load capacity corresponds to \(N\) (there are not available slots in the racks of the warehouse);
* The items stocked have prismatic form and are characterized by the same sizes (\(e_{w}\), \(e_{l}\), \(e_{h}\)) and weight, the storing approach is based on only one-item for one-slot of the rack;
* The information order is known in advance;
* The picking of one-item does not depend by the position of the other items (racking system is adopted);
* The material handling phase is implemented by means of forklifts;
* Only one item is picked by the forklift for each loading/unloading cycle;
* The \(P\)/\(D\) point is placed near to the storage one, in the center-bottom level of the warehouse, as shown in Figures 3 and 4;
* The size of the warehouse is given;
* Class based storage is the stocked strategy adopted;
* The emission of the activities required for loading/unloading the pallet from rack are not considered, when the forklift is stopped. This assumption is considered acceptable since the time required for this operation is negligible when compared to the time required to reach the pallet;
* The energy and the time required for the pallet retrieving/stocking does not depend on the following: weight of the item, lift speed of the forks, and height of the slot where the item is stocked;
* Acceleration and deceleration of the forklift are not considered;  
The process of pallet picking is composed by the following sequence of activities:  
1. the forklift starts moving from the \(P\)/\(D\) point travelling at a constant speed;
2. the forklift stops in the storage area and pick the selected item;
3. the forklift, with the load, goes back (moving on the same path of point number 1) to P/D point at a constant speed;  
The process of pallet stocking is composed by the following sequence of activities:  
1. the forklift, with the load, starts moving from the \(P\)/\(D\) point travelling at a constant speed;
2. the forklift stops in the storage area and stock the selected item;
3. the forklift goes back (moving on the same path of point number 1) to P/D point at a constant speed;The optimization purpose consists in minimizing the objective function considering the Carbon Footprint generated by the movement of the forklift. A comparison between forklift equipped with LPG engine versus an electrical one has been considered.